Average Error: 0.0 → 0.0
Time: 3.7s
Precision: 64
\[x \cdot y + z \cdot \left(1 - y\right)\]
↓
\[\mathsf{fma}\left(x, y, z \cdot 1 + \left(-y\right) \cdot z\right)\]
x \cdot y + z \cdot \left(1 - y\right)
↓
\mathsf{fma}\left(x, y, z \cdot 1 + \left(-y\right) \cdot z\right)
double f(double x, double y, double z) {
        double r362823 = x;
        double r362824 = y;
        double r362825 = r362823 * r362824;
        double r362826 = z;
        double r362827 = 1.0;
        double r362828 = r362827 - r362824;
        double r362829 = r362826 * r362828;
        double r362830 = r362825 + r362829;
        return r362830;
}
↓
double f(double x, double y, double z) {
        double r362831 = x;
        double r362832 = y;
        double r362833 = z;
        double r362834 = 1.0;
        double r362835 = r362833 * r362834;
        double r362836 = -r362832;
        double r362837 = r362836 * r362833;
        double r362838 = r362835 + r362837;
        double r362839 = fma(r362831, r362832, r362838);
        return r362839;
}

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. Using strategy rm

  4. Applied sub-neg0.0

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

  5. Applied distribute-lft-in0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019326 +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))))