Average Error: 0.0 → 0.0
Time: 3.5s
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 r71120 = 2.30753;
        double r71121 = x;
        double r71122 = 0.27061;
        double r71123 = r71121 * r71122;
        double r71124 = r71120 + r71123;
        double r71125 = 1.0;
        double r71126 = 0.99229;
        double r71127 = 0.04481;
        double r71128 = r71121 * r71127;
        double r71129 = r71126 + r71128;
        double r71130 = r71121 * r71129;
        double r71131 = r71125 + r71130;
        double r71132 = r71124 / r71131;
        double r71133 = r71132 - r71121;
        return r71133;
}
↓
double f(double x) {
        double r71134 = 1.0;
        double r71135 = 1.0;
        double r71136 = x;
        double r71137 = 0.99229;
        double r71138 = 0.04481;
        double r71139 = r71136 * r71138;
        double r71140 = r71137 + r71139;
        double r71141 = r71136 * r71140;
        double r71142 = r71135 + r71141;
        double r71143 = 2.30753;
        double r71144 = 0.27061;
        double r71145 = r71136 * r71144;
        double r71146 = r71143 + r71145;
        double r71147 = r71142 / r71146;
        double r71148 = 3.0;
        double r71149 = pow(r71147, r71148);
        double r71150 = cbrt(r71149);
        double r71151 = r71134 / r71150;
        double r71152 = r71151 - r71136;
        return r71152;
}

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))