Average Error: 0.2 → 0.2
Time: 3.7s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[1 - \left(\frac{1}{x \cdot 9} + \frac{\frac{y}{3}}{\sqrt{x}}\right)\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
1 - \left(\frac{1}{x \cdot 9} + \frac{\frac{y}{3}}{\sqrt{x}}\right)
double f(double x, double y) {
        double r385772 = 1.0;
        double r385773 = x;
        double r385774 = 9.0;
        double r385775 = r385773 * r385774;
        double r385776 = r385772 / r385775;
        double r385777 = r385772 - r385776;
        double r385778 = y;
        double r385779 = 3.0;
        double r385780 = sqrt(r385773);
        double r385781 = r385779 * r385780;
        double r385782 = r385778 / r385781;
        double r385783 = r385777 - r385782;
        return r385783;
}
↓
double f(double x, double y) {
        double r385784 = 1.0;
        double r385785 = x;
        double r385786 = 9.0;
        double r385787 = r385785 * r385786;
        double r385788 = r385784 / r385787;
        double r385789 = y;
        double r385790 = 3.0;
        double r385791 = r385789 / r385790;
        double r385792 = sqrt(r385785);
        double r385793 = r385791 / r385792;
        double r385794 = r385788 + r385793;
        double r385795 = r385784 - r385794;
        return r385795;
}

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

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*0.2

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

  5. Applied associate--l-0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020018 
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, D"
  :precision binary64

  :herbie-target
  (- (- 1 (/ (/ 1 x) 9)) (/ y (* 3 (sqrt x))))

  (- (- 1 (/ 1 (* x 9))) (/ y (* 3 (sqrt x)))))