Average Error: 0.0 → 0.0
Time: 12.9s
Precision: 64
\[x \cdot y + z \cdot \left(1 - y\right)\]
↓
\[\mathsf{fma}\left(z, 1 - y, x \cdot y\right)\]
x \cdot y + z \cdot \left(1 - y\right)
↓
\mathsf{fma}\left(z, 1 - y, x \cdot y\right)
double f(double x, double y, double z) {
        double r29322912 = x;
        double r29322913 = y;
        double r29322914 = r29322912 * r29322913;
        double r29322915 = z;
        double r29322916 = 1.0;
        double r29322917 = r29322916 - r29322913;
        double r29322918 = r29322915 * r29322917;
        double r29322919 = r29322914 + r29322918;
        return r29322919;
}
↓
double f(double x, double y, double z) {
        double r29322920 = z;
        double r29322921 = 1.0;
        double r29322922 = y;
        double r29322923 = r29322921 - r29322922;
        double r29322924 = x;
        double r29322925 = r29322924 * r29322922;
        double r29322926 = fma(r29322920, r29322923, r29322925);
        return r29322926;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019200 +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))))