Average Error: 0.0 → 0.0
Time: 12.8s
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 r70375 = x;
        double r70376 = 2.30753;
        double r70377 = 0.27061;
        double r70378 = r70375 * r70377;
        double r70379 = r70376 + r70378;
        double r70380 = 1.0;
        double r70381 = 0.99229;
        double r70382 = 0.04481;
        double r70383 = r70375 * r70382;
        double r70384 = r70381 + r70383;
        double r70385 = r70384 * r70375;
        double r70386 = r70380 + r70385;
        double r70387 = r70379 / r70386;
        double r70388 = r70375 - r70387;
        return r70388;
}
↓
double f(double x) {
        double r70389 = x;
        double r70390 = 2.30753;
        double r70391 = 0.27061;
        double r70392 = r70389 * r70391;
        double r70393 = r70390 + r70392;
        double r70394 = 1.0;
        double r70395 = 0.99229;
        double r70396 = 0.04481;
        double r70397 = r70389 * r70396;
        double r70398 = r70395 + r70397;
        double r70399 = r70398 * r70389;
        double r70400 = r70394 + r70399;
        double r70401 = r70393 / r70400;
        double r70402 = r70389 - r70401;
        return r70402;
}

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 2019325 +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)))))