Average Error: 0.0 → 0.0
Time: 2.6s
Precision: 64
\[\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\]
↓
\[\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(x \cdot \left(\sqrt[3]{0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469} \cdot \sqrt[3]{0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469}\right)\right) \cdot \sqrt[3]{0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469}} - x\]
\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x
↓
\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(x \cdot \left(\sqrt[3]{0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469} \cdot \sqrt[3]{0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469}\right)\right) \cdot \sqrt[3]{0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469}} - x
double f(double x) {
        double r83185 = 2.30753;
        double r83186 = x;
        double r83187 = 0.27061;
        double r83188 = r83186 * r83187;
        double r83189 = r83185 + r83188;
        double r83190 = 1.0;
        double r83191 = 0.99229;
        double r83192 = 0.04481;
        double r83193 = r83186 * r83192;
        double r83194 = r83191 + r83193;
        double r83195 = r83186 * r83194;
        double r83196 = r83190 + r83195;
        double r83197 = r83189 / r83196;
        double r83198 = r83197 - r83186;
        return r83198;
}
↓
double f(double x) {
        double r83199 = 2.30753;
        double r83200 = x;
        double r83201 = 0.27061;
        double r83202 = r83200 * r83201;
        double r83203 = r83199 + r83202;
        double r83204 = 1.0;
        double r83205 = 0.99229;
        double r83206 = 0.04481;
        double r83207 = r83200 * r83206;
        double r83208 = r83205 + r83207;
        double r83209 = cbrt(r83208);
        double r83210 = r83209 * r83209;
        double r83211 = r83200 * r83210;
        double r83212 = r83211 * r83209;
        double r83213 = r83204 + r83212;
        double r83214 = r83203 / r83213;
        double r83215 = r83214 - r83200;
        return r83215;
}

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

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

  4. Applied associate-*r*0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019352 +o rules:numerics
(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))