Average Error: 0.0 → 0.0
Time: 1.5s
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 r590962 = x;
        double r590963 = y;
        double r590964 = r590962 * r590963;
        double r590965 = z;
        double r590966 = 1.0;
        double r590967 = r590966 - r590963;
        double r590968 = r590965 * r590967;
        double r590969 = r590964 + r590968;
        return r590969;
}
↓
double f(double x, double y, double z) {
        double r590970 = x;
        double r590971 = y;
        double r590972 = z;
        double r590973 = 1.0;
        double r590974 = r590973 - r590971;
        double r590975 = r590972 * r590974;
        double r590976 = fma(r590970, r590971, r590975);
        return r590976;
}

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 2020001 +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))))