Average Error: 0.0 → 0.0
Time: 3.8s
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 r780127 = 1.0;
        double r780128 = x;
        double r780129 = r780127 - r780128;
        double r780130 = y;
        double r780131 = r780129 * r780130;
        double r780132 = z;
        double r780133 = r780128 * r780132;
        double r780134 = r780131 + r780133;
        return r780134;
}
↓
double f(double x, double y, double z) {
        double r780135 = 1.0;
        double r780136 = x;
        double r780137 = r780135 - r780136;
        double r780138 = y;
        double r780139 = z;
        double r780140 = r780136 * r780139;
        double r780141 = fma(r780137, r780138, r780140);
        return r780141;
}

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 2020045 +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)))