Average Error: 0.0 → 0.0
Time: 1.1s
Precision: 64
\[x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]
↓
\[x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]
x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{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}
double f(double x) {
        double r86559 = x;
        double r86560 = 2.30753;
        double r86561 = 0.27061;
        double r86562 = r86559 * r86561;
        double r86563 = r86560 + r86562;
        double r86564 = 1.0;
        double r86565 = 0.99229;
        double r86566 = 0.04481;
        double r86567 = r86559 * r86566;
        double r86568 = r86565 + r86567;
        double r86569 = r86568 * r86559;
        double r86570 = r86564 + r86569;
        double r86571 = r86563 / r86570;
        double r86572 = r86559 - r86571;
        return r86572;
}
↓
double f(double x) {
        double r86573 = x;
        double r86574 = 2.30753;
        double r86575 = 0.27061;
        double r86576 = r86573 * r86575;
        double r86577 = r86574 + r86576;
        double r86578 = 1.0;
        double r86579 = 0.99229;
        double r86580 = 0.04481;
        double r86581 = r86573 * r86580;
        double r86582 = r86579 + r86581;
        double r86583 = r86582 * r86573;
        double r86584 = r86578 + r86583;
        double r86585 = r86577 / r86584;
        double r86586 = r86573 - r86585;
        return r86586;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019353 
(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)))))