Average Error: 0.0 → 0.0
Time: 6.2s
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 r452818 = x;
        double r452819 = y;
        double r452820 = r452818 * r452819;
        double r452821 = z;
        double r452822 = 1.0;
        double r452823 = r452822 - r452819;
        double r452824 = r452821 * r452823;
        double r452825 = r452820 + r452824;
        return r452825;
}
↓
double f(double x, double y, double z) {
        double r452826 = x;
        double r452827 = y;
        double r452828 = z;
        double r452829 = 1.0;
        double r452830 = r452829 - r452827;
        double r452831 = r452828 * r452830;
        double r452832 = fma(r452826, r452827, r452831);
        return r452832;
}

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 2019323 +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))))