Average Error: 0.2 → 0.2
Time: 22.6s
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 r290317 = 1.0;
        double r290318 = x;
        double r290319 = 9.0;
        double r290320 = r290318 * r290319;
        double r290321 = r290317 / r290320;
        double r290322 = r290317 - r290321;
        double r290323 = y;
        double r290324 = 3.0;
        double r290325 = sqrt(r290318);
        double r290326 = r290324 * r290325;
        double r290327 = r290323 / r290326;
        double r290328 = r290322 - r290327;
        return r290328;
}
↓
double f(double x, double y) {
        double r290329 = 1.0;
        double r290330 = x;
        double r290331 = r290329 / r290330;
        double r290332 = 9.0;
        double r290333 = r290331 / r290332;
        double r290334 = r290329 - r290333;
        double r290335 = y;
        double r290336 = 3.0;
        double r290337 = r290335 / r290336;
        double r290338 = sqrt(r290330);
        double r290339 = r290337 / r290338;
        double r290340 = r290334 - r290339;
        return r290340;
}

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

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

  5. Applied associate-/r*0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019303 +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)))))