Average Error: 0.0 → 0.0
Time: 1.2s
Precision: 64
\[x \cdot y + z \cdot \left(1 - y\right)\]
↓
\[\mathsf{fma}\left(x, y, z \cdot 1 + z \cdot \left(-y\right)\right)\]
x \cdot y + z \cdot \left(1 - y\right)
↓
\mathsf{fma}\left(x, y, z \cdot 1 + z \cdot \left(-y\right)\right)
double f(double x, double y, double z) {
        double r618004 = x;
        double r618005 = y;
        double r618006 = r618004 * r618005;
        double r618007 = z;
        double r618008 = 1.0;
        double r618009 = r618008 - r618005;
        double r618010 = r618007 * r618009;
        double r618011 = r618006 + r618010;
        return r618011;
}
↓
double f(double x, double y, double z) {
        double r618012 = x;
        double r618013 = y;
        double r618014 = z;
        double r618015 = 1.0;
        double r618016 = r618014 * r618015;
        double r618017 = -r618013;
        double r618018 = r618014 * r618017;
        double r618019 = r618016 + r618018;
        double r618020 = fma(r618012, r618013, r618019);
        return r618020;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020036 +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))))