Average Error: 0.0 → 0.0
Time: 777.0ms
Precision: 64
\[\left(1 - x\right) \cdot y + x \cdot z\]
↓
\[\mathsf{fma}\left(1 - x, y, x \cdot z\right)\]
\left(1 - x\right) \cdot y + x \cdot z
↓
\mathsf{fma}\left(1 - x, y, x \cdot z\right)
double f(double x, double y, double z) {
        double r673642 = 1.0;
        double r673643 = x;
        double r673644 = r673642 - r673643;
        double r673645 = y;
        double r673646 = r673644 * r673645;
        double r673647 = z;
        double r673648 = r673643 * r673647;
        double r673649 = r673646 + r673648;
        return r673649;
}
↓
double f(double x, double y, double z) {
        double r673650 = 1.0;
        double r673651 = x;
        double r673652 = r673650 - r673651;
        double r673653 = y;
        double r673654 = z;
        double r673655 = r673651 * r673654;
        double r673656 = fma(r673652, r673653, r673655);
        return r673656;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Color.HSV:lerp  from diagrams-contrib-1.3.0.5"
  :precision binary64

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

  (+ (* (- 1 x) y) (* x z)))