Average Error: 0.0 → 0.0
Time: 1.7s
Precision: 64
\[x \cdot y + z \cdot \left(1 - y\right)\]
↓
\[\mathsf{fma}\left(y, x - z, z \cdot 1\right)\]
x \cdot y + z \cdot \left(1 - y\right)
↓
\mathsf{fma}\left(y, x - z, z \cdot 1\right)
double f(double x, double y, double z) {
        double r688181 = x;
        double r688182 = y;
        double r688183 = r688181 * r688182;
        double r688184 = z;
        double r688185 = 1.0;
        double r688186 = r688185 - r688182;
        double r688187 = r688184 * r688186;
        double r688188 = r688183 + r688187;
        return r688188;
}
↓
double f(double x, double y, double z) {
        double r688189 = y;
        double r688190 = x;
        double r688191 = z;
        double r688192 = r688190 - r688191;
        double r688193 = 1.0;
        double r688194 = r688191 * r688193;
        double r688195 = fma(r688189, r688192, r688194);
        return r688195;
}

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. Taylor expanded around 0 0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020081 +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))))