Average Error: 0.0 → 0.0
Time: 7.3s
Precision: 64
\[x \cdot y + z \cdot \left(1 - y\right)\]
↓
\[\mathsf{fma}\left(x, y, \left(1 - y\right) \cdot z\right)\]
x \cdot y + z \cdot \left(1 - y\right)
↓
\mathsf{fma}\left(x, y, \left(1 - y\right) \cdot z\right)
double f(double x, double y, double z) {
        double r33343831 = x;
        double r33343832 = y;
        double r33343833 = r33343831 * r33343832;
        double r33343834 = z;
        double r33343835 = 1.0;
        double r33343836 = r33343835 - r33343832;
        double r33343837 = r33343834 * r33343836;
        double r33343838 = r33343833 + r33343837;
        return r33343838;
}
↓
double f(double x, double y, double z) {
        double r33343839 = x;
        double r33343840 = y;
        double r33343841 = 1.0;
        double r33343842 = r33343841 - r33343840;
        double r33343843 = z;
        double r33343844 = r33343842 * r33343843;
        double r33343845 = fma(r33343839, r33343840, r33343844);
        return r33343845;
}

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \left(1 - y\right) \cdot z\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, y, \left(1 - y\right) \cdot z\right)\]

Reproduce

herbie shell --seed 2019170 +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))))