Average Error: 0.2 → 0.2
Time: 1.5m
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{\frac{y}{3}}{\sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{\frac{y}{3}}{\sqrt{x}}
double f(double x, double y) {
        double r11787941 = 1.0;
        double r11787942 = x;
        double r11787943 = 9.0;
        double r11787944 = r11787942 * r11787943;
        double r11787945 = r11787941 / r11787944;
        double r11787946 = r11787941 - r11787945;
        double r11787947 = y;
        double r11787948 = 3.0;
        double r11787949 = sqrt(r11787942);
        double r11787950 = r11787948 * r11787949;
        double r11787951 = r11787947 / r11787950;
        double r11787952 = r11787946 - r11787951;
        return r11787952;
}
↓
double f(double x, double y) {
        double r11787953 = 1.0;
        double r11787954 = x;
        double r11787955 = r11787953 / r11787954;
        double r11787956 = 9.0;
        double r11787957 = r11787955 / r11787956;
        double r11787958 = r11787953 - r11787957;
        double r11787959 = y;
        double r11787960 = 3.0;
        double r11787961 = r11787959 / r11787960;
        double r11787962 = sqrt(r11787954);
        double r11787963 = r11787961 / r11787962;
        double r11787964 = r11787958 - r11787963;
        return r11787964;
}

Error

Bits error versus x

Bits error versus y

Try it out

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-/r*0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019200 +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)))))