Average Error: 0.0 → 0.0
Time: 13.2s
Precision: 64
\[x \cdot y + z \cdot \left(1.0 - y\right)\]
↓
\[\mathsf{fma}\left(x, y, \left(1.0 - y\right) \cdot z\right)\]
x \cdot y + z \cdot \left(1.0 - y\right)
↓
\mathsf{fma}\left(x, y, \left(1.0 - y\right) \cdot z\right)
double f(double x, double y, double z) {
        double r30934056 = x;
        double r30934057 = y;
        double r30934058 = r30934056 * r30934057;
        double r30934059 = z;
        double r30934060 = 1.0;
        double r30934061 = r30934060 - r30934057;
        double r30934062 = r30934059 * r30934061;
        double r30934063 = r30934058 + r30934062;
        return r30934063;
}
↓
double f(double x, double y, double z) {
        double r30934064 = x;
        double r30934065 = y;
        double r30934066 = 1.0;
        double r30934067 = r30934066 - r30934065;
        double r30934068 = z;
        double r30934069 = r30934067 * r30934068;
        double r30934070 = fma(r30934064, r30934065, r30934069);
        return r30934070;
}

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

    \[x \cdot y + z \cdot \left(1.0 - y\right)\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \left(1.0 - y\right) \cdot z\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, y, \left(1.0 - y\right) \cdot z\right)\]

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment:bezierClip from diagrams-lib-1.3.0.3"

  :herbie-target
  (- z (* (- z x) y))

  (+ (* x y) (* z (- 1.0 y))))