Average Error: 0.0 → 0.0
Time: 3.7s
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 r761302 = 1.0;
        double r761303 = x;
        double r761304 = r761302 - r761303;
        double r761305 = y;
        double r761306 = r761304 * r761305;
        double r761307 = z;
        double r761308 = r761303 * r761307;
        double r761309 = r761306 + r761308;
        return r761309;
}
↓
double f(double x, double y, double z) {
        double r761310 = 1.0;
        double r761311 = x;
        double r761312 = r761310 - r761311;
        double r761313 = y;
        double r761314 = z;
        double r761315 = r761311 * r761314;
        double r761316 = fma(r761312, r761313, r761315);
        return r761316;
}

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 2020062 +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)))