Average Error: 0.0 → 0.0
Time: 10.8s
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 r31031747 = x;
        double r31031748 = y;
        double r31031749 = r31031747 * r31031748;
        double r31031750 = z;
        double r31031751 = 1.0;
        double r31031752 = r31031751 - r31031748;
        double r31031753 = r31031750 * r31031752;
        double r31031754 = r31031749 + r31031753;
        return r31031754;
}
↓
double f(double x, double y, double z) {
        double r31031755 = z;
        double r31031756 = 1.0;
        double r31031757 = y;
        double r31031758 = r31031756 - r31031757;
        double r31031759 = x;
        double r31031760 = r31031759 * r31031757;
        double r31031761 = fma(r31031755, r31031758, r31031760);
        return r31031761;
}

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))))