Average Error: 0.2 → 0.2
Time: 3.4s
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 r448314 = 1.0;
        double r448315 = x;
        double r448316 = 9.0;
        double r448317 = r448315 * r448316;
        double r448318 = r448314 / r448317;
        double r448319 = r448314 - r448318;
        double r448320 = y;
        double r448321 = 3.0;
        double r448322 = sqrt(r448315);
        double r448323 = r448321 * r448322;
        double r448324 = r448320 / r448323;
        double r448325 = r448319 - r448324;
        return r448325;
}
↓
double f(double x, double y) {
        double r448326 = 1.0;
        double r448327 = x;
        double r448328 = 9.0;
        double r448329 = r448327 * r448328;
        double r448330 = r448326 / r448329;
        double r448331 = r448326 - r448330;
        double r448332 = y;
        double r448333 = 3.0;
        double r448334 = r448332 / r448333;
        double r448335 = sqrt(r448327);
        double r448336 = r448334 / r448335;
        double r448337 = r448331 - r448336;
        return r448337;
}

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 2020025 
(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)))))