Average Error: 0.0 → 0.0
Time: 2.9s
Precision: 64
\[\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\]
↓
\[\sqrt[3]{{\left(\sqrt[3]{\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} \cdot \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)}} \cdot \sqrt[3]{\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)}}\right)}^{3}} - x\]
\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x
↓
\sqrt[3]{{\left(\sqrt[3]{\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} \cdot \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)}} \cdot \sqrt[3]{\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)}}\right)}^{3}} - x
double f(double x) {
        double r77360 = 2.30753;
        double r77361 = x;
        double r77362 = 0.27061;
        double r77363 = r77361 * r77362;
        double r77364 = r77360 + r77363;
        double r77365 = 1.0;
        double r77366 = 0.99229;
        double r77367 = 0.04481;
        double r77368 = r77361 * r77367;
        double r77369 = r77366 + r77368;
        double r77370 = r77361 * r77369;
        double r77371 = r77365 + r77370;
        double r77372 = r77364 / r77371;
        double r77373 = r77372 - r77361;
        return r77373;
}
↓
double f(double x) {
        double r77374 = 2.30753;
        double r77375 = x;
        double r77376 = 0.27061;
        double r77377 = r77375 * r77376;
        double r77378 = r77374 + r77377;
        double r77379 = 1.0;
        double r77380 = 0.99229;
        double r77381 = 0.04481;
        double r77382 = r77375 * r77381;
        double r77383 = r77380 + r77382;
        double r77384 = r77375 * r77383;
        double r77385 = r77379 + r77384;
        double r77386 = r77378 / r77385;
        double r77387 = r77386 * r77386;
        double r77388 = cbrt(r77387);
        double r77389 = cbrt(r77386);
        double r77390 = r77388 * r77389;
        double r77391 = 3.0;
        double r77392 = pow(r77390, r77391);
        double r77393 = cbrt(r77392);
        double r77394 = r77393 - r77375;
        return r77394;
}

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

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

  3. Applied add-cbrt-cube0.0

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

  4. Applied add-cbrt-cube21.1

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

  5. Applied cbrt-undiv21.1

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

  6. Simplified0.0

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

  8. Applied add-cube-cbrt1.0

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

  9. Simplified0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2019346 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, C"
  :precision binary64
  (- (/ (+ 2.30753 (* x 0.27061)) (+ 1 (* x (+ 0.99229 (* x 0.04481))))) x))