Average Error: 0.0 → 0.0
Time: 18.4s
Precision: 64
\[\left(1 - x\right) \cdot y + x \cdot z\]
↓
\[\mathsf{fma}\left(y, 1 - x, z \cdot x\right)\]
\left(1 - x\right) \cdot y + x \cdot z
↓
\mathsf{fma}\left(y, 1 - x, z \cdot x\right)
double f(double x, double y, double z) {
        double r28303120 = 1.0;
        double r28303121 = x;
        double r28303122 = r28303120 - r28303121;
        double r28303123 = y;
        double r28303124 = r28303122 * r28303123;
        double r28303125 = z;
        double r28303126 = r28303121 * r28303125;
        double r28303127 = r28303124 + r28303126;
        return r28303127;
}
↓
double f(double x, double y, double z) {
        double r28303128 = y;
        double r28303129 = 1.0;
        double r28303130 = x;
        double r28303131 = r28303129 - r28303130;
        double r28303132 = z;
        double r28303133 = r28303132 * r28303130;
        double r28303134 = fma(r28303128, r28303131, r28303133);
        return r28303134;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019200 +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)))