Average Error: 0.2 → 0.2
Time: 3.8s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{\frac{y}{3}}{\sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{\frac{y}{3}}{\sqrt{x}}
double f(double x, double y) {
        double r473038 = 1.0;
        double r473039 = x;
        double r473040 = 9.0;
        double r473041 = r473039 * r473040;
        double r473042 = r473038 / r473041;
        double r473043 = r473038 - r473042;
        double r473044 = y;
        double r473045 = 3.0;
        double r473046 = sqrt(r473039);
        double r473047 = r473045 * r473046;
        double r473048 = r473044 / r473047;
        double r473049 = r473043 - r473048;
        return r473049;
}
↓
double f(double x, double y) {
        double r473050 = 1.0;
        double r473051 = x;
        double r473052 = 9.0;
        double r473053 = r473051 * r473052;
        double r473054 = r473050 / r473053;
        double r473055 = r473050 - r473054;
        double r473056 = y;
        double r473057 = 3.0;
        double r473058 = r473056 / r473057;
        double r473059 = sqrt(r473051);
        double r473060 = r473058 / r473059;
        double r473061 = r473055 - r473060;
        return r473061;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020027 
(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)))))