Average Error: 0.0 → 0.0
Time: 901.0ms
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 r771061 = 1.0;
        double r771062 = x;
        double r771063 = r771061 - r771062;
        double r771064 = y;
        double r771065 = r771063 * r771064;
        double r771066 = z;
        double r771067 = r771062 * r771066;
        double r771068 = r771065 + r771067;
        return r771068;
}
↓
double f(double x, double y, double z) {
        double r771069 = 1.0;
        double r771070 = x;
        double r771071 = r771069 - r771070;
        double r771072 = y;
        double r771073 = z;
        double r771074 = r771070 * r771073;
        double r771075 = fma(r771071, r771072, r771074);
        return r771075;
}

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 2020033 +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)))