Average Error: 0.2 → 0.2
Time: 13.2s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{\frac{y}{3}}{\sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{\frac{y}{3}}{\sqrt{x}}
double f(double x, double y) {
        double r562734 = 1.0;
        double r562735 = x;
        double r562736 = 9.0;
        double r562737 = r562735 * r562736;
        double r562738 = r562734 / r562737;
        double r562739 = r562734 - r562738;
        double r562740 = y;
        double r562741 = 3.0;
        double r562742 = sqrt(r562735);
        double r562743 = r562741 * r562742;
        double r562744 = r562740 / r562743;
        double r562745 = r562739 - r562744;
        return r562745;
}
↓
double f(double x, double y) {
        double r562746 = 1.0;
        double r562747 = x;
        double r562748 = 9.0;
        double r562749 = r562747 * r562748;
        double r562750 = r562746 / r562749;
        double r562751 = r562746 - r562750;
        double r562752 = y;
        double r562753 = 3.0;
        double r562754 = r562752 / r562753;
        double r562755 = sqrt(r562747);
        double r562756 = r562754 / r562755;
        double r562757 = r562751 - r562756;
        return r562757;
}

Error

Bits error versus x

Bits error versus y

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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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020100 +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)))))