Average Error: 0.0 → 0.0
Time: 2.3s
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 r727658 = 1.0;
        double r727659 = x;
        double r727660 = r727658 - r727659;
        double r727661 = y;
        double r727662 = r727660 * r727661;
        double r727663 = z;
        double r727664 = r727659 * r727663;
        double r727665 = r727662 + r727664;
        return r727665;
}
↓
double f(double x, double y, double z) {
        double r727666 = 1.0;
        double r727667 = x;
        double r727668 = r727666 - r727667;
        double r727669 = y;
        double r727670 = z;
        double r727671 = r727667 * r727670;
        double r727672 = fma(r727668, r727669, r727671);
        return r727672;
}

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 2019353 +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)))