Average Error: 0.2 → 0.2
Time: 11.9s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{0.1111111111111111}{x}\right) - \frac{\frac{y}{3}}{\sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{0.1111111111111111}{x}\right) - \frac{\frac{y}{3}}{\sqrt{x}}
double f(double x, double y) {
        double r360266 = 1.0;
        double r360267 = x;
        double r360268 = 9.0;
        double r360269 = r360267 * r360268;
        double r360270 = r360266 / r360269;
        double r360271 = r360266 - r360270;
        double r360272 = y;
        double r360273 = 3.0;
        double r360274 = sqrt(r360267);
        double r360275 = r360273 * r360274;
        double r360276 = r360272 / r360275;
        double r360277 = r360271 - r360276;
        return r360277;
}
↓
double f(double x, double y) {
        double r360278 = 1.0;
        double r360279 = 0.1111111111111111;
        double r360280 = x;
        double r360281 = r360279 / r360280;
        double r360282 = r360278 - r360281;
        double r360283 = y;
        double r360284 = 3.0;
        double r360285 = r360283 / r360284;
        double r360286 = sqrt(r360280);
        double r360287 = r360285 / r360286;
        double r360288 = r360282 - r360287;
        return r360288;
}

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
Herbie0.2
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]

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. Taylor expanded around 0 0.2

    \[\leadsto \left(1 - \color{blue}{\frac{0.1111111111111111}{x}}\right) - \frac{\frac{y}{3}}{\sqrt{x}}\]

  5. Final simplification0.2

    \[\leadsto \left(1 - \frac{0.1111111111111111}{x}\right) - \frac{\frac{y}{3}}{\sqrt{x}}\]

Reproduce

herbie shell --seed 2020047 +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)))))