Average Error: 0.0 → 0.0
Time: 7.7s
Precision: 64
\[x \cdot y + z \cdot \left(1 - y\right)\]
↓
\[\mathsf{fma}\left(x, y, \left(1 - y\right) \cdot z\right)\]
x \cdot y + z \cdot \left(1 - y\right)
↓
\mathsf{fma}\left(x, y, \left(1 - y\right) \cdot z\right)
double f(double x, double y, double z) {
        double r609056 = x;
        double r609057 = y;
        double r609058 = r609056 * r609057;
        double r609059 = z;
        double r609060 = 1.0;
        double r609061 = r609060 - r609057;
        double r609062 = r609059 * r609061;
        double r609063 = r609058 + r609062;
        return r609063;
}
↓
double f(double x, double y, double z) {
        double r609064 = x;
        double r609065 = y;
        double r609066 = 1.0;
        double r609067 = r609066 - r609065;
        double r609068 = z;
        double r609069 = r609067 * r609068;
        double r609070 = fma(r609064, r609065, r609069);
        return r609070;
}

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

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

Reproduce

herbie shell --seed 2019196 +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))))