Average Error: 0.0 → 0.0
Time: 5.3s
Precision: 64
\[\left(1 - x\right) \cdot y + x \cdot z\]
↓
\[\mathsf{fma}\left(x, z - y, 1 \cdot y\right)\]
\left(1 - x\right) \cdot y + x \cdot z
↓
\mathsf{fma}\left(x, z - y, 1 \cdot y\right)
double f(double x, double y, double z) {
        double r34332522 = 1.0;
        double r34332523 = x;
        double r34332524 = r34332522 - r34332523;
        double r34332525 = y;
        double r34332526 = r34332524 * r34332525;
        double r34332527 = z;
        double r34332528 = r34332523 * r34332527;
        double r34332529 = r34332526 + r34332528;
        return r34332529;
}
↓
double f(double x, double y, double z) {
        double r34332530 = x;
        double r34332531 = z;
        double r34332532 = y;
        double r34332533 = r34332531 - r34332532;
        double r34332534 = 1.0;
        double r34332535 = r34332534 * r34332532;
        double r34332536 = fma(r34332530, r34332533, r34332535);
        return r34332536;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.0
Target0.0
Herbie0.0
\[y - x \cdot \left(y - z\right)\]

Derivation

  1. Initial program 0.0

    \[\left(1 - x\right) \cdot y + x \cdot z\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, z - y, y \cdot 1\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, z - y, 1 \cdot y\right)\]

Reproduce

herbie shell --seed 2019192 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Color.HSV:lerp  from diagrams-contrib-1.3.0.5"

  :herbie-target
  (- y (* x (- y z)))

  (+ (* (- 1.0 x) y) (* x z)))