Average Error: 0.0 → 0.0
Time: 1.8s
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 r741720 = 1.0;
        double r741721 = x;
        double r741722 = r741720 - r741721;
        double r741723 = y;
        double r741724 = r741722 * r741723;
        double r741725 = z;
        double r741726 = r741721 * r741725;
        double r741727 = r741724 + r741726;
        return r741727;
}
↓
double f(double x, double y, double z) {
        double r741728 = 1.0;
        double r741729 = x;
        double r741730 = r741728 - r741729;
        double r741731 = y;
        double r741732 = z;
        double r741733 = r741729 * r741732;
        double r741734 = fma(r741730, r741731, r741733);
        return r741734;
}

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 2020047 +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)))