Average Error: 0.2 → 0.2
Time: 4.8s
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 r358189 = 1.0;
        double r358190 = x;
        double r358191 = 9.0;
        double r358192 = r358190 * r358191;
        double r358193 = r358189 / r358192;
        double r358194 = r358189 - r358193;
        double r358195 = y;
        double r358196 = 3.0;
        double r358197 = sqrt(r358190);
        double r358198 = r358196 * r358197;
        double r358199 = r358195 / r358198;
        double r358200 = r358194 - r358199;
        return r358200;
}
↓
double f(double x, double y) {
        double r358201 = 1.0;
        double r358202 = x;
        double r358203 = 9.0;
        double r358204 = r358202 * r358203;
        double r358205 = r358201 / r358204;
        double r358206 = r358201 - r358205;
        double r358207 = y;
        double r358208 = 3.0;
        double r358209 = r358207 / r358208;
        double r358210 = sqrt(r358202);
        double r358211 = r358209 / r358210;
        double r358212 = r358206 - r358211;
        return r358212;
}

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 2019354 
(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)))))