Average Error: 0.0 → 0.0
Time: 1.7s
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 r210738 = x;
        double r210739 = y;
        double r210740 = r210738 * r210739;
        double r210741 = z;
        double r210742 = 1.0;
        double r210743 = r210742 - r210739;
        double r210744 = r210741 * r210743;
        double r210745 = r210740 + r210744;
        return r210745;
}
↓
double f(double x, double y, double z) {
        double r210746 = x;
        double r210747 = y;
        double r210748 = z;
        double r210749 = 1.0;
        double r210750 = r210749 - r210747;
        double r210751 = r210748 * r210750;
        double r210752 = fma(r210746, r210747, r210751);
        return r210752;
}

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 2019362 +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))))