Average Error: 0.0 → 0.0
Time: 19.4s
Precision: 64
\[x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]
↓
\[x - \frac{\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x} \cdot \left(2.307529999999999859028321225196123123169 - x \cdot 0.2706100000000000171951342053944244980812\right)}{2.307529999999999859028321225196123123169 - x \cdot 0.2706100000000000171951342053944244980812}\]
x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}
↓
x - \frac{\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x} \cdot \left(2.307529999999999859028321225196123123169 - x \cdot 0.2706100000000000171951342053944244980812\right)}{2.307529999999999859028321225196123123169 - x \cdot 0.2706100000000000171951342053944244980812}
double f(double x) {
        double r78336 = x;
        double r78337 = 2.30753;
        double r78338 = 0.27061;
        double r78339 = r78336 * r78338;
        double r78340 = r78337 + r78339;
        double r78341 = 1.0;
        double r78342 = 0.99229;
        double r78343 = 0.04481;
        double r78344 = r78336 * r78343;
        double r78345 = r78342 + r78344;
        double r78346 = r78345 * r78336;
        double r78347 = r78341 + r78346;
        double r78348 = r78340 / r78347;
        double r78349 = r78336 - r78348;
        return r78349;
}
↓
double f(double x) {
        double r78350 = x;
        double r78351 = 2.30753;
        double r78352 = 0.27061;
        double r78353 = r78350 * r78352;
        double r78354 = r78351 + r78353;
        double r78355 = 1.0;
        double r78356 = 0.99229;
        double r78357 = 0.04481;
        double r78358 = r78350 * r78357;
        double r78359 = r78356 + r78358;
        double r78360 = r78359 * r78350;
        double r78361 = r78355 + r78360;
        double r78362 = r78354 / r78361;
        double r78363 = r78351 - r78353;
        double r78364 = r78362 * r78363;
        double r78365 = r78364 / r78363;
        double r78366 = r78350 - r78365;
        return r78366;
}

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 clear-num0.0

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

  5. Applied flip-+16.1

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

  6. Applied associate-/r/16.1

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

  7. Applied associate-/r*16.1

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019323 
(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)))))