Average Error: 0.0 → 0.0
Time: 1.3s
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 r715247 = x;
        double r715248 = y;
        double r715249 = r715247 * r715248;
        double r715250 = z;
        double r715251 = 1.0;
        double r715252 = r715251 - r715248;
        double r715253 = r715250 * r715252;
        double r715254 = r715249 + r715253;
        return r715254;
}
↓
double f(double x, double y, double z) {
        double r715255 = y;
        double r715256 = x;
        double r715257 = z;
        double r715258 = r715256 - r715257;
        double r715259 = 1.0;
        double r715260 = r715257 * r715259;
        double r715261 = fma(r715255, r715258, r715260);
        return r715261;
}

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 2020002 +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))))