Average Error: 0.0 → 0.0
Time: 10.8s
Precision: 64
\[\left(1 - x\right) \cdot y + x \cdot z\]
↓
\[\mathsf{fma}\left(y, 1, \left(z - y\right) \cdot x\right)\]
\left(1 - x\right) \cdot y + x \cdot z
↓
\mathsf{fma}\left(y, 1, \left(z - y\right) \cdot x\right)
double f(double x, double y, double z) {
        double r27408470 = 1.0;
        double r27408471 = x;
        double r27408472 = r27408470 - r27408471;
        double r27408473 = y;
        double r27408474 = r27408472 * r27408473;
        double r27408475 = z;
        double r27408476 = r27408471 * r27408475;
        double r27408477 = r27408474 + r27408476;
        return r27408477;
}
↓
double f(double x, double y, double z) {
        double r27408478 = y;
        double r27408479 = 1.0;
        double r27408480 = z;
        double r27408481 = r27408480 - r27408478;
        double r27408482 = x;
        double r27408483 = r27408481 * r27408482;
        double r27408484 = fma(r27408478, r27408479, r27408483);
        return r27408484;
}

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, 1, x \cdot \left(z - y\right)\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(y, 1, \left(z - y\right) \cdot x\right)\]

Reproduce

herbie shell --seed 2019170 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Color.HSV:lerp  from diagrams-contrib-1.3.0.5"

  :herbie-target
  (- y (* x (- y z)))

  (+ (* (- 1.0 x) y) (* x z)))