Average Error: 0.0 → 0.0
Time: 17.5s
Precision: 64
\[x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]
↓
\[x - \left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \sqrt[3]{\frac{1}{{\left(1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x\right)}^{3}}}\]
x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}
↓
x - \left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \sqrt[3]{\frac{1}{{\left(1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x\right)}^{3}}}
double f(double x) {
        double r109383 = x;
        double r109384 = 2.30753;
        double r109385 = 0.27061;
        double r109386 = r109383 * r109385;
        double r109387 = r109384 + r109386;
        double r109388 = 1.0;
        double r109389 = 0.99229;
        double r109390 = 0.04481;
        double r109391 = r109383 * r109390;
        double r109392 = r109389 + r109391;
        double r109393 = r109392 * r109383;
        double r109394 = r109388 + r109393;
        double r109395 = r109387 / r109394;
        double r109396 = r109383 - r109395;
        return r109396;
}
↓
double f(double x) {
        double r109397 = x;
        double r109398 = 2.30753;
        double r109399 = 0.27061;
        double r109400 = r109397 * r109399;
        double r109401 = r109398 + r109400;
        double r109402 = 1.0;
        double r109403 = 1.0;
        double r109404 = 0.99229;
        double r109405 = 0.04481;
        double r109406 = r109397 * r109405;
        double r109407 = r109404 + r109406;
        double r109408 = r109407 * r109397;
        double r109409 = r109403 + r109408;
        double r109410 = 3.0;
        double r109411 = pow(r109409, r109410);
        double r109412 = r109402 / r109411;
        double r109413 = cbrt(r109412);
        double r109414 = r109401 * r109413;
        double r109415 = r109397 - r109414;
        return r109415;
}

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 div-inv0.0

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

  5. Applied add-cbrt-cube0.0

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

  6. Applied add-cbrt-cube0.0

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

  7. Applied cbrt-undiv0.0

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019303 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, D"
  :precision binary64
  (- x (/ (+ 2.30753 (* x 0.27061000000000002)) (+ 1 (* (+ 0.992290000000000005 (* x 0.044810000000000003)) x)))))