Average Error: 0.2 → 0.3
Time: 4.3s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{\frac{1}{x}}{\sqrt[3]{9} \cdot \sqrt[3]{9}}}{\sqrt[3]{9}}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{\frac{\frac{1}{x}}{\sqrt[3]{9} \cdot \sqrt[3]{9}}}{\sqrt[3]{9}}\right) - \frac{y}{3 \cdot \sqrt{x}}
double f(double x, double y) {
        double r338453 = 1.0;
        double r338454 = x;
        double r338455 = 9.0;
        double r338456 = r338454 * r338455;
        double r338457 = r338453 / r338456;
        double r338458 = r338453 - r338457;
        double r338459 = y;
        double r338460 = 3.0;
        double r338461 = sqrt(r338454);
        double r338462 = r338460 * r338461;
        double r338463 = r338459 / r338462;
        double r338464 = r338458 - r338463;
        return r338464;
}
↓
double f(double x, double y) {
        double r338465 = 1.0;
        double r338466 = x;
        double r338467 = r338465 / r338466;
        double r338468 = 9.0;
        double r338469 = cbrt(r338468);
        double r338470 = r338469 * r338469;
        double r338471 = r338467 / r338470;
        double r338472 = r338471 / r338469;
        double r338473 = r338465 - r338472;
        double r338474 = y;
        double r338475 = 3.0;
        double r338476 = sqrt(r338466);
        double r338477 = r338475 * r338476;
        double r338478 = r338474 / r338477;
        double r338479 = r338473 - r338478;
        return r338479;
}

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

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 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 add-cube-cbrt0.2

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

  6. Applied associate-/r*0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2020062 
(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)))))