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 r611255 = x;
        double r611256 = y;
        double r611257 = r611255 * r611256;
        double r611258 = z;
        double r611259 = 1.0;
        double r611260 = r611259 - r611256;
        double r611261 = r611258 * r611260;
        double r611262 = r611257 + r611261;
        return r611262;
}
↓
double f(double x, double y, double z) {
        double r611263 = x;
        double r611264 = y;
        double r611265 = z;
        double r611266 = 1.0;
        double r611267 = r611266 - r611264;
        double r611268 = r611265 * r611267;
        double r611269 = fma(r611263, r611264, r611268);
        return r611269;
}

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 2020039 +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))))