Average Error: 0.0 → 0.0
Time: 1.6s
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 r657972 = x;
        double r657973 = y;
        double r657974 = r657972 * r657973;
        double r657975 = z;
        double r657976 = 1.0;
        double r657977 = r657976 - r657973;
        double r657978 = r657975 * r657977;
        double r657979 = r657974 + r657978;
        return r657979;
}
↓
double f(double x, double y, double z) {
        double r657980 = x;
        double r657981 = y;
        double r657982 = z;
        double r657983 = 1.0;
        double r657984 = r657982 * r657983;
        double r657985 = -r657981;
        double r657986 = r657982 * r657985;
        double r657987 = r657984 + r657986;
        double r657988 = fma(r657980, r657981, r657987);
        return r657988;
}

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 2020024 +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))))