Average Error: 0.0 → 0.0
Time: 9.5s
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 r719339 = x;
        double r719340 = y;
        double r719341 = r719339 * r719340;
        double r719342 = z;
        double r719343 = 1.0;
        double r719344 = r719343 - r719340;
        double r719345 = r719342 * r719344;
        double r719346 = r719341 + r719345;
        return r719346;
}
↓
double f(double x, double y, double z) {
        double r719347 = x;
        double r719348 = y;
        double r719349 = z;
        double r719350 = 1.0;
        double r719351 = r719350 - r719348;
        double r719352 = r719349 * r719351;
        double r719353 = fma(r719347, r719348, r719352);
        return r719353;
}

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 2020045 +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))))