Average Error: 0.0 → 0.0
Time: 1.4s
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 r741045 = x;
        double r741046 = y;
        double r741047 = r741045 * r741046;
        double r741048 = z;
        double r741049 = 1.0;
        double r741050 = r741049 - r741046;
        double r741051 = r741048 * r741050;
        double r741052 = r741047 + r741051;
        return r741052;
}
↓
double f(double x, double y, double z) {
        double r741053 = x;
        double r741054 = y;
        double r741055 = z;
        double r741056 = 1.0;
        double r741057 = r741056 - r741054;
        double r741058 = r741055 * r741057;
        double r741059 = fma(r741053, r741054, r741058);
        return r741059;
}

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 2020083 +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))))