Average Error: 0.2 → 0.2
Time: 21.2s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{0.1111111111111111049432054187491303309798}{x}\right) - \frac{\frac{y}{3}}{\sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{0.1111111111111111049432054187491303309798}{x}\right) - \frac{\frac{y}{3}}{\sqrt{x}}
double f(double x, double y) {
        double r396422 = 1.0;
        double r396423 = x;
        double r396424 = 9.0;
        double r396425 = r396423 * r396424;
        double r396426 = r396422 / r396425;
        double r396427 = r396422 - r396426;
        double r396428 = y;
        double r396429 = 3.0;
        double r396430 = sqrt(r396423);
        double r396431 = r396429 * r396430;
        double r396432 = r396428 / r396431;
        double r396433 = r396427 - r396432;
        return r396433;
}
↓
double f(double x, double y) {
        double r396434 = 1.0;
        double r396435 = 0.1111111111111111;
        double r396436 = x;
        double r396437 = r396435 / r396436;
        double r396438 = r396434 - r396437;
        double r396439 = y;
        double r396440 = 3.0;
        double r396441 = r396439 / r396440;
        double r396442 = sqrt(r396436);
        double r396443 = r396441 / r396442;
        double r396444 = r396438 - r396443;
        return r396444;
}

Error

Bits error versus x

Bits error versus y

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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

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

  4. Taylor expanded around 0 0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019322 +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)))))