Average Error: 0.0 → 0.0
Time: 3.7s
Precision: 64
\[\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
↓
\[\frac{1}{\sqrt[3]{{\left(\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(0.044810000000000003, x, 0.992290000000000005\right), 1\right)}{\mathsf{fma}\left(0.27061000000000002, x, 2.30753\right)}\right)}^{3}}} - x\]
\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x
↓
\frac{1}{\sqrt[3]{{\left(\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(0.044810000000000003, x, 0.992290000000000005\right), 1\right)}{\mathsf{fma}\left(0.27061000000000002, x, 2.30753\right)}\right)}^{3}}} - x
double code(double x) {
	return (((2.30753 + (x * 0.27061)) / (1.0 + (x * (0.99229 + (x * 0.04481))))) - x);
}
↓
double code(double x) {
	return ((1.0 / cbrt(pow((fma(x, fma(0.04481, x, 0.99229), 1.0) / fma(0.27061, x, 2.30753)), 3.0))) - x);
}

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 clear-num0.0

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

  4. Simplified0.0

    \[\leadsto \frac{1}{\color{blue}{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(0.044810000000000003, x, 0.992290000000000005\right), 1\right)}{\mathsf{fma}\left(0.27061000000000002, x, 2.30753\right)}}} - x\]
  5. Using strategy rm

  6. Applied add-cbrt-cube21.8

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

  7. Applied add-cbrt-cube21.8

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

  8. Applied cbrt-undiv21.8

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

  9. Simplified0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(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))