Average Error: 0.2 → 0.2
Time: 4.6s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
\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 r384514 = 1.0;
        double r384515 = x;
        double r384516 = 9.0;
        double r384517 = r384515 * r384516;
        double r384518 = r384514 / r384517;
        double r384519 = r384514 - r384518;
        double r384520 = y;
        double r384521 = 3.0;
        double r384522 = sqrt(r384515);
        double r384523 = r384521 * r384522;
        double r384524 = r384520 / r384523;
        double r384525 = r384519 - r384524;
        return r384525;
}
↓
double f(double x, double y) {
        double r384526 = 1.0;
        double r384527 = x;
        double r384528 = r384526 / r384527;
        double r384529 = 9.0;
        double r384530 = r384528 / r384529;
        double r384531 = r384526 - r384530;
        double r384532 = y;
        double r384533 = 3.0;
        double r384534 = sqrt(r384527);
        double r384535 = r384533 * r384534;
        double r384536 = r384532 / r384535;
        double r384537 = r384531 - r384536;
        return r384537;
}

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

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2020021 +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)))))