Average Error: 0.0 → 0.0
Time: 3.5s
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 r807126 = 1.0;
        double r807127 = x;
        double r807128 = r807126 - r807127;
        double r807129 = y;
        double r807130 = r807128 * r807129;
        double r807131 = z;
        double r807132 = r807127 * r807131;
        double r807133 = r807130 + r807132;
        return r807133;
}
↓
double f(double x, double y, double z) {
        double r807134 = 1.0;
        double r807135 = x;
        double r807136 = r807134 - r807135;
        double r807137 = y;
        double r807138 = z;
        double r807139 = r807135 * r807138;
        double r807140 = fma(r807136, r807137, r807139);
        return r807140;
}

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 2020036 +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)))