Average Error: 0.0 → 0.0
Time: 1.1s
Precision: 64
\[x \cdot y + z \cdot \left(1 - y\right)\]
↓
\[\mathsf{fma}\left(x, y, z \cdot \left(1 - y\right)\right)\]
x \cdot y + z \cdot \left(1 - y\right)
↓
\mathsf{fma}\left(x, y, z \cdot \left(1 - y\right)\right)
double f(double x, double y, double z) {
        double r750906 = x;
        double r750907 = y;
        double r750908 = r750906 * r750907;
        double r750909 = z;
        double r750910 = 1.0;
        double r750911 = r750910 - r750907;
        double r750912 = r750909 * r750911;
        double r750913 = r750908 + r750912;
        return r750913;
}
↓
double f(double x, double y, double z) {
        double r750914 = x;
        double r750915 = y;
        double r750916 = z;
        double r750917 = 1.0;
        double r750918 = r750917 - r750915;
        double r750919 = r750916 * r750918;
        double r750920 = fma(r750914, r750915, r750919);
        return r750920;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.0
Target0.0
Herbie0.0
\[z - \left(z - x\right) \cdot y\]

Derivation

  1. Initial program 0.0

    \[x \cdot y + z \cdot \left(1 - y\right)\]

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment:bezierClip from diagrams-lib-1.3.0.3"
  :precision binary64

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

  (+ (* x y) (* z (- 1 y))))