Average Error: 0.2 → 0.2
Time: 12.3s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3} \cdot {x}^{\frac{-1}{2}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3} \cdot {x}^{\frac{-1}{2}}
double f(double x, double y) {
        double r247203 = 1.0;
        double r247204 = x;
        double r247205 = 9.0;
        double r247206 = r247204 * r247205;
        double r247207 = r247203 / r247206;
        double r247208 = r247203 - r247207;
        double r247209 = y;
        double r247210 = 3.0;
        double r247211 = sqrt(r247204);
        double r247212 = r247210 * r247211;
        double r247213 = r247209 / r247212;
        double r247214 = r247208 - r247213;
        return r247214;
}
↓
double f(double x, double y) {
        double r247215 = 1.0;
        double r247216 = x;
        double r247217 = r247215 / r247216;
        double r247218 = 9.0;
        double r247219 = r247217 / r247218;
        double r247220 = r247215 - r247219;
        double r247221 = y;
        double r247222 = 3.0;
        double r247223 = r247221 / r247222;
        double r247224 = -0.5;
        double r247225 = pow(r247216, r247224);
        double r247226 = r247223 * r247225;
        double r247227 = r247220 - r247226;
        return r247227;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Using strategy rm

  7. Applied pow1/20.2

    \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3} \cdot \frac{1}{\color{blue}{{x}^{\frac{1}{2}}}}\]

  8. Applied pow-flip0.2

    \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3} \cdot \color{blue}{{x}^{\left(-\frac{1}{2}\right)}}\]

  9. Simplified0.2

    \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3} \cdot {x}^{\color{blue}{\frac{-1}{2}}}\]
  10. Using strategy rm

  11. Applied associate-/r*0.2

    \[\leadsto \left(1 - \color{blue}{\frac{\frac{1}{x}}{9}}\right) - \frac{y}{3} \cdot {x}^{\frac{-1}{2}}\]

  12. Final simplification0.2

    \[\leadsto \left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3} \cdot {x}^{\frac{-1}{2}}\]

Reproduce

herbie shell --seed 2019306 
(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)))))