Average Error: 0.2 → 0.3
Time: 5.8s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{0.1111111111111111049432054187491303309798}{x}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{0.1111111111111111049432054187491303309798}{x}\right) - \frac{y}{3 \cdot \sqrt{x}}
double f(double x, double y) {
        double r483933 = 1.0;
        double r483934 = x;
        double r483935 = 9.0;
        double r483936 = r483934 * r483935;
        double r483937 = r483933 / r483936;
        double r483938 = r483933 - r483937;
        double r483939 = y;
        double r483940 = 3.0;
        double r483941 = sqrt(r483934);
        double r483942 = r483940 * r483941;
        double r483943 = r483939 / r483942;
        double r483944 = r483938 - r483943;
        return r483944;
}
↓
double f(double x, double y) {
        double r483945 = 1.0;
        double r483946 = 0.1111111111111111;
        double r483947 = x;
        double r483948 = r483946 / r483947;
        double r483949 = r483945 - r483948;
        double r483950 = y;
        double r483951 = 3.0;
        double r483952 = sqrt(r483947);
        double r483953 = r483951 * r483952;
        double r483954 = r483950 / r483953;
        double r483955 = r483949 - r483954;
        return r483955;
}

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

Derivation

  1. Initial program 0.2

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

  2. Taylor expanded around 0 0.3

    \[\leadsto \left(1 - \color{blue}{\frac{0.1111111111111111049432054187491303309798}{x}}\right) - \frac{y}{3 \cdot \sqrt{x}}\]

  3. Final simplification0.3

    \[\leadsto \left(1 - \frac{0.1111111111111111049432054187491303309798}{x}\right) - \frac{y}{3 \cdot \sqrt{x}}\]

Reproduce

herbie shell --seed 2020001 
(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)))))