Average Error: 0.2 → 0.2
Time: 15.6s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{\frac{y}{3}}{\sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{\frac{y}{3}}{\sqrt{x}}
double f(double x, double y) {
        double r280038 = 1.0;
        double r280039 = x;
        double r280040 = 9.0;
        double r280041 = r280039 * r280040;
        double r280042 = r280038 / r280041;
        double r280043 = r280038 - r280042;
        double r280044 = y;
        double r280045 = 3.0;
        double r280046 = sqrt(r280039);
        double r280047 = r280045 * r280046;
        double r280048 = r280044 / r280047;
        double r280049 = r280043 - r280048;
        return r280049;
}
↓
double f(double x, double y) {
        double r280050 = 1.0;
        double r280051 = x;
        double r280052 = r280050 / r280051;
        double r280053 = 9.0;
        double r280054 = r280052 / r280053;
        double r280055 = r280050 - r280054;
        double r280056 = y;
        double r280057 = 3.0;
        double r280058 = r280056 / r280057;
        double r280059 = sqrt(r280051);
        double r280060 = r280058 / r280059;
        double r280061 = r280055 - r280060;
        return r280061;
}

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

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

  5. Applied associate-/r*0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019194 
(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)))))