Average Error: 0.0 → 0.0
Time: 9.5s
Precision: 64
\[\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\]
↓
\[\frac{0.2706100000000000171951342053944244980812 \cdot x + 2.307529999999999859028321225196123123169}{\left(\left(0.992290000000000005364597654988756403327 + 0.04481000000000000260680366181986755691469 \cdot x\right) \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) + 1} - x\]
\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x
↓
\frac{0.2706100000000000171951342053944244980812 \cdot x + 2.307529999999999859028321225196123123169}{\left(\left(0.992290000000000005364597654988756403327 + 0.04481000000000000260680366181986755691469 \cdot x\right) \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) + 1} - x
double f(double x) {
        double r61582 = 2.30753;
        double r61583 = x;
        double r61584 = 0.27061;
        double r61585 = r61583 * r61584;
        double r61586 = r61582 + r61585;
        double r61587 = 1.0;
        double r61588 = 0.99229;
        double r61589 = 0.04481;
        double r61590 = r61583 * r61589;
        double r61591 = r61588 + r61590;
        double r61592 = r61583 * r61591;
        double r61593 = r61587 + r61592;
        double r61594 = r61586 / r61593;
        double r61595 = r61594 - r61583;
        return r61595;
}
↓
double f(double x) {
        double r61596 = 0.27061;
        double r61597 = x;
        double r61598 = r61596 * r61597;
        double r61599 = 2.30753;
        double r61600 = r61598 + r61599;
        double r61601 = 0.99229;
        double r61602 = 0.04481;
        double r61603 = r61602 * r61597;
        double r61604 = r61601 + r61603;
        double r61605 = cbrt(r61597);
        double r61606 = r61604 * r61605;
        double r61607 = r61605 * r61605;
        double r61608 = r61606 * r61607;
        double r61609 = 1.0;
        double r61610 = r61608 + r61609;
        double r61611 = r61600 / r61610;
        double r61612 = r61611 - r61597;
        return r61612;
}

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-cube-cbrt0.0

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

  4. Applied associate-*l*0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019194 
(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))