Average Error: 0.0 → 0.0
Time: 9.1s
Precision: 64
\[x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}\]
↓
\[x - \sqrt[3]{{\left(\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \frac{1}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}\right)}^{3}}\]
x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}
↓
x - \sqrt[3]{{\left(\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \frac{1}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}\right)}^{3}}
double f(double x) {
        double r95941 = x;
        double r95942 = 2.30753;
        double r95943 = 0.27061;
        double r95944 = r95941 * r95943;
        double r95945 = r95942 + r95944;
        double r95946 = 1.0;
        double r95947 = 0.99229;
        double r95948 = 0.04481;
        double r95949 = r95941 * r95948;
        double r95950 = r95947 + r95949;
        double r95951 = r95950 * r95941;
        double r95952 = r95946 + r95951;
        double r95953 = r95945 / r95952;
        double r95954 = r95941 - r95953;
        return r95954;
}
↓
double f(double x) {
        double r95955 = x;
        double r95956 = 2.30753;
        double r95957 = 0.27061;
        double r95958 = r95955 * r95957;
        double r95959 = r95956 + r95958;
        double r95960 = 1.0;
        double r95961 = 1.0;
        double r95962 = 0.99229;
        double r95963 = 0.04481;
        double r95964 = r95955 * r95963;
        double r95965 = r95962 + r95964;
        double r95966 = r95965 * r95955;
        double r95967 = r95961 + r95966;
        double r95968 = r95960 / r95967;
        double r95969 = r95959 * r95968;
        double r95970 = 3.0;
        double r95971 = pow(r95969, r95970);
        double r95972 = cbrt(r95971);
        double r95973 = r95955 - r95972;
        return r95973;
}

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

    \[x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}\]
  2. Using strategy rm

  3. Applied add-cbrt-cube0.0

    \[\leadsto x - \frac{2.30753 + x \cdot 0.27061000000000002}{\color{blue}{\sqrt[3]{\left(\left(1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x\right) \cdot \left(1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x\right)\right) \cdot \left(1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x\right)}}}\]

  4. Applied add-cbrt-cube21.7

    \[\leadsto x - \frac{\color{blue}{\sqrt[3]{\left(\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)}}}{\sqrt[3]{\left(\left(1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x\right) \cdot \left(1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x\right)\right) \cdot \left(1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x\right)}}\]

  5. Applied cbrt-undiv21.7

    \[\leadsto x - \color{blue}{\sqrt[3]{\frac{\left(\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)}{\left(\left(1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x\right) \cdot \left(1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x\right)\right) \cdot \left(1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x\right)}}}\]

  6. Simplified0.0

    \[\leadsto x - \sqrt[3]{\color{blue}{{\left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}\right)}^{3}}}\]
  7. Using strategy rm

  8. Applied div-inv0.0

    \[\leadsto x - \sqrt[3]{{\color{blue}{\left(\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \frac{1}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}\right)}}^{3}}\]

  9. Final simplification0.0

    \[\leadsto x - \sqrt[3]{{\left(\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \frac{1}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}\right)}^{3}}\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, D"
  :precision binary64
  (- x (/ (+ 2.30753 (* x 0.27061)) (+ 1 (* (+ 0.99229 (* x 0.04481)) x)))))