Average Error: 0.0 → 0.0
Time: 12.9s
Precision: 64
\[x \cdot y + z \cdot \left(1.0 - y\right)\]
↓
\[\mathsf{fma}\left(x, y, \left(1.0 - y\right) \cdot z\right)\]
x \cdot y + z \cdot \left(1.0 - y\right)
↓
\mathsf{fma}\left(x, y, \left(1.0 - y\right) \cdot z\right)
double f(double x, double y, double z) {
        double r26382788 = x;
        double r26382789 = y;
        double r26382790 = r26382788 * r26382789;
        double r26382791 = z;
        double r26382792 = 1.0;
        double r26382793 = r26382792 - r26382789;
        double r26382794 = r26382791 * r26382793;
        double r26382795 = r26382790 + r26382794;
        return r26382795;
}
↓
double f(double x, double y, double z) {
        double r26382796 = x;
        double r26382797 = y;
        double r26382798 = 1.0;
        double r26382799 = r26382798 - r26382797;
        double r26382800 = z;
        double r26382801 = r26382799 * r26382800;
        double r26382802 = fma(r26382796, r26382797, r26382801);
        return r26382802;
}

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

    \[x \cdot y + z \cdot \left(1.0 - y\right)\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \left(1.0 - y\right) \cdot z\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, y, \left(1.0 - y\right) \cdot z\right)\]

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment:bezierClip from diagrams-lib-1.3.0.3"

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

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