Average Error: 0.0 → 0.0
Time: 3.6s
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 r901014 = 1.0;
        double r901015 = x;
        double r901016 = r901014 - r901015;
        double r901017 = y;
        double r901018 = r901016 * r901017;
        double r901019 = z;
        double r901020 = r901015 * r901019;
        double r901021 = r901018 + r901020;
        return r901021;
}
↓
double f(double x, double y, double z) {
        double r901022 = 1.0;
        double r901023 = x;
        double r901024 = r901022 - r901023;
        double r901025 = y;
        double r901026 = z;
        double r901027 = r901023 * r901026;
        double r901028 = fma(r901024, r901025, r901027);
        return r901028;
}

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 2019351 +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)))