Average Error: 0.0 → 0.0
Time: 1.1s
Precision: 64
\[x \cdot y + z \cdot \left(1 - y\right)\]
↓
\[\mathsf{fma}\left(x, y, z \cdot 1 + z \cdot \left(-y\right)\right)\]
x \cdot y + z \cdot \left(1 - y\right)
↓
\mathsf{fma}\left(x, y, z \cdot 1 + z \cdot \left(-y\right)\right)
double f(double x, double y, double z) {
        double r756309 = x;
        double r756310 = y;
        double r756311 = r756309 * r756310;
        double r756312 = z;
        double r756313 = 1.0;
        double r756314 = r756313 - r756310;
        double r756315 = r756312 * r756314;
        double r756316 = r756311 + r756315;
        return r756316;
}
↓
double f(double x, double y, double z) {
        double r756317 = x;
        double r756318 = y;
        double r756319 = z;
        double r756320 = 1.0;
        double r756321 = r756319 * r756320;
        double r756322 = -r756318;
        double r756323 = r756319 * r756322;
        double r756324 = r756321 + r756323;
        double r756325 = fma(r756317, r756318, r756324);
        return r756325;
}

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. Using strategy rm

  4. Applied sub-neg0.0

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

  5. Applied distribute-lft-in0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020057 +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))))