Average Error: 0.2 → 0.2
Time: 21.8s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{1}{\frac{\sqrt{x}}{\frac{y}{3}}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{1}{\frac{\sqrt{x}}{\frac{y}{3}}}
double f(double x, double y) {
        double r308209 = 1.0;
        double r308210 = x;
        double r308211 = 9.0;
        double r308212 = r308210 * r308211;
        double r308213 = r308209 / r308212;
        double r308214 = r308209 - r308213;
        double r308215 = y;
        double r308216 = 3.0;
        double r308217 = sqrt(r308210);
        double r308218 = r308216 * r308217;
        double r308219 = r308215 / r308218;
        double r308220 = r308214 - r308219;
        return r308220;
}
↓
double f(double x, double y) {
        double r308221 = 1.0;
        double r308222 = x;
        double r308223 = r308221 / r308222;
        double r308224 = 9.0;
        double r308225 = r308223 / r308224;
        double r308226 = r308221 - r308225;
        double r308227 = 1.0;
        double r308228 = sqrt(r308222);
        double r308229 = y;
        double r308230 = 3.0;
        double r308231 = r308229 / r308230;
        double r308232 = r308228 / r308231;
        double r308233 = r308227 / r308232;
        double r308234 = r308226 - r308233;
        return r308234;
}

Error

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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 *-un-lft-identity0.2

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

  6. Applied *-un-lft-identity0.2

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

  7. Applied distribute-lft-out--0.2

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

  8. Simplified0.2

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

  10. Applied *-un-lft-identity0.2

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

  11. Applied *-un-lft-identity0.2

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

  12. Applied times-frac0.2

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

  13. Applied associate-/l*0.2

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

  14. Final simplification0.2

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(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)))))