Average Error: 0.0 → 0.0
Time: 8.5s
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 r434169 = x;
        double r434170 = y;
        double r434171 = r434169 * r434170;
        double r434172 = z;
        double r434173 = 1.0;
        double r434174 = r434173 - r434170;
        double r434175 = r434172 * r434174;
        double r434176 = r434171 + r434175;
        return r434176;
}
↓
double f(double x, double y, double z) {
        double r434177 = x;
        double r434178 = y;
        double r434179 = z;
        double r434180 = 1.0;
        double r434181 = r434180 - r434178;
        double r434182 = r434179 * r434181;
        double r434183 = fma(r434177, r434178, r434182);
        return r434183;
}

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 2019325 +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))))