Average Error: 0.2 → 0.3
Time: 20.9s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\sqrt{x}} \cdot \frac{1}{3}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{\sqrt{x}} \cdot \frac{1}{3}
double f(double x, double y) {
        double r305774 = 1.0;
        double r305775 = x;
        double r305776 = 9.0;
        double r305777 = r305775 * r305776;
        double r305778 = r305774 / r305777;
        double r305779 = r305774 - r305778;
        double r305780 = y;
        double r305781 = 3.0;
        double r305782 = sqrt(r305775);
        double r305783 = r305781 * r305782;
        double r305784 = r305780 / r305783;
        double r305785 = r305779 - r305784;
        return r305785;
}
↓
double f(double x, double y) {
        double r305786 = 1.0;
        double r305787 = x;
        double r305788 = 9.0;
        double r305789 = r305787 * r305788;
        double r305790 = r305786 / r305789;
        double r305791 = r305786 - r305790;
        double r305792 = y;
        double r305793 = sqrt(r305787);
        double r305794 = r305792 / r305793;
        double r305795 = 1.0;
        double r305796 = 3.0;
        double r305797 = r305795 / r305796;
        double r305798 = r305794 * r305797;
        double r305799 = r305791 - r305798;
        return r305799;
}

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. Simplified0.2

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

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

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

  5. Applied times-frac0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019195 
(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)))))