Average Error: 0.2 → 0.2
Time: 16.9s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{1}{\frac{3}{\frac{y}{\sqrt{x}}}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{1}{\frac{3}{\frac{y}{\sqrt{x}}}}
double f(double x, double y) {
        double r257056 = 1.0;
        double r257057 = x;
        double r257058 = 9.0;
        double r257059 = r257057 * r257058;
        double r257060 = r257056 / r257059;
        double r257061 = r257056 - r257060;
        double r257062 = y;
        double r257063 = 3.0;
        double r257064 = sqrt(r257057);
        double r257065 = r257063 * r257064;
        double r257066 = r257062 / r257065;
        double r257067 = r257061 - r257066;
        return r257067;
}
↓
double f(double x, double y) {
        double r257068 = 1.0;
        double r257069 = x;
        double r257070 = 9.0;
        double r257071 = r257069 * r257070;
        double r257072 = r257068 / r257071;
        double r257073 = r257068 - r257072;
        double r257074 = 1.0;
        double r257075 = 3.0;
        double r257076 = y;
        double r257077 = sqrt(r257069);
        double r257078 = r257076 / r257077;
        double r257079 = r257075 / r257078;
        double r257080 = r257074 / r257079;
        double r257081 = r257073 - r257080;
        return r257081;
}

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 clear-num0.2

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

  5. Applied add-sqr-sqrt0.2

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

  6. Applied associate-/l*0.2

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

  7. Simplified0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(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)))))