Average Error: 0.0 → 0.0
Time: 795.0ms
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 r772187 = 1.0;
        double r772188 = x;
        double r772189 = r772187 - r772188;
        double r772190 = y;
        double r772191 = r772189 * r772190;
        double r772192 = z;
        double r772193 = r772188 * r772192;
        double r772194 = r772191 + r772193;
        return r772194;
}
↓
double f(double x, double y, double z) {
        double r772195 = 1.0;
        double r772196 = x;
        double r772197 = r772195 - r772196;
        double r772198 = y;
        double r772199 = z;
        double r772200 = r772196 * r772199;
        double r772201 = fma(r772197, r772198, r772200);
        return r772201;
}

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 2020056 +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)))