Average Error: 0.0 → 0.0
Time: 887.0ms
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 r623262 = x;
        double r623263 = y;
        double r623264 = r623262 * r623263;
        double r623265 = z;
        double r623266 = 1.0;
        double r623267 = r623266 - r623263;
        double r623268 = r623265 * r623267;
        double r623269 = r623264 + r623268;
        return r623269;
}
↓
double f(double x, double y, double z) {
        double r623270 = x;
        double r623271 = y;
        double r623272 = z;
        double r623273 = 1.0;
        double r623274 = r623273 - r623271;
        double r623275 = r623272 * r623274;
        double r623276 = fma(r623270, r623271, r623275);
        return r623276;
}

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 2020062 +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))))