Average Error: 0.0 → 0.0
Time: 1.3s
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 r740244 = 1.0;
        double r740245 = x;
        double r740246 = r740244 - r740245;
        double r740247 = y;
        double r740248 = r740246 * r740247;
        double r740249 = z;
        double r740250 = r740245 * r740249;
        double r740251 = r740248 + r740250;
        return r740251;
}
↓
double f(double x, double y, double z) {
        double r740252 = 1.0;
        double r740253 = x;
        double r740254 = r740252 - r740253;
        double r740255 = y;
        double r740256 = z;
        double r740257 = r740253 * r740256;
        double r740258 = fma(r740254, r740255, r740257);
        return r740258;
}

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 2020064 +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)))