Average Error: 0.2 → 0.2
Time: 4.7s
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 r517274 = 1.0;
        double r517275 = x;
        double r517276 = 9.0;
        double r517277 = r517275 * r517276;
        double r517278 = r517274 / r517277;
        double r517279 = r517274 - r517278;
        double r517280 = y;
        double r517281 = 3.0;
        double r517282 = sqrt(r517275);
        double r517283 = r517281 * r517282;
        double r517284 = r517280 / r517283;
        double r517285 = r517279 - r517284;
        return r517285;
}
↓
double f(double x, double y) {
        double r517286 = 1.0;
        double r517287 = x;
        double r517288 = r517286 / r517287;
        double r517289 = 9.0;
        double r517290 = r517288 / r517289;
        double r517291 = r517286 - r517290;
        double r517292 = y;
        double r517293 = 3.0;
        double r517294 = r517292 / r517293;
        double r517295 = sqrt(r517287);
        double r517296 = r517294 / r517295;
        double r517297 = r517291 - r517296;
        return r517297;
}

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 2019362 
(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)))))