Average Error: 0.0 → 0.0
Time: 8.9s
Precision: 64
\[\left(1 - x\right) \cdot y + x \cdot z\]
↓
\[\mathsf{fma}\left(x, z - y, 1 \cdot y\right)\]
\left(1 - x\right) \cdot y + x \cdot z
↓
\mathsf{fma}\left(x, z - y, 1 \cdot y\right)
double f(double x, double y, double z) {
        double r522380 = 1.0;
        double r522381 = x;
        double r522382 = r522380 - r522381;
        double r522383 = y;
        double r522384 = r522382 * r522383;
        double r522385 = z;
        double r522386 = r522381 * r522385;
        double r522387 = r522384 + r522386;
        return r522387;
}
↓
double f(double x, double y, double z) {
        double r522388 = x;
        double r522389 = z;
        double r522390 = y;
        double r522391 = r522389 - r522390;
        double r522392 = 1.0;
        double r522393 = r522392 * r522390;
        double r522394 = fma(r522388, r522391, r522393);
        return r522394;
}

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, z - y, y \cdot 1\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, z - y, 1 \cdot y\right)\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Color.HSV:lerp  from diagrams-contrib-1.3.0.5"

  :herbie-target
  (- y (* x (- y z)))

  (+ (* (- 1.0 x) y) (* x z)))