diff --git a/acb/dot_fmpz.c b/acb/dot_fmpz.c
index dd52cdfb..54e3cded 100644
--- a/acb/dot_fmpz.c
+++ b/acb/dot_fmpz.c
@@ -138,8 +138,6 @@ acb_dot_fmpz(acb_t res, const acb_t initial, int subtract, acb_srcptr x, slong x
         }
     }
 
-    TMP_END;
-
     arb_dot(((arb_ptr) res) + 0, (initial == NULL) ? NULL : ((arb_srcptr) initial) + 0, subtract, ((arb_srcptr) x) + 0, 2 * xstep, t, 1, len, prec);
     arb_dot(((arb_ptr) res) + 1, (initial == NULL) ? NULL : ((arb_srcptr) initial) + 1, subtract, ((arb_srcptr) x) + 1, 2 * xstep, t, 1, len, prec);
 
diff --git a/arb/dot_fmpz.c b/arb/dot_fmpz.c
index 56b1a5ff..630051c2 100644
--- a/arb/dot_fmpz.c
+++ b/arb/dot_fmpz.c
@@ -138,8 +138,6 @@ arb_dot_fmpz(arb_t res, const arb_t initial, int subtract, arb_srcptr x, slong x
         }
     }
 
-    TMP_END;
-
     arb_dot(res, initial, subtract, x, xstep, t, 1, len, prec);
 
     TMP_END;
diff --git a/arb_fmpz_poly/evaluate_acb_rectangular.c b/arb_fmpz_poly/evaluate_acb_rectangular.c
index b5147f78..b9e9988e 100644
--- a/arb_fmpz_poly/evaluate_acb_rectangular.c
+++ b/arb_fmpz_poly/evaluate_acb_rectangular.c
@@ -15,7 +15,7 @@ void
 _arb_fmpz_poly_evaluate_acb_rectangular(acb_t y, const fmpz * poly,
     slong len, const acb_t x, slong prec)
 {
-    slong i, j, m, r;
+    slong i, m, r;
     acb_ptr xs;
     acb_t s, t, c;
 
@@ -36,15 +36,14 @@ _arb_fmpz_poly_evaluate_acb_rectangular(acb_t y, const fmpz * poly,
     _acb_vec_set_powers(xs, x, m + 1, prec);
 
     acb_set_fmpz(y, poly + (r - 1) * m);
-    for (j = 1; (r - 1) * m + j < len; j++)
-        acb_addmul_fmpz(y, xs + j, poly + (r - 1) * m + j, prec);
+    acb_dot_fmpz(y, y, 0, xs + 1, 1,
+        poly + (r - 1) * m + 1, 1, len - (r - 1) * m - 1, prec);
 
     for (i = r - 2; i >= 0; i--)
     {
         acb_set_fmpz(s, poly + i * m);
-        for (j = 1; j < m; j++)
-            acb_addmul_fmpz(s, xs + j, poly + i * m + j, prec);
-
+        acb_dot_fmpz(s, s, 0, xs + 1, 1,
+            poly + i * m + 1, 1, m - 1, prec);
         acb_mul(y, y, xs + m, prec);
         acb_add(y, y, s, prec);
     }
diff --git a/arb_fmpz_poly/evaluate_arb.c b/arb_fmpz_poly/evaluate_arb.c
index 80fa2d33..a0503cab 100644
--- a/arb_fmpz_poly/evaluate_arb.c
+++ b/arb_fmpz_poly/evaluate_arb.c
@@ -15,17 +15,24 @@ void
 _arb_fmpz_poly_evaluate_arb(arb_t res, const fmpz * f, slong len,
                            const arb_t x, slong prec)
 {
-    if ((prec >= 1024) && (len >= 5 + 20000 / prec))
+    if (len >= 6 && len >= 5 + 2500 / (FLINT_MAX(prec, 64) + 64))
     {
-        slong fbits;
-
-        fbits = _fmpz_vec_max_bits(f, len);
-
-        if (fbits <= prec / 2)
+        /* todo: improve this tuning? */
+        if (prec > 1024)
         {
-            _arb_fmpz_poly_evaluate_arb_rectangular(res, f, len, x, prec);
-            return;
+            slong fbits;
+            fbits = _fmpz_vec_max_bits(f, len);
+            fbits = FLINT_ABS(fbits);
+
+            if (fbits > prec / 2)
+            {
+                _arb_fmpz_poly_evaluate_arb_horner(res, f, len, x, prec);
+                return;
+            }
         }
+
+        _arb_fmpz_poly_evaluate_arb_rectangular(res, f, len, x, prec);
+        return;
     }
 
     _arb_fmpz_poly_evaluate_arb_horner(res, f, len, x, prec);
diff --git a/arb_fmpz_poly/evaluate_arb_rectangular.c b/arb_fmpz_poly/evaluate_arb_rectangular.c
index dfd9f4d3..33b9c21e 100644
--- a/arb_fmpz_poly/evaluate_arb_rectangular.c
+++ b/arb_fmpz_poly/evaluate_arb_rectangular.c
@@ -15,7 +15,7 @@ void
 _arb_fmpz_poly_evaluate_arb_rectangular(arb_t y, const fmpz * poly,
     slong len, const arb_t x, slong prec)
 {
-    slong i, j, m, r;
+    slong i, m, r;
     arb_ptr xs;
     arb_t s, t, c;
 
@@ -36,15 +36,14 @@ _arb_fmpz_poly_evaluate_arb_rectangular(arb_t y, const fmpz * poly,
     _arb_vec_set_powers(xs, x, m + 1, prec);
 
     arb_set_fmpz(y, poly + (r - 1) * m);
-    for (j = 1; (r - 1) * m + j < len; j++)
-        arb_addmul_fmpz(y, xs + j, poly + (r - 1) * m + j, prec);
+    arb_dot_fmpz(y, y, 0, xs + 1, 1,
+        poly + (r - 1) * m + 1, 1, len - (r - 1) * m - 1, prec);
 
     for (i = r - 2; i >= 0; i--)
     {
         arb_set_fmpz(s, poly + i * m);
-        for (j = 1; j < m; j++)
-            arb_addmul_fmpz(s, xs + j, poly + i * m + j, prec);
-
+        arb_dot_fmpz(s, s, 0, xs + 1, 1,
+            poly + i * m + 1, 1, m - 1, prec);
         arb_mul(y, y, xs + m, prec);
         arb_add(y, y, s, prec);
     }