Average Error: 0.0 → 0.0
Time: 1.5s
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 r592519 = x;
        double r592520 = y;
        double r592521 = r592519 * r592520;
        double r592522 = z;
        double r592523 = 1.0;
        double r592524 = r592523 - r592520;
        double r592525 = r592522 * r592524;
        double r592526 = r592521 + r592525;
        return r592526;
}
↓
double f(double x, double y, double z) {
        double r592527 = x;
        double r592528 = y;
        double r592529 = z;
        double r592530 = 1.0;
        double r592531 = r592530 - r592528;
        double r592532 = r592529 * r592531;
        double r592533 = fma(r592527, r592528, r592532);
        return r592533;
}

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 2020001 +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))))