Average Error: 0.2 → 0.3
Time: 21.5s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{\left(\sqrt[3]{3} \cdot \sqrt{x}\right) \cdot \left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right)}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{\left(\sqrt[3]{3} \cdot \sqrt{x}\right) \cdot \left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right)}
double f(double x, double y) {
        double r14943791 = 1.0;
        double r14943792 = x;
        double r14943793 = 9.0;
        double r14943794 = r14943792 * r14943793;
        double r14943795 = r14943791 / r14943794;
        double r14943796 = r14943791 - r14943795;
        double r14943797 = y;
        double r14943798 = 3.0;
        double r14943799 = sqrt(r14943792);
        double r14943800 = r14943798 * r14943799;
        double r14943801 = r14943797 / r14943800;
        double r14943802 = r14943796 - r14943801;
        return r14943802;
}
↓
double f(double x, double y) {
        double r14943803 = 1.0;
        double r14943804 = x;
        double r14943805 = r14943803 / r14943804;
        double r14943806 = 9.0;
        double r14943807 = r14943805 / r14943806;
        double r14943808 = r14943803 - r14943807;
        double r14943809 = y;
        double r14943810 = 3.0;
        double r14943811 = cbrt(r14943810);
        double r14943812 = sqrt(r14943804);
        double r14943813 = r14943811 * r14943812;
        double r14943814 = r14943811 * r14943811;
        double r14943815 = r14943813 * r14943814;
        double r14943816 = r14943809 / r14943815;
        double r14943817 = r14943808 - r14943816;
        return r14943817;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.3
Herbie0.3
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]

Derivation

  1. Initial program 0.2

    \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
  2. Using strategy rm

  3. Applied associate-/r*0.3

    \[\leadsto \left(1 - \color{blue}{\frac{\frac{1}{x}}{9}}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt0.3

    \[\leadsto \left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{\color{blue}{\left(\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \sqrt[3]{3}\right)} \cdot \sqrt{x}}\]

  6. Applied associate-*l*0.3

    \[\leadsto \left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{\color{blue}{\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \left(\sqrt[3]{3} \cdot \sqrt{x}\right)}}\]

  7. Final simplification0.3

    \[\leadsto \left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{\left(\sqrt[3]{3} \cdot \sqrt{x}\right) \cdot \left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right)}\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, D"

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

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