Average Error: 0.2 → 0.3
Time: 6.1s
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 r467076 = 1.0;
        double r467077 = x;
        double r467078 = 9.0;
        double r467079 = r467077 * r467078;
        double r467080 = r467076 / r467079;
        double r467081 = r467076 - r467080;
        double r467082 = y;
        double r467083 = 3.0;
        double r467084 = sqrt(r467077);
        double r467085 = r467083 * r467084;
        double r467086 = r467082 / r467085;
        double r467087 = r467081 - r467086;
        return r467087;
}
↓
double f(double x, double y) {
        double r467088 = 1.0;
        double r467089 = 0.1111111111111111;
        double r467090 = x;
        double r467091 = r467089 / r467090;
        double r467092 = r467088 - r467091;
        double r467093 = y;
        double r467094 = 3.0;
        double r467095 = sqrt(r467090);
        double r467096 = r467094 * r467095;
        double r467097 = r467093 / r467096;
        double r467098 = r467092 - r467097;
        return r467098;
}

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)))))