Average Error: 0.0 → 0.0
Time: 2.4s
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 r751038 = 1.0;
        double r751039 = x;
        double r751040 = r751038 - r751039;
        double r751041 = y;
        double r751042 = r751040 * r751041;
        double r751043 = z;
        double r751044 = r751039 * r751043;
        double r751045 = r751042 + r751044;
        return r751045;
}
↓
double f(double x, double y, double z) {
        double r751046 = 1.0;
        double r751047 = x;
        double r751048 = r751046 - r751047;
        double r751049 = y;
        double r751050 = z;
        double r751051 = r751047 * r751050;
        double r751052 = fma(r751048, r751049, r751051);
        return r751052;
}

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 2020081 +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)))