Average Error: 0.2 → 0.3
Time: 21.1s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{\frac{1}{x}}{\sqrt[3]{9} \cdot \sqrt[3]{9}}}{\sqrt[3]{9}}\right) - \frac{\frac{y}{3}}{\sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{\frac{\frac{1}{x}}{\sqrt[3]{9} \cdot \sqrt[3]{9}}}{\sqrt[3]{9}}\right) - \frac{\frac{y}{3}}{\sqrt{x}}
double f(double x, double y) {
        double r18603210 = 1.0;
        double r18603211 = x;
        double r18603212 = 9.0;
        double r18603213 = r18603211 * r18603212;
        double r18603214 = r18603210 / r18603213;
        double r18603215 = r18603210 - r18603214;
        double r18603216 = y;
        double r18603217 = 3.0;
        double r18603218 = sqrt(r18603211);
        double r18603219 = r18603217 * r18603218;
        double r18603220 = r18603216 / r18603219;
        double r18603221 = r18603215 - r18603220;
        return r18603221;
}
↓
double f(double x, double y) {
        double r18603222 = 1.0;
        double r18603223 = x;
        double r18603224 = r18603222 / r18603223;
        double r18603225 = 9.0;
        double r18603226 = cbrt(r18603225);
        double r18603227 = r18603226 * r18603226;
        double r18603228 = r18603224 / r18603227;
        double r18603229 = r18603228 / r18603226;
        double r18603230 = r18603222 - r18603229;
        double r18603231 = y;
        double r18603232 = 3.0;
        double r18603233 = r18603231 / r18603232;
        double r18603234 = sqrt(r18603223);
        double r18603235 = r18603233 / r18603234;
        double r18603236 = r18603230 - r18603235;
        return r18603236;
}

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
Herbie0.3
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]

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. Using strategy rm

  7. Applied add-cube-cbrt0.2

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

  8. Applied associate-/r*0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019170 
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, D"

  :herbie-target
  (- (- 1.0 (/ (/ 1.0 x) 9.0)) (/ y (* 3.0 (sqrt x))))

  (- (- 1.0 (/ 1.0 (* x 9.0))) (/ y (* 3.0 (sqrt x)))))