Average Error: 0.2 → 0.2
Time: 11.9s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{1}{3} \cdot \frac{y}{\sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{1}{3} \cdot \frac{y}{\sqrt{x}}
double f(double x, double y) {
        double r254375 = 1.0;
        double r254376 = x;
        double r254377 = 9.0;
        double r254378 = r254376 * r254377;
        double r254379 = r254375 / r254378;
        double r254380 = r254375 - r254379;
        double r254381 = y;
        double r254382 = 3.0;
        double r254383 = sqrt(r254376);
        double r254384 = r254382 * r254383;
        double r254385 = r254381 / r254384;
        double r254386 = r254380 - r254385;
        return r254386;
}
↓
double f(double x, double y) {
        double r254387 = 1.0;
        double r254388 = x;
        double r254389 = r254387 / r254388;
        double r254390 = 9.0;
        double r254391 = r254389 / r254390;
        double r254392 = r254387 - r254391;
        double r254393 = 1.0;
        double r254394 = 3.0;
        double r254395 = r254393 / r254394;
        double r254396 = y;
        double r254397 = sqrt(r254388);
        double r254398 = r254396 / r254397;
        double r254399 = r254395 * r254398;
        double r254400 = r254392 - r254399;
        return r254400;
}

Error

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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 *-un-lft-identity0.2

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

  6. Applied times-frac0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2019303 
(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)))))