Average Error: 0.0 → 0.0
Time: 4.2s
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 r987797 = 1.0;
        double r987798 = x;
        double r987799 = r987797 - r987798;
        double r987800 = y;
        double r987801 = r987799 * r987800;
        double r987802 = z;
        double r987803 = r987798 * r987802;
        double r987804 = r987801 + r987803;
        return r987804;
}
↓
double f(double x, double y, double z) {
        double r987805 = 1.0;
        double r987806 = x;
        double r987807 = r987805 - r987806;
        double r987808 = y;
        double r987809 = z;
        double r987810 = r987806 * r987809;
        double r987811 = fma(r987807, r987808, r987810);
        return r987811;
}

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 2020042 +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)))