Average Error: 0.0 → 0.0
Time: 726.0ms
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 r866798 = 1.0;
        double r866799 = x;
        double r866800 = r866798 - r866799;
        double r866801 = y;
        double r866802 = r866800 * r866801;
        double r866803 = z;
        double r866804 = r866799 * r866803;
        double r866805 = r866802 + r866804;
        return r866805;
}
↓
double f(double x, double y, double z) {
        double r866806 = 1.0;
        double r866807 = x;
        double r866808 = r866806 - r866807;
        double r866809 = y;
        double r866810 = z;
        double r866811 = r866807 * r866810;
        double r866812 = fma(r866808, r866809, r866811);
        return r866812;
}

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 2020024 +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)))