Average Error: 0.4 → 0.4
Time: 16.0s
Precision: 64
\[\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\]
↓
\[\left(1.0 \cdot \sqrt{x}\right) \cdot \left(-3.0\right) + \sqrt{x} \cdot \left(\left(\frac{1.0}{9.0 \cdot x} + y\right) \cdot 3.0\right)\]
\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)
↓
\left(1.0 \cdot \sqrt{x}\right) \cdot \left(-3.0\right) + \sqrt{x} \cdot \left(\left(\frac{1.0}{9.0 \cdot x} + y\right) \cdot 3.0\right)
double f(double x, double y) {
        double r22242823 = 3.0;
        double r22242824 = x;
        double r22242825 = sqrt(r22242824);
        double r22242826 = r22242823 * r22242825;
        double r22242827 = y;
        double r22242828 = 1.0;
        double r22242829 = 9.0;
        double r22242830 = r22242824 * r22242829;
        double r22242831 = r22242828 / r22242830;
        double r22242832 = r22242827 + r22242831;
        double r22242833 = r22242832 - r22242828;
        double r22242834 = r22242826 * r22242833;
        return r22242834;
}
↓
double f(double x, double y) {
        double r22242835 = 1.0;
        double r22242836 = x;
        double r22242837 = sqrt(r22242836);
        double r22242838 = r22242835 * r22242837;
        double r22242839 = 3.0;
        double r22242840 = -r22242839;
        double r22242841 = r22242838 * r22242840;
        double r22242842 = 9.0;
        double r22242843 = r22242842 * r22242836;
        double r22242844 = r22242835 / r22242843;
        double r22242845 = y;
        double r22242846 = r22242844 + r22242845;
        double r22242847 = r22242846 * r22242839;
        double r22242848 = r22242837 * r22242847;
        double r22242849 = r22242841 + r22242848;
        return r22242849;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.4
Target0.4
Herbie0.4
\[3.0 \cdot \left(y \cdot \sqrt{x} + \left(\frac{1.0}{x \cdot 9.0} - 1.0\right) \cdot \sqrt{x}\right)\]

Derivation

  1. Initial program 0.4

    \[\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\]
  2. Using strategy rm

  3. Applied associate-*l*0.4

    \[\leadsto \color{blue}{3.0 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\right)}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt0.4

    \[\leadsto \color{blue}{\left(\left(\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}\right) \cdot \sqrt[3]{3.0}\right)} \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\right)\]

  6. Applied associate-*l*0.6

    \[\leadsto \color{blue}{\left(\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}\right) \cdot \left(\sqrt[3]{3.0} \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\right)\right)}\]
  7. Using strategy rm

  8. Applied sub-neg0.6

    \[\leadsto \left(\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}\right) \cdot \left(\sqrt[3]{3.0} \cdot \left(\sqrt{x} \cdot \color{blue}{\left(\left(y + \frac{1.0}{x \cdot 9.0}\right) + \left(-1.0\right)\right)}\right)\right)\]

  9. Applied distribute-lft-in0.6

    \[\leadsto \left(\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}\right) \cdot \left(\sqrt[3]{3.0} \cdot \color{blue}{\left(\sqrt{x} \cdot \left(y + \frac{1.0}{x \cdot 9.0}\right) + \sqrt{x} \cdot \left(-1.0\right)\right)}\right)\]

  10. Applied distribute-lft-in0.6

    \[\leadsto \left(\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}\right) \cdot \color{blue}{\left(\sqrt[3]{3.0} \cdot \left(\sqrt{x} \cdot \left(y + \frac{1.0}{x \cdot 9.0}\right)\right) + \sqrt[3]{3.0} \cdot \left(\sqrt{x} \cdot \left(-1.0\right)\right)\right)}\]

  11. Applied distribute-lft-in0.6

    \[\leadsto \color{blue}{\left(\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}\right) \cdot \left(\sqrt[3]{3.0} \cdot \left(\sqrt{x} \cdot \left(y + \frac{1.0}{x \cdot 9.0}\right)\right)\right) + \left(\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}\right) \cdot \left(\sqrt[3]{3.0} \cdot \left(\sqrt{x} \cdot \left(-1.0\right)\right)\right)}\]

  12. Simplified0.5

    \[\leadsto \color{blue}{\left(3.0 \cdot \left(\frac{1.0}{9.0 \cdot x} + y\right)\right) \cdot \sqrt{x}} + \left(\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}\right) \cdot \left(\sqrt[3]{3.0} \cdot \left(\sqrt{x} \cdot \left(-1.0\right)\right)\right)\]

  13. Simplified0.4

    \[\leadsto \left(3.0 \cdot \left(\frac{1.0}{9.0 \cdot x} + y\right)\right) \cdot \sqrt{x} + \color{blue}{\left(\sqrt{x} \cdot 1.0\right) \cdot \left(-3.0\right)}\]

  14. Final simplification0.4

    \[\leadsto \left(1.0 \cdot \sqrt{x}\right) \cdot \left(-3.0\right) + \sqrt{x} \cdot \left(\left(\frac{1.0}{9.0 \cdot x} + y\right) \cdot 3.0\right)\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"

  :herbie-target
  (* 3.0 (+ (* y (sqrt x)) (* (- (/ 1.0 (* x 9.0)) 1.0) (sqrt x))))

  (* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))