Average Error: 0.0 → 0.0
Time: 6.6s
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 r40293042 = x;
        double r40293043 = y;
        double r40293044 = r40293042 * r40293043;
        double r40293045 = z;
        double r40293046 = 1.0;
        double r40293047 = r40293046 - r40293043;
        double r40293048 = r40293045 * r40293047;
        double r40293049 = r40293044 + r40293048;
        return r40293049;
}
↓
double f(double x, double y, double z) {
        double r40293050 = x;
        double r40293051 = y;
        double r40293052 = z;
        double r40293053 = 1.0;
        double r40293054 = r40293053 - r40293051;
        double r40293055 = r40293052 * r40293054;
        double r40293056 = fma(r40293050, r40293051, r40293055);
        return r40293056;
}

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 2019174 +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))))