Average Error: 0.0 → 0.0
Time: 1.6s
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 r648862 = x;
        double r648863 = y;
        double r648864 = r648862 * r648863;
        double r648865 = z;
        double r648866 = 1.0;
        double r648867 = r648866 - r648863;
        double r648868 = r648865 * r648867;
        double r648869 = r648864 + r648868;
        return r648869;
}
↓
double f(double x, double y, double z) {
        double r648870 = x;
        double r648871 = y;
        double r648872 = z;
        double r648873 = 1.0;
        double r648874 = r648873 - r648871;
        double r648875 = r648872 * r648874;
        double r648876 = fma(r648870, r648871, r648875);
        return r648876;
}

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 2020035 +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))))