Average Error: 0.0 → 0.0
Time: 1.2s
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 r785058 = x;
        double r785059 = y;
        double r785060 = r785058 * r785059;
        double r785061 = z;
        double r785062 = 1.0;
        double r785063 = r785062 - r785059;
        double r785064 = r785061 * r785063;
        double r785065 = r785060 + r785064;
        return r785065;
}
↓
double f(double x, double y, double z) {
        double r785066 = x;
        double r785067 = y;
        double r785068 = z;
        double r785069 = 1.0;
        double r785070 = r785068 * r785069;
        double r785071 = -r785067;
        double r785072 = r785068 * r785071;
        double r785073 = r785070 + r785072;
        double r785074 = fma(r785066, r785067, r785073);
        return r785074;
}

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 2019354 +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))))