Average Error: 0.0 → 0.0
Time: 3.9s
Precision: 64
\[x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]
↓
\[x - \left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \frac{1}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]
x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}
↓
x - \left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \frac{1}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}
double f(double x) {
        double r105559 = x;
        double r105560 = 2.30753;
        double r105561 = 0.27061;
        double r105562 = r105559 * r105561;
        double r105563 = r105560 + r105562;
        double r105564 = 1.0;
        double r105565 = 0.99229;
        double r105566 = 0.04481;
        double r105567 = r105559 * r105566;
        double r105568 = r105565 + r105567;
        double r105569 = r105568 * r105559;
        double r105570 = r105564 + r105569;
        double r105571 = r105563 / r105570;
        double r105572 = r105559 - r105571;
        return r105572;
}
↓
double f(double x) {
        double r105573 = x;
        double r105574 = 2.30753;
        double r105575 = 0.27061;
        double r105576 = r105573 * r105575;
        double r105577 = r105574 + r105576;
        double r105578 = 1.0;
        double r105579 = 1.0;
        double r105580 = 0.99229;
        double r105581 = 0.04481;
        double r105582 = r105573 * r105581;
        double r105583 = r105580 + r105582;
        double r105584 = r105583 * r105573;
        double r105585 = r105579 + r105584;
        double r105586 = r105578 / r105585;
        double r105587 = r105577 * r105586;
        double r105588 = r105573 - r105587;
        return r105588;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]
  2. Using strategy rm

  3. Applied div-inv0.0

    \[\leadsto x - \color{blue}{\left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \frac{1}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}}\]

  4. Final simplification0.0

    \[\leadsto x - \left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \frac{1}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]

Reproduce

herbie shell --seed 2019347 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, D"
  :precision binary64
  (- x (/ (+ 2.30753 (* x 0.27061)) (+ 1 (* (+ 0.99229 (* x 0.04481)) x)))))