Average Error: 0.0 → 0.0
Time: 12.8s
Precision: 64
\[\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\]
↓
\[\sqrt[3]{\left(\frac{2.307529999999999859028321225196123123169 + 0.2706100000000000171951342053944244980812 \cdot x}{1 + \left(0.992290000000000005364597654988756403327 + 0.04481000000000000260680366181986755691469 \cdot x\right) \cdot x} \cdot \frac{2.307529999999999859028321225196123123169 + 0.2706100000000000171951342053944244980812 \cdot x}{1 + \left(0.992290000000000005364597654988756403327 + 0.04481000000000000260680366181986755691469 \cdot x\right) \cdot x}\right) \cdot \frac{2.307529999999999859028321225196123123169 + 0.2706100000000000171951342053944244980812 \cdot x}{1 + \left(0.992290000000000005364597654988756403327 + 0.04481000000000000260680366181986755691469 \cdot x\right) \cdot x}} - x\]
\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x
↓
\sqrt[3]{\left(\frac{2.307529999999999859028321225196123123169 + 0.2706100000000000171951342053944244980812 \cdot x}{1 + \left(0.992290000000000005364597654988756403327 + 0.04481000000000000260680366181986755691469 \cdot x\right) \cdot x} \cdot \frac{2.307529999999999859028321225196123123169 + 0.2706100000000000171951342053944244980812 \cdot x}{1 + \left(0.992290000000000005364597654988756403327 + 0.04481000000000000260680366181986755691469 \cdot x\right) \cdot x}\right) \cdot \frac{2.307529999999999859028321225196123123169 + 0.2706100000000000171951342053944244980812 \cdot x}{1 + \left(0.992290000000000005364597654988756403327 + 0.04481000000000000260680366181986755691469 \cdot x\right) \cdot x}} - x
double f(double x) {
        double r4171021 = 2.30753;
        double r4171022 = x;
        double r4171023 = 0.27061;
        double r4171024 = r4171022 * r4171023;
        double r4171025 = r4171021 + r4171024;
        double r4171026 = 1.0;
        double r4171027 = 0.99229;
        double r4171028 = 0.04481;
        double r4171029 = r4171022 * r4171028;
        double r4171030 = r4171027 + r4171029;
        double r4171031 = r4171022 * r4171030;
        double r4171032 = r4171026 + r4171031;
        double r4171033 = r4171025 / r4171032;
        double r4171034 = r4171033 - r4171022;
        return r4171034;
}
↓
double f(double x) {
        double r4171035 = 2.30753;
        double r4171036 = 0.27061;
        double r4171037 = x;
        double r4171038 = r4171036 * r4171037;
        double r4171039 = r4171035 + r4171038;
        double r4171040 = 1.0;
        double r4171041 = 0.99229;
        double r4171042 = 0.04481;
        double r4171043 = r4171042 * r4171037;
        double r4171044 = r4171041 + r4171043;
        double r4171045 = r4171044 * r4171037;
        double r4171046 = r4171040 + r4171045;
        double r4171047 = r4171039 / r4171046;
        double r4171048 = r4171047 * r4171047;
        double r4171049 = r4171048 * r4171047;
        double r4171050 = cbrt(r4171049);
        double r4171051 = r4171050 - r4171037;
        return r4171051;
}

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

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019169 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, C"
  (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))