Average Error: 0.2 → 0.2
Time: 15.0s
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 r340341 = 1.0;
        double r340342 = x;
        double r340343 = 9.0;
        double r340344 = r340342 * r340343;
        double r340345 = r340341 / r340344;
        double r340346 = r340341 - r340345;
        double r340347 = y;
        double r340348 = 3.0;
        double r340349 = sqrt(r340342);
        double r340350 = r340348 * r340349;
        double r340351 = r340347 / r340350;
        double r340352 = r340346 - r340351;
        return r340352;
}
↓
double f(double x, double y) {
        double r340353 = 1.0;
        double r340354 = x;
        double r340355 = r340353 / r340354;
        double r340356 = 9.0;
        double r340357 = r340355 / r340356;
        double r340358 = r340353 - r340357;
        double r340359 = y;
        double r340360 = 3.0;
        double r340361 = r340359 / r340360;
        double r340362 = sqrt(r340354);
        double r340363 = r340361 / r340362;
        double r340364 = r340358 - r340363;
        return r340364;
}

Error

Bits error versus x

Bits error versus y

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Results

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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 2019194 
(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)))))