Average Error: 0.0 → 0.0
Time: 12.0s
Precision: 64
\[\frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x\]
↓
\[\sqrt[3]{\frac{0.27061 \cdot x + 2.30753}{x \cdot \left(x \cdot 0.04481 + 0.99229\right) + 1.0} \cdot \left(\left(\frac{1}{x \cdot \left(x \cdot 0.04481 + 0.99229\right) + 1.0} \cdot \left(0.27061 \cdot x + 2.30753\right)\right) \cdot \frac{0.27061 \cdot x + 2.30753}{x \cdot \left(x \cdot 0.04481 + 0.99229\right) + 1.0}\right)} - x\]
\frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x
↓
\sqrt[3]{\frac{0.27061 \cdot x + 2.30753}{x \cdot \left(x \cdot 0.04481 + 0.99229\right) + 1.0} \cdot \left(\left(\frac{1}{x \cdot \left(x \cdot 0.04481 + 0.99229\right) + 1.0} \cdot \left(0.27061 \cdot x + 2.30753\right)\right) \cdot \frac{0.27061 \cdot x + 2.30753}{x \cdot \left(x \cdot 0.04481 + 0.99229\right) + 1.0}\right)} - x
double f(double x) {
        double r3656960 = 2.30753;
        double r3656961 = x;
        double r3656962 = 0.27061;
        double r3656963 = r3656961 * r3656962;
        double r3656964 = r3656960 + r3656963;
        double r3656965 = 1.0;
        double r3656966 = 0.99229;
        double r3656967 = 0.04481;
        double r3656968 = r3656961 * r3656967;
        double r3656969 = r3656966 + r3656968;
        double r3656970 = r3656961 * r3656969;
        double r3656971 = r3656965 + r3656970;
        double r3656972 = r3656964 / r3656971;
        double r3656973 = r3656972 - r3656961;
        return r3656973;
}
↓
double f(double x) {
        double r3656974 = 0.27061;
        double r3656975 = x;
        double r3656976 = r3656974 * r3656975;
        double r3656977 = 2.30753;
        double r3656978 = r3656976 + r3656977;
        double r3656979 = 0.04481;
        double r3656980 = r3656975 * r3656979;
        double r3656981 = 0.99229;
        double r3656982 = r3656980 + r3656981;
        double r3656983 = r3656975 * r3656982;
        double r3656984 = 1.0;
        double r3656985 = r3656983 + r3656984;
        double r3656986 = r3656978 / r3656985;
        double r3656987 = 1.0;
        double r3656988 = r3656987 / r3656985;
        double r3656989 = r3656988 * r3656978;
        double r3656990 = r3656989 * r3656986;
        double r3656991 = r3656986 * r3656990;
        double r3656992 = cbrt(r3656991);
        double r3656993 = r3656992 - r3656975;
        return r3656993;
}

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-cbrt-cube0.0

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

  5. Applied div-inv0.0

    \[\leadsto \sqrt[3]{\left(\frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} \cdot \color{blue}{\left(\left(2.30753 + x \cdot 0.27061\right) \cdot \frac{1}{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}\right)}\right) \cdot \frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}} - x\]

  6. Final simplification0.0

    \[\leadsto \sqrt[3]{\frac{0.27061 \cdot x + 2.30753}{x \cdot \left(x \cdot 0.04481 + 0.99229\right) + 1.0} \cdot \left(\left(\frac{1}{x \cdot \left(x \cdot 0.04481 + 0.99229\right) + 1.0} \cdot \left(0.27061 \cdot x + 2.30753\right)\right) \cdot \frac{0.27061 \cdot x + 2.30753}{x \cdot \left(x \cdot 0.04481 + 0.99229\right) + 1.0}\right)} - x\]

Reproduce

herbie shell --seed 2019163 
(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))