Average Error: 0.0 → 0.0
Time: 19.4s
Precision: 64
\[x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]
↓
\[x - \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x} \cdot \left(2.307529999999999859028321225196123123169 - x \cdot 0.2706100000000000171951342053944244980812\right)\right) \cdot \frac{1}{2.307529999999999859028321225196123123169 - x \cdot 0.2706100000000000171951342053944244980812}\]
x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}
↓
x - \left(\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)\right) \cdot \frac{1}{2.307529999999999859028321225196123123169 - x \cdot 0.2706100000000000171951342053944244980812}
double f(double x) {
        double r90356 = x;
        double r90357 = 2.30753;
        double r90358 = 0.27061;
        double r90359 = r90356 * r90358;
        double r90360 = r90357 + r90359;
        double r90361 = 1.0;
        double r90362 = 0.99229;
        double r90363 = 0.04481;
        double r90364 = r90356 * r90363;
        double r90365 = r90362 + r90364;
        double r90366 = r90365 * r90356;
        double r90367 = r90361 + r90366;
        double r90368 = r90360 / r90367;
        double r90369 = r90356 - r90368;
        return r90369;
}
↓
double f(double x) {
        double r90370 = x;
        double r90371 = 2.30753;
        double r90372 = 0.27061;
        double r90373 = r90370 * r90372;
        double r90374 = r90371 + r90373;
        double r90375 = 1.0;
        double r90376 = 0.99229;
        double r90377 = 0.04481;
        double r90378 = r90370 * r90377;
        double r90379 = r90376 + r90378;
        double r90380 = r90379 * r90370;
        double r90381 = r90375 + r90380;
        double r90382 = r90374 / r90381;
        double r90383 = r90371 - r90373;
        double r90384 = r90382 * r90383;
        double r90385 = 1.0;
        double r90386 = r90385 / r90383;
        double r90387 = r90384 * r90386;
        double r90388 = r90370 - r90387;
        return r90388;
}

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 add-cube-cbrt16.1

    \[\leadsto x - \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\frac{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}{2.307529999999999859028321225196123123169 \cdot 2.307529999999999859028321225196123123169 - \left(x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \left(x \cdot 0.2706100000000000171951342053944244980812\right)} \cdot \left(2.307529999999999859028321225196123123169 - x \cdot 0.2706100000000000171951342053944244980812\right)}\]

  8. Applied times-frac16.1

    \[\leadsto x - \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}{2.307529999999999859028321225196123123169 \cdot 2.307529999999999859028321225196123123169 - \left(x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \left(x \cdot 0.2706100000000000171951342053944244980812\right)}} \cdot \frac{\sqrt[3]{1}}{2.307529999999999859028321225196123123169 - x \cdot 0.2706100000000000171951342053944244980812}}\]

  9. Simplified0.0

    \[\leadsto x - \color{blue}{\left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x} \cdot \left(2.307529999999999859028321225196123123169 - x \cdot 0.2706100000000000171951342053944244980812\right)\right)} \cdot \frac{\sqrt[3]{1}}{2.307529999999999859028321225196123123169 - x \cdot 0.2706100000000000171951342053944244980812}\]

  10. Simplified0.0

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

  11. Final simplification0.0

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

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)))))