Average Error: 0.0 → 0.0
Time: 3.6s
Precision: 64
\[\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
↓
\[\frac{1}{\sqrt[3]{{\left(\frac{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}{2.30753 + x \cdot 0.27061000000000002}\right)}^{3}}} - x\]
\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x
↓
\frac{1}{\sqrt[3]{{\left(\frac{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}{2.30753 + x \cdot 0.27061000000000002}\right)}^{3}}} - x
double f(double x) {
        double r83117 = 2.30753;
        double r83118 = x;
        double r83119 = 0.27061;
        double r83120 = r83118 * r83119;
        double r83121 = r83117 + r83120;
        double r83122 = 1.0;
        double r83123 = 0.99229;
        double r83124 = 0.04481;
        double r83125 = r83118 * r83124;
        double r83126 = r83123 + r83125;
        double r83127 = r83118 * r83126;
        double r83128 = r83122 + r83127;
        double r83129 = r83121 / r83128;
        double r83130 = r83129 - r83118;
        return r83130;
}
↓
double f(double x) {
        double r83131 = 1.0;
        double r83132 = 1.0;
        double r83133 = x;
        double r83134 = 0.99229;
        double r83135 = 0.04481;
        double r83136 = r83133 * r83135;
        double r83137 = r83134 + r83136;
        double r83138 = r83133 * r83137;
        double r83139 = r83132 + r83138;
        double r83140 = 2.30753;
        double r83141 = 0.27061;
        double r83142 = r83133 * r83141;
        double r83143 = r83140 + r83142;
        double r83144 = r83139 / r83143;
        double r83145 = 3.0;
        double r83146 = pow(r83144, r83145);
        double r83147 = cbrt(r83146);
        double r83148 = r83131 / r83147;
        double r83149 = r83148 - r83133;
        return r83149;
}

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

    \[\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
  2. Using strategy rm

  3. Applied clear-num0.0

    \[\leadsto \color{blue}{\frac{1}{\frac{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}{2.30753 + x \cdot 0.27061000000000002}}} - x\]
  4. Using strategy rm

  5. Applied add-cbrt-cube21.8

    \[\leadsto \frac{1}{\frac{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}{\color{blue}{\sqrt[3]{\left(\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)}}}} - x\]

  6. Applied add-cbrt-cube21.8

    \[\leadsto \frac{1}{\frac{\color{blue}{\sqrt[3]{\left(\left(1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)\right) \cdot \left(1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)\right)\right) \cdot \left(1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)\right)}}}{\sqrt[3]{\left(\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)}}} - x\]

  7. Applied cbrt-undiv21.8

    \[\leadsto \frac{1}{\color{blue}{\sqrt[3]{\frac{\left(\left(1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)\right) \cdot \left(1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)\right)\right) \cdot \left(1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)\right)}{\left(\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)}}}} - x\]

  8. Simplified0.0

    \[\leadsto \frac{1}{\sqrt[3]{\color{blue}{{\left(\frac{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}{2.30753 + x \cdot 0.27061000000000002}\right)}^{3}}}} - x\]

  9. Final simplification0.0

    \[\leadsto \frac{1}{\sqrt[3]{{\left(\frac{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}{2.30753 + x \cdot 0.27061000000000002}\right)}^{3}}} - x\]

Reproduce

herbie shell --seed 2020060 
(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))