Average Error: 0.2 → 0.2
Time: 18.9s
Precision: 64
\[\left(1.0 - \frac{1.0}{x \cdot 9.0}\right) - \frac{y}{3.0 \cdot \sqrt{x}}\]
↓
\[\left(1.0 - \frac{\frac{1.0}{x}}{9.0}\right) - \frac{\frac{y}{3.0}}{\sqrt{x}}\]
\left(1.0 - \frac{1.0}{x \cdot 9.0}\right) - \frac{y}{3.0 \cdot \sqrt{x}}
↓
\left(1.0 - \frac{\frac{1.0}{x}}{9.0}\right) - \frac{\frac{y}{3.0}}{\sqrt{x}}
double f(double x, double y) {
        double r16593443 = 1.0;
        double r16593444 = x;
        double r16593445 = 9.0;
        double r16593446 = r16593444 * r16593445;
        double r16593447 = r16593443 / r16593446;
        double r16593448 = r16593443 - r16593447;
        double r16593449 = y;
        double r16593450 = 3.0;
        double r16593451 = sqrt(r16593444);
        double r16593452 = r16593450 * r16593451;
        double r16593453 = r16593449 / r16593452;
        double r16593454 = r16593448 - r16593453;
        return r16593454;
}
↓
double f(double x, double y) {
        double r16593455 = 1.0;
        double r16593456 = x;
        double r16593457 = r16593455 / r16593456;
        double r16593458 = 9.0;
        double r16593459 = r16593457 / r16593458;
        double r16593460 = r16593455 - r16593459;
        double r16593461 = y;
        double r16593462 = 3.0;
        double r16593463 = r16593461 / r16593462;
        double r16593464 = sqrt(r16593456);
        double r16593465 = r16593463 / r16593464;
        double r16593466 = r16593460 - r16593465;
        return r16593466;
}

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
\[\left(1.0 - \frac{\frac{1.0}{x}}{9.0}\right) - \frac{y}{3.0 \cdot \sqrt{x}}\]

Derivation

  1. Initial program 0.2

    \[\left(1.0 - \frac{1.0}{x \cdot 9.0}\right) - \frac{y}{3.0 \cdot \sqrt{x}}\]
  2. Using strategy rm

  3. Applied associate-/r*0.2

    \[\leadsto \left(1.0 - \frac{1.0}{x \cdot 9.0}\right) - \color{blue}{\frac{\frac{y}{3.0}}{\sqrt{x}}}\]
  4. Using strategy rm

  5. Applied associate-/r*0.2

    \[\leadsto \left(1.0 - \color{blue}{\frac{\frac{1.0}{x}}{9.0}}\right) - \frac{\frac{y}{3.0}}{\sqrt{x}}\]

  6. Final simplification0.2

    \[\leadsto \left(1.0 - \frac{\frac{1.0}{x}}{9.0}\right) - \frac{\frac{y}{3.0}}{\sqrt{x}}\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, D"

  :herbie-target
  (- (- 1.0 (/ (/ 1.0 x) 9.0)) (/ y (* 3.0 (sqrt x))))

  (- (- 1.0 (/ 1.0 (* x 9.0))) (/ y (* 3.0 (sqrt x)))))