Average Error: 0.0 → 0.0
Time: 1.6s
Precision: 64
\[x \cdot y + z \cdot \left(1 - y\right)\]
↓
\[\mathsf{fma}\left(x, y, z \cdot \left(1 - y\right)\right)\]
x \cdot y + z \cdot \left(1 - y\right)
↓
\mathsf{fma}\left(x, y, z \cdot \left(1 - y\right)\right)
double f(double x, double y, double z) {
        double r2133212 = x;
        double r2133213 = y;
        double r2133214 = r2133212 * r2133213;
        double r2133215 = z;
        double r2133216 = 1.0;
        double r2133217 = r2133216 - r2133213;
        double r2133218 = r2133215 * r2133217;
        double r2133219 = r2133214 + r2133218;
        return r2133219;
}
↓
double f(double x, double y, double z) {
        double r2133220 = x;
        double r2133221 = y;
        double r2133222 = z;
        double r2133223 = 1.0;
        double r2133224 = r2133223 - r2133221;
        double r2133225 = r2133222 * r2133224;
        double r2133226 = fma(r2133220, r2133221, r2133225);
        return r2133226;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020018 +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))))