Average Error: 0.0 → 0.0
Time: 2.6s
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 r116371 = x;
        double r116372 = 2.30753;
        double r116373 = 0.27061;
        double r116374 = r116371 * r116373;
        double r116375 = r116372 + r116374;
        double r116376 = 1.0;
        double r116377 = 0.99229;
        double r116378 = 0.04481;
        double r116379 = r116371 * r116378;
        double r116380 = r116377 + r116379;
        double r116381 = r116380 * r116371;
        double r116382 = r116376 + r116381;
        double r116383 = r116375 / r116382;
        double r116384 = r116371 - r116383;
        return r116384;
}
↓
double f(double x) {
        double r116385 = x;
        double r116386 = 2.30753;
        double r116387 = 0.27061;
        double r116388 = r116385 * r116387;
        double r116389 = r116386 + r116388;
        double r116390 = 1.0;
        double r116391 = 0.99229;
        double r116392 = 0.04481;
        double r116393 = r116385 * r116392;
        double r116394 = r116391 + r116393;
        double r116395 = r116394 * r116385;
        double r116396 = r116390 + r116395;
        double r116397 = r116389 / r116396;
        double r116398 = r116385 - r116397;
        return r116398;
}

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 2019362 +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)))))