Average Error: 0.0 → 0.0
Time: 6.0s
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 r381913 = x;
        double r381914 = y;
        double r381915 = r381913 * r381914;
        double r381916 = z;
        double r381917 = 1.0;
        double r381918 = r381917 - r381914;
        double r381919 = r381916 * r381918;
        double r381920 = r381915 + r381919;
        return r381920;
}
↓
double f(double x, double y, double z) {
        double r381921 = x;
        double r381922 = y;
        double r381923 = z;
        double r381924 = 1.0;
        double r381925 = r381923 * r381924;
        double r381926 = -r381922;
        double r381927 = r381926 * r381923;
        double r381928 = r381925 + r381927;
        double r381929 = fma(r381921, r381922, r381928);
        return r381929;
}

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 2019304 +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))))