Average Error: 0.0 → 0.0
Time: 7.1s
Precision: 64
\[x \cdot y + z \cdot \left(1 - y\right)\]
↓
\[\mathsf{fma}\left(x, y, z \cdot 1 + \left(-y\right) \cdot z\right)\]
x \cdot y + z \cdot \left(1 - y\right)
↓
\mathsf{fma}\left(x, y, z \cdot 1 + \left(-y\right) \cdot z\right)
double f(double x, double y, double z) {
        double r418413 = x;
        double r418414 = y;
        double r418415 = r418413 * r418414;
        double r418416 = z;
        double r418417 = 1.0;
        double r418418 = r418417 - r418414;
        double r418419 = r418416 * r418418;
        double r418420 = r418415 + r418419;
        return r418420;
}
↓
double f(double x, double y, double z) {
        double r418421 = x;
        double r418422 = y;
        double r418423 = z;
        double r418424 = 1.0;
        double r418425 = r418423 * r418424;
        double r418426 = -r418422;
        double r418427 = r418426 * r418423;
        double r418428 = r418425 + r418427;
        double r418429 = fma(r418421, r418422, r418428);
        return r418429;
}

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. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019323 +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))))