Average Error: 0.0 → 0.0
Time: 1.9s
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 r714942 = 1.0;
        double r714943 = x;
        double r714944 = r714942 - r714943;
        double r714945 = y;
        double r714946 = r714944 * r714945;
        double r714947 = z;
        double r714948 = r714943 * r714947;
        double r714949 = r714946 + r714948;
        return r714949;
}
↓
double f(double x, double y, double z) {
        double r714950 = 1.0;
        double r714951 = x;
        double r714952 = r714950 - r714951;
        double r714953 = y;
        double r714954 = z;
        double r714955 = r714951 * r714954;
        double r714956 = fma(r714952, r714953, r714955);
        return r714956;
}

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 2020083 +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)))