Average Error: 0.0 → 0.0
Time: 10.2s
Precision: 64
\[x \cdot y + z \cdot \left(1.0 - y\right)\]
↓
\[\mathsf{fma}\left(1.0 - y, z, y \cdot x\right)\]
x \cdot y + z \cdot \left(1.0 - y\right)
↓
\mathsf{fma}\left(1.0 - y, z, y \cdot x\right)
double f(double x, double y, double z) {
        double r28883702 = x;
        double r28883703 = y;
        double r28883704 = r28883702 * r28883703;
        double r28883705 = z;
        double r28883706 = 1.0;
        double r28883707 = r28883706 - r28883703;
        double r28883708 = r28883705 * r28883707;
        double r28883709 = r28883704 + r28883708;
        return r28883709;
}
↓
double f(double x, double y, double z) {
        double r28883710 = 1.0;
        double r28883711 = y;
        double r28883712 = r28883710 - r28883711;
        double r28883713 = z;
        double r28883714 = x;
        double r28883715 = r28883711 * r28883714;
        double r28883716 = fma(r28883712, r28883713, r28883715);
        return r28883716;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019163 +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))))