Average Error: 0.0 → 0.0
Time: 6.3s
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 r417860 = x;
        double r417861 = y;
        double r417862 = r417860 * r417861;
        double r417863 = z;
        double r417864 = 1.0;
        double r417865 = r417864 - r417861;
        double r417866 = r417863 * r417865;
        double r417867 = r417862 + r417866;
        return r417867;
}
↓
double f(double x, double y, double z) {
        double r417868 = x;
        double r417869 = y;
        double r417870 = z;
        double r417871 = 1.0;
        double r417872 = r417871 - r417869;
        double r417873 = r417870 * r417872;
        double r417874 = fma(r417868, r417869, r417873);
        return r417874;
}

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 2019235 +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))))