Average Error: 0.0 → 0.0
Time: 17.1s
Precision: 64
\[\frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x\]
↓
\[\frac{\frac{0.27061 \cdot x + 2.30753}{\sqrt[3]{x \cdot \left(x \cdot 0.04481 + 0.99229\right) + 1.0} \cdot \sqrt[3]{x \cdot \left(x \cdot 0.04481 + 0.99229\right) + 1.0}}}{\sqrt[3]{x \cdot \left(x \cdot 0.04481 + 0.99229\right) + 1.0}} - x\]
\frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x
↓
\frac{\frac{0.27061 \cdot x + 2.30753}{\sqrt[3]{x \cdot \left(x \cdot 0.04481 + 0.99229\right) + 1.0} \cdot \sqrt[3]{x \cdot \left(x \cdot 0.04481 + 0.99229\right) + 1.0}}}{\sqrt[3]{x \cdot \left(x \cdot 0.04481 + 0.99229\right) + 1.0}} - x
double f(double x) {
        double r5288141 = 2.30753;
        double r5288142 = x;
        double r5288143 = 0.27061;
        double r5288144 = r5288142 * r5288143;
        double r5288145 = r5288141 + r5288144;
        double r5288146 = 1.0;
        double r5288147 = 0.99229;
        double r5288148 = 0.04481;
        double r5288149 = r5288142 * r5288148;
        double r5288150 = r5288147 + r5288149;
        double r5288151 = r5288142 * r5288150;
        double r5288152 = r5288146 + r5288151;
        double r5288153 = r5288145 / r5288152;
        double r5288154 = r5288153 - r5288142;
        return r5288154;
}
↓
double f(double x) {
        double r5288155 = 0.27061;
        double r5288156 = x;
        double r5288157 = r5288155 * r5288156;
        double r5288158 = 2.30753;
        double r5288159 = r5288157 + r5288158;
        double r5288160 = 0.04481;
        double r5288161 = r5288156 * r5288160;
        double r5288162 = 0.99229;
        double r5288163 = r5288161 + r5288162;
        double r5288164 = r5288156 * r5288163;
        double r5288165 = 1.0;
        double r5288166 = r5288164 + r5288165;
        double r5288167 = cbrt(r5288166);
        double r5288168 = r5288167 * r5288167;
        double r5288169 = r5288159 / r5288168;
        double r5288170 = r5288169 / r5288167;
        double r5288171 = r5288170 - r5288156;
        return r5288171;
}

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

    \[\frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.0

    \[\leadsto \frac{2.30753 + x \cdot 0.27061}{\color{blue}{\left(\sqrt[3]{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} \cdot \sqrt[3]{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}\right) \cdot \sqrt[3]{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}}} - x\]

  4. Applied associate-/r*0.0

    \[\leadsto \color{blue}{\frac{\frac{2.30753 + x \cdot 0.27061}{\sqrt[3]{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} \cdot \sqrt[3]{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}}}{\sqrt[3]{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}}} - x\]

  5. Final simplification0.0

    \[\leadsto \frac{\frac{0.27061 \cdot x + 2.30753}{\sqrt[3]{x \cdot \left(x \cdot 0.04481 + 0.99229\right) + 1.0} \cdot \sqrt[3]{x \cdot \left(x \cdot 0.04481 + 0.99229\right) + 1.0}}}{\sqrt[3]{x \cdot \left(x \cdot 0.04481 + 0.99229\right) + 1.0}} - x\]

Reproduce

herbie shell --seed 2019164 
(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))