Average Error: 0.2 → 0.2
Time: 10.6s
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 r249950 = 1.0;
        double r249951 = x;
        double r249952 = 9.0;
        double r249953 = r249951 * r249952;
        double r249954 = r249950 / r249953;
        double r249955 = r249950 - r249954;
        double r249956 = y;
        double r249957 = 3.0;
        double r249958 = sqrt(r249951);
        double r249959 = r249957 * r249958;
        double r249960 = r249956 / r249959;
        double r249961 = r249955 - r249960;
        return r249961;
}
↓
double f(double x, double y) {
        double r249962 = 1.0;
        double r249963 = x;
        double r249964 = 9.0;
        double r249965 = r249963 * r249964;
        double r249966 = r249962 / r249965;
        double r249967 = r249962 - r249966;
        double r249968 = y;
        double r249969 = 3.0;
        double r249970 = r249968 / r249969;
        double r249971 = sqrt(r249963);
        double r249972 = r249970 / r249971;
        double r249973 = r249967 - r249972;
        return r249973;
}

Error

Bits error versus x

Bits error versus y

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Results

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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 2019291 
(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)))))