Average Error: 0.2 → 0.2
Time: 8.1s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3} \cdot \frac{1}{\sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3} \cdot \frac{1}{\sqrt{x}}
double f(double x, double y) {
        double r427244 = 1.0;
        double r427245 = x;
        double r427246 = 9.0;
        double r427247 = r427245 * r427246;
        double r427248 = r427244 / r427247;
        double r427249 = r427244 - r427248;
        double r427250 = y;
        double r427251 = 3.0;
        double r427252 = sqrt(r427245);
        double r427253 = r427251 * r427252;
        double r427254 = r427250 / r427253;
        double r427255 = r427249 - r427254;
        return r427255;
}
↓
double f(double x, double y) {
        double r427256 = 1.0;
        double r427257 = x;
        double r427258 = 9.0;
        double r427259 = r427257 * r427258;
        double r427260 = r427256 / r427259;
        double r427261 = r427256 - r427260;
        double r427262 = y;
        double r427263 = 3.0;
        double r427264 = r427262 / r427263;
        double r427265 = 1.0;
        double r427266 = sqrt(r427257);
        double r427267 = r427265 / r427266;
        double r427268 = r427264 * r427267;
        double r427269 = r427261 - r427268;
        return r427269;
}

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
Target0.2
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 div-inv0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020043 
(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)))))