Average Error: 5.9 → 0.3
Time: 3.2s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\left(1 - x\right) \cdot \frac{1}{\frac{y \cdot 3}{3 - x}}\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\left(1 - x\right) \cdot \frac{1}{\frac{y \cdot 3}{3 - x}}
double f(double x, double y) {
        double r587848 = 1.0;
        double r587849 = x;
        double r587850 = r587848 - r587849;
        double r587851 = 3.0;
        double r587852 = r587851 - r587849;
        double r587853 = r587850 * r587852;
        double r587854 = y;
        double r587855 = r587854 * r587851;
        double r587856 = r587853 / r587855;
        return r587856;
}
↓
double f(double x, double y) {
        double r587857 = 1.0;
        double r587858 = x;
        double r587859 = r587857 - r587858;
        double r587860 = 1.0;
        double r587861 = y;
        double r587862 = 3.0;
        double r587863 = r587861 * r587862;
        double r587864 = r587862 - r587858;
        double r587865 = r587863 / r587864;
        double r587866 = r587860 / r587865;
        double r587867 = r587859 * r587866;
        return r587867;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original5.9
Target0.1
Herbie0.3
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

Derivation

  1. Initial program 5.9

    \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
  2. Using strategy rm

  3. Applied associate-/l*0.3

    \[\leadsto \color{blue}{\frac{1 - x}{\frac{y \cdot 3}{3 - x}}}\]
  4. Using strategy rm

  5. Applied div-inv0.3

    \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{1}{\frac{y \cdot 3}{3 - x}}}\]

  6. Final simplification0.3

    \[\leadsto \left(1 - x\right) \cdot \frac{1}{\frac{y \cdot 3}{3 - x}}\]

Reproduce

herbie shell --seed 2020024 
(FPCore (x y)
  :name "Diagrams.TwoD.Arc:bezierFromSweepQ1 from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (* (/ (- 1 x) y) (/ (- 3 x) 3))

  (/ (* (- 1 x) (- 3 x)) (* y 3)))