Average Error: 0.0 → 0.0
Time: 1.0s
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 r56492 = x;
        double r56493 = 2.30753;
        double r56494 = 0.27061;
        double r56495 = r56492 * r56494;
        double r56496 = r56493 + r56495;
        double r56497 = 1.0;
        double r56498 = 0.99229;
        double r56499 = 0.04481;
        double r56500 = r56492 * r56499;
        double r56501 = r56498 + r56500;
        double r56502 = r56501 * r56492;
        double r56503 = r56497 + r56502;
        double r56504 = r56496 / r56503;
        double r56505 = r56492 - r56504;
        return r56505;
}
↓
double f(double x) {
        double r56506 = x;
        double r56507 = 2.30753;
        double r56508 = 0.27061;
        double r56509 = r56506 * r56508;
        double r56510 = r56507 + r56509;
        double r56511 = 1.0;
        double r56512 = 0.99229;
        double r56513 = 0.04481;
        double r56514 = r56506 * r56513;
        double r56515 = r56512 + r56514;
        double r56516 = r56515 * r56506;
        double r56517 = r56511 + r56516;
        double r56518 = r56510 / r56517;
        double r56519 = r56506 - r56518;
        return r56519;
}

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 2020001 +o rules:numerics
(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)))))