Average Error: 0.2 → 0.3
Time: 7.3s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{1}{3} \cdot \frac{y}{\sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{1}{3} \cdot \frac{y}{\sqrt{x}}
double f(double x, double y) {
        double r264644 = 1.0;
        double r264645 = x;
        double r264646 = 9.0;
        double r264647 = r264645 * r264646;
        double r264648 = r264644 / r264647;
        double r264649 = r264644 - r264648;
        double r264650 = y;
        double r264651 = 3.0;
        double r264652 = sqrt(r264645);
        double r264653 = r264651 * r264652;
        double r264654 = r264650 / r264653;
        double r264655 = r264649 - r264654;
        return r264655;
}
↓
double f(double x, double y) {
        double r264656 = 1.0;
        double r264657 = x;
        double r264658 = r264656 / r264657;
        double r264659 = 9.0;
        double r264660 = r264658 / r264659;
        double r264661 = r264656 - r264660;
        double r264662 = 1.0;
        double r264663 = 3.0;
        double r264664 = r264662 / r264663;
        double r264665 = y;
        double r264666 = sqrt(r264657);
        double r264667 = r264665 / r264666;
        double r264668 = r264664 * r264667;
        double r264669 = r264661 - r264668;
        return r264669;
}

Error

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Bits error versus y

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Results

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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

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

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

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

  6. Applied times-frac0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2020046 
(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)))))