Average Error: 0.0 → 0.0
Time: 36.8s
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 r32196006 = x;
        double r32196007 = y;
        double r32196008 = r32196006 * r32196007;
        double r32196009 = z;
        double r32196010 = 1.0;
        double r32196011 = r32196010 - r32196007;
        double r32196012 = r32196009 * r32196011;
        double r32196013 = r32196008 + r32196012;
        return r32196013;
}
↓
double f(double x, double y, double z) {
        double r32196014 = x;
        double r32196015 = y;
        double r32196016 = 1.0;
        double r32196017 = r32196016 - r32196015;
        double r32196018 = z;
        double r32196019 = r32196017 * r32196018;
        double r32196020 = fma(r32196014, r32196015, r32196019);
        return r32196020;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019168 +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))))