Average Error: 0.0 → 0.0
Time: 5.6s
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 r376611 = x;
        double r376612 = y;
        double r376613 = r376611 * r376612;
        double r376614 = z;
        double r376615 = 1.0;
        double r376616 = r376615 - r376612;
        double r376617 = r376614 * r376616;
        double r376618 = r376613 + r376617;
        return r376618;
}
↓
double f(double x, double y, double z) {
        double r376619 = x;
        double r376620 = y;
        double r376621 = z;
        double r376622 = 1.0;
        double r376623 = r376621 * r376622;
        double r376624 = -r376620;
        double r376625 = r376624 * r376621;
        double r376626 = r376623 + r376625;
        double r376627 = fma(r376619, r376620, r376626);
        return r376627;
}

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 2019347 +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))))