Average Error: 0.0 → 0.0
Time: 14.7s
Precision: 64
\[\frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x\]
↓
\[\frac{1}{\frac{\left(0.99229 + 0.04481 \cdot x\right) \cdot x + 1.0}{x \cdot 0.27061 + 2.30753}} - x\]
\frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x
↓
\frac{1}{\frac{\left(0.99229 + 0.04481 \cdot x\right) \cdot x + 1.0}{x \cdot 0.27061 + 2.30753}} - x
double f(double x) {
        double r4222137 = 2.30753;
        double r4222138 = x;
        double r4222139 = 0.27061;
        double r4222140 = r4222138 * r4222139;
        double r4222141 = r4222137 + r4222140;
        double r4222142 = 1.0;
        double r4222143 = 0.99229;
        double r4222144 = 0.04481;
        double r4222145 = r4222138 * r4222144;
        double r4222146 = r4222143 + r4222145;
        double r4222147 = r4222138 * r4222146;
        double r4222148 = r4222142 + r4222147;
        double r4222149 = r4222141 / r4222148;
        double r4222150 = r4222149 - r4222138;
        return r4222150;
}
↓
double f(double x) {
        double r4222151 = 1.0;
        double r4222152 = 0.99229;
        double r4222153 = 0.04481;
        double r4222154 = x;
        double r4222155 = r4222153 * r4222154;
        double r4222156 = r4222152 + r4222155;
        double r4222157 = r4222156 * r4222154;
        double r4222158 = 1.0;
        double r4222159 = r4222157 + r4222158;
        double r4222160 = 0.27061;
        double r4222161 = r4222154 * r4222160;
        double r4222162 = 2.30753;
        double r4222163 = r4222161 + r4222162;
        double r4222164 = r4222159 / r4222163;
        double r4222165 = r4222151 / r4222164;
        double r4222166 = r4222165 - r4222154;
        return r4222166;
}

Error

Bits error versus x

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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 clear-num0.0

    \[\leadsto \color{blue}{\frac{1}{\frac{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}{2.30753 + x \cdot 0.27061}}} - x\]

  4. Final simplification0.0

    \[\leadsto \frac{1}{\frac{\left(0.99229 + 0.04481 \cdot x\right) \cdot x + 1.0}{x \cdot 0.27061 + 2.30753}} - x\]

Reproduce

herbie shell --seed 2019162 
(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))