Average Error: 0.2 → 0.2
Time: 19.6s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{\frac{y}{3}}{\sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{\frac{y}{3}}{\sqrt{x}}
double f(double x, double y) {
        double r226366 = 1.0;
        double r226367 = x;
        double r226368 = 9.0;
        double r226369 = r226367 * r226368;
        double r226370 = r226366 / r226369;
        double r226371 = r226366 - r226370;
        double r226372 = y;
        double r226373 = 3.0;
        double r226374 = sqrt(r226367);
        double r226375 = r226373 * r226374;
        double r226376 = r226372 / r226375;
        double r226377 = r226371 - r226376;
        return r226377;
}
↓
double f(double x, double y) {
        double r226378 = 1.0;
        double r226379 = x;
        double r226380 = 9.0;
        double r226381 = r226379 * r226380;
        double r226382 = r226378 / r226381;
        double r226383 = r226378 - r226382;
        double r226384 = y;
        double r226385 = 3.0;
        double r226386 = r226384 / r226385;
        double r226387 = sqrt(r226379);
        double r226388 = r226386 / r226387;
        double r226389 = r226383 - r226388;
        return r226389;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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Target

Original0.2
Target0.3
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. Simplified0.2

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

  4. Applied associate-/r*0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019174 +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)))))