Average Error: 0.0 → 0.0
Time: 897.0ms
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 r662520 = x;
        double r662521 = y;
        double r662522 = r662520 * r662521;
        double r662523 = z;
        double r662524 = 1.0;
        double r662525 = r662524 - r662521;
        double r662526 = r662523 * r662525;
        double r662527 = r662522 + r662526;
        return r662527;
}
↓
double f(double x, double y, double z) {
        double r662528 = x;
        double r662529 = y;
        double r662530 = z;
        double r662531 = 1.0;
        double r662532 = r662531 - r662529;
        double r662533 = r662530 * r662532;
        double r662534 = fma(r662528, r662529, r662533);
        return r662534;
}

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))))