Average Error: 0.0 → 0.1
Time: 8.9s
Precision: 64
\[\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
↓
\[\frac{\frac{2.30753 + x \cdot 0.27061000000000002}{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}}{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} - x\]
\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x
↓
\frac{\frac{2.30753 + x \cdot 0.27061000000000002}{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}}{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} - x
double f(double x) {
        double r114136 = 2.30753;
        double r114137 = x;
        double r114138 = 0.27061;
        double r114139 = r114137 * r114138;
        double r114140 = r114136 + r114139;
        double r114141 = 1.0;
        double r114142 = 0.99229;
        double r114143 = 0.04481;
        double r114144 = r114137 * r114143;
        double r114145 = r114142 + r114144;
        double r114146 = r114137 * r114145;
        double r114147 = r114141 + r114146;
        double r114148 = r114140 / r114147;
        double r114149 = r114148 - r114137;
        return r114149;
}
↓
double f(double x) {
        double r114150 = 2.30753;
        double r114151 = x;
        double r114152 = 0.27061;
        double r114153 = r114151 * r114152;
        double r114154 = r114150 + r114153;
        double r114155 = 1.0;
        double r114156 = 0.99229;
        double r114157 = 0.04481;
        double r114158 = r114151 * r114157;
        double r114159 = r114156 + r114158;
        double r114160 = r114151 * r114159;
        double r114161 = r114155 + r114160;
        double r114162 = sqrt(r114161);
        double r114163 = r114154 / r114162;
        double r114164 = r114163 / r114162;
        double r114165 = r114164 - r114151;
        return r114165;
}

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 add-sqr-sqrt0.1

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

  4. Applied associate-/r*0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020042 
(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))