Average Error: 0.0 → 0.0
Time: 4.3s
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 r532647 = x;
        double r532648 = y;
        double r532649 = r532647 * r532648;
        double r532650 = z;
        double r532651 = 1.0;
        double r532652 = r532651 - r532648;
        double r532653 = r532650 * r532652;
        double r532654 = r532649 + r532653;
        return r532654;
}
↓
double f(double x, double y, double z) {
        double r532655 = x;
        double r532656 = y;
        double r532657 = z;
        double r532658 = 1.0;
        double r532659 = r532657 * r532658;
        double r532660 = -r532656;
        double r532661 = r532660 * r532657;
        double r532662 = r532659 + r532661;
        double r532663 = fma(r532655, r532656, r532662);
        return r532663;
}

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 2019350 +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))))