Average Error: 0.0 → 0.0
Time: 1.2s
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 r668650 = x;
        double r668651 = y;
        double r668652 = r668650 * r668651;
        double r668653 = z;
        double r668654 = 1.0;
        double r668655 = r668654 - r668651;
        double r668656 = r668653 * r668655;
        double r668657 = r668652 + r668656;
        return r668657;
}
↓
double f(double x, double y, double z) {
        double r668658 = x;
        double r668659 = y;
        double r668660 = z;
        double r668661 = 1.0;
        double r668662 = r668661 - r668659;
        double r668663 = r668660 * r668662;
        double r668664 = fma(r668658, r668659, r668663);
        return r668664;
}

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 2019353 +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))))