Average Error: 0.0 → 0.0
Time: 1.5s
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 r646970 = x;
        double r646971 = y;
        double r646972 = r646970 * r646971;
        double r646973 = z;
        double r646974 = 1.0;
        double r646975 = r646974 - r646971;
        double r646976 = r646973 * r646975;
        double r646977 = r646972 + r646976;
        return r646977;
}
↓
double f(double x, double y, double z) {
        double r646978 = x;
        double r646979 = y;
        double r646980 = z;
        double r646981 = 1.0;
        double r646982 = r646981 - r646979;
        double r646983 = r646980 * r646982;
        double r646984 = fma(r646978, r646979, r646983);
        return r646984;
}

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 2020046 +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))))