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 r809140 = 1.0;
        double r809141 = x;
        double r809142 = r809140 - r809141;
        double r809143 = y;
        double r809144 = r809142 * r809143;
        double r809145 = z;
        double r809146 = r809141 * r809145;
        double r809147 = r809144 + r809146;
        return r809147;
}
↓
double f(double x, double y, double z) {
        double r809148 = 1.0;
        double r809149 = x;
        double r809150 = r809148 - r809149;
        double r809151 = y;
        double r809152 = z;
        double r809153 = r809149 * r809152;
        double r809154 = fma(r809150, r809151, r809153);
        return r809154;
}

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)))