Average Error: 0.0 → 0.0
Time: 3.3s
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 r801038 = 1.0;
        double r801039 = x;
        double r801040 = r801038 - r801039;
        double r801041 = y;
        double r801042 = r801040 * r801041;
        double r801043 = z;
        double r801044 = r801039 * r801043;
        double r801045 = r801042 + r801044;
        return r801045;
}
↓
double f(double x, double y, double z) {
        double r801046 = 1.0;
        double r801047 = x;
        double r801048 = r801046 - r801047;
        double r801049 = y;
        double r801050 = z;
        double r801051 = r801047 * r801050;
        double r801052 = fma(r801048, r801049, r801051);
        return r801052;
}

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 2020062 +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)))