Average Error: 0.0 → 0.0
Time: 1.5s
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 r664408 = x;
        double r664409 = y;
        double r664410 = r664408 * r664409;
        double r664411 = z;
        double r664412 = 1.0;
        double r664413 = r664412 - r664409;
        double r664414 = r664411 * r664413;
        double r664415 = r664410 + r664414;
        return r664415;
}
↓
double f(double x, double y, double z) {
        double r664416 = x;
        double r664417 = y;
        double r664418 = z;
        double r664419 = 1.0;
        double r664420 = r664418 * r664419;
        double r664421 = -r664417;
        double r664422 = r664418 * r664421;
        double r664423 = r664420 + r664422;
        double r664424 = fma(r664416, r664417, r664423);
        return r664424;
}

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 2020036 +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))))