Average Error: 0.2 → 0.2
Time: 17.4s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3 \cdot \sqrt{x}}
double f(double x, double y) {
        double r233801 = 1.0;
        double r233802 = x;
        double r233803 = 9.0;
        double r233804 = r233802 * r233803;
        double r233805 = r233801 / r233804;
        double r233806 = r233801 - r233805;
        double r233807 = y;
        double r233808 = 3.0;
        double r233809 = sqrt(r233802);
        double r233810 = r233808 * r233809;
        double r233811 = r233807 / r233810;
        double r233812 = r233806 - r233811;
        return r233812;
}
↓
double f(double x, double y) {
        double r233813 = 1.0;
        double r233814 = x;
        double r233815 = r233813 / r233814;
        double r233816 = 9.0;
        double r233817 = r233815 / r233816;
        double r233818 = r233813 - r233817;
        double r233819 = y;
        double r233820 = 3.0;
        double r233821 = sqrt(r233814);
        double r233822 = r233820 * r233821;
        double r233823 = r233819 / r233822;
        double r233824 = r233818 - r233823;
        return r233824;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2019304 
(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)))))