Average Error: 0.2 → 0.2
Time: 10.1s
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 r454348 = 1.0;
        double r454349 = x;
        double r454350 = 9.0;
        double r454351 = r454349 * r454350;
        double r454352 = r454348 / r454351;
        double r454353 = r454348 - r454352;
        double r454354 = y;
        double r454355 = 3.0;
        double r454356 = sqrt(r454349);
        double r454357 = r454355 * r454356;
        double r454358 = r454354 / r454357;
        double r454359 = r454353 - r454358;
        return r454359;
}
↓
double f(double x, double y) {
        double r454360 = 1.0;
        double r454361 = x;
        double r454362 = r454360 / r454361;
        double r454363 = 9.0;
        double r454364 = r454362 / r454363;
        double r454365 = r454360 - r454364;
        double r454366 = y;
        double r454367 = 3.0;
        double r454368 = r454366 / r454367;
        double r454369 = sqrt(r454361);
        double r454370 = r454368 / r454369;
        double r454371 = r454365 - r454370;
        return r454371;
}

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

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

  5. Applied associate-/r*0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020042 
(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)))))