Average Error: 0.2 → 0.3
Time: 3.4s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{0.1111111111111111}{x}\right) - y \cdot \frac{1}{3 \cdot \sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{0.1111111111111111}{x}\right) - y \cdot \frac{1}{3 \cdot \sqrt{x}}
double f(double x, double y) {
        double r493333 = 1.0;
        double r493334 = x;
        double r493335 = 9.0;
        double r493336 = r493334 * r493335;
        double r493337 = r493333 / r493336;
        double r493338 = r493333 - r493337;
        double r493339 = y;
        double r493340 = 3.0;
        double r493341 = sqrt(r493334);
        double r493342 = r493340 * r493341;
        double r493343 = r493339 / r493342;
        double r493344 = r493338 - r493343;
        return r493344;
}
↓
double f(double x, double y) {
        double r493345 = 1.0;
        double r493346 = 0.1111111111111111;
        double r493347 = x;
        double r493348 = r493346 / r493347;
        double r493349 = r493345 - r493348;
        double r493350 = y;
        double r493351 = 1.0;
        double r493352 = 3.0;
        double r493353 = sqrt(r493347);
        double r493354 = r493352 * r493353;
        double r493355 = r493351 / r493354;
        double r493356 = r493350 * r493355;
        double r493357 = r493349 - r493356;
        return r493357;
}

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

Derivation

  1. Initial program 0.2

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

  3. Applied div-inv0.2

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

  4. Taylor expanded around 0 0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2020060 
(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)))))