Average Error: 0.0 → 0.0
Time: 8.0s
Precision: 64
\[x \cdot y + z \cdot \left(1.0 - y\right)\]
↓
\[\mathsf{fma}\left(x, y, \left(1.0 - y\right) \cdot z\right)\]
x \cdot y + z \cdot \left(1.0 - y\right)
↓
\mathsf{fma}\left(x, y, \left(1.0 - y\right) \cdot z\right)
double f(double x, double y, double z) {
        double r11601364 = x;
        double r11601365 = y;
        double r11601366 = r11601364 * r11601365;
        double r11601367 = z;
        double r11601368 = 1.0;
        double r11601369 = r11601368 - r11601365;
        double r11601370 = r11601367 * r11601369;
        double r11601371 = r11601366 + r11601370;
        return r11601371;
}
↓
double f(double x, double y, double z) {
        double r11601372 = x;
        double r11601373 = y;
        double r11601374 = 1.0;
        double r11601375 = r11601374 - r11601373;
        double r11601376 = z;
        double r11601377 = r11601375 * r11601376;
        double r11601378 = fma(r11601372, r11601373, r11601377);
        return r11601378;
}

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

    \[x \cdot y + z \cdot \left(1.0 - y\right)\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \left(1.0 - y\right) \cdot z\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, y, \left(1.0 - y\right) \cdot z\right)\]

Reproduce

herbie shell --seed 2019156 +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))))