Average Error: 0.0 → 0.0
Time: 2.5s
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 r651028 = x;
        double r651029 = y;
        double r651030 = r651028 * r651029;
        double r651031 = z;
        double r651032 = 1.0;
        double r651033 = r651032 - r651029;
        double r651034 = r651031 * r651033;
        double r651035 = r651030 + r651034;
        return r651035;
}
↓
double f(double x, double y, double z) {
        double r651036 = x;
        double r651037 = y;
        double r651038 = z;
        double r651039 = 1.0;
        double r651040 = r651039 - r651037;
        double r651041 = r651038 * r651040;
        double r651042 = fma(r651036, r651037, r651041);
        return r651042;
}

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 2020047 +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))))