Average Error: 0.0 → 0.0
Time: 2.3s
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 r1358260 = x;
        double r1358261 = y;
        double r1358262 = r1358260 * r1358261;
        double r1358263 = z;
        double r1358264 = 1.0;
        double r1358265 = r1358264 - r1358261;
        double r1358266 = r1358263 * r1358265;
        double r1358267 = r1358262 + r1358266;
        return r1358267;
}
↓
double f(double x, double y, double z) {
        double r1358268 = x;
        double r1358269 = y;
        double r1358270 = z;
        double r1358271 = 1.0;
        double r1358272 = r1358271 - r1358269;
        double r1358273 = r1358270 * r1358272;
        double r1358274 = fma(r1358268, r1358269, r1358273);
        return r1358274;
}

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 2020034 +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))))