Average Error: 0.0 → 0.0
Time: 11.9s
Precision: 64
\[d1 \cdot d2 + d1 \cdot d3\]
↓
\[\mathsf{fma}\left(d1, d2, \left(d1 \cdot d3\right)\right)\]
d1 \cdot d2 + d1 \cdot d3
↓
\mathsf{fma}\left(d1, d2, \left(d1 \cdot d3\right)\right)
double f(double d1, double d2, double d3) {
        double r56021614 = d1;
        double r56021615 = d2;
        double r56021616 = r56021614 * r56021615;
        double r56021617 = d3;
        double r56021618 = r56021614 * r56021617;
        double r56021619 = r56021616 + r56021618;
        return r56021619;
}
↓
double f(double d1, double d2, double d3) {
        double r56021620 = d1;
        double r56021621 = d2;
        double r56021622 = d3;
        double r56021623 = r56021620 * r56021622;
        double r56021624 = fma(r56021620, r56021621, r56021623);
        return r56021624;
}

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Target

Original0.0
Target0.0
Herbie0.0
\[d1 \cdot \left(d2 + d3\right)\]

Derivation

  1. Initial program 0.0

    \[d1 \cdot d2 + d1 \cdot d3\]
  2. Using strategy rm

  3. Applied fma-def0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(d1, d2, \left(d1 \cdot d3\right)\right)}\]

  4. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(d1, d2, \left(d1 \cdot d3\right)\right)\]

Reproduce

herbie shell --seed 2019128 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath dist"

  :herbie-target
  (* d1 (+ d2 d3))

  (+ (* d1 d2) (* d1 d3)))