Average Error: 0.0 → 0.0
Time: 3.4s
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 r473094 = x;
        double r473095 = y;
        double r473096 = r473094 * r473095;
        double r473097 = z;
        double r473098 = 1.0;
        double r473099 = r473098 - r473095;
        double r473100 = r473097 * r473099;
        double r473101 = r473096 + r473100;
        return r473101;
}
↓
double f(double x, double y, double z) {
        double r473102 = x;
        double r473103 = y;
        double r473104 = z;
        double r473105 = 1.0;
        double r473106 = r473105 - r473103;
        double r473107 = r473104 * r473106;
        double r473108 = fma(r473102, r473103, r473107);
        return r473108;
}

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 2019303 +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))))