Average Error: 0.2 → 0.2
Time: 6.6s
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 r271255 = 1.0;
        double r271256 = x;
        double r271257 = 9.0;
        double r271258 = r271256 * r271257;
        double r271259 = r271255 / r271258;
        double r271260 = r271255 - r271259;
        double r271261 = y;
        double r271262 = 3.0;
        double r271263 = sqrt(r271256);
        double r271264 = r271262 * r271263;
        double r271265 = r271261 / r271264;
        double r271266 = r271260 - r271265;
        return r271266;
}
↓
double f(double x, double y) {
        double r271267 = 1.0;
        double r271268 = x;
        double r271269 = 9.0;
        double r271270 = r271268 * r271269;
        double r271271 = r271267 / r271270;
        double r271272 = r271267 - r271271;
        double r271273 = y;
        double r271274 = 3.0;
        double r271275 = r271273 / r271274;
        double r271276 = sqrt(r271268);
        double r271277 = r271275 / r271276;
        double r271278 = r271272 - r271277;
        return r271278;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2019308 
(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)))))