Average Error: 0.0 → 0.0
Time: 3.0s
Precision: binary64
\[0.70711 \cdot \left(\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x\right)\]
↓
\[0.70711 \cdot \left(\sqrt[3]{{\left(\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}\right)}^{3}} - x\right)\]
0.70711 \cdot \left(\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x\right)
↓
0.70711 \cdot \left(\sqrt[3]{{\left(\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}\right)}^{3}} - x\right)
(FPCore (x)
 :precision binary64
 (*
  0.70711
  (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x)))
↓
(FPCore (x)
 :precision binary64
 (*
  0.70711
  (-
   (cbrt
    (pow
     (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
     3.0))
   x)))
double code(double x) {
	return ((double) (0.70711 * ((double) ((((double) (2.30753 + ((double) (x * 0.27061)))) / ((double) (1.0 + ((double) (x * ((double) (0.99229 + ((double) (x * 0.04481))))))))) - x))));
}
↓
double code(double x) {
	return ((double) (0.70711 * ((double) (((double) cbrt(((double) pow((((double) (2.30753 + ((double) (x * 0.27061)))) / ((double) (1.0 + ((double) (x * ((double) (0.99229 + ((double) (x * 0.04481))))))))), 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

    \[0.70711 \cdot \left(\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x\right)\]
  2. Using strategy rm

  3. Applied add-cbrt-cube0.0

    \[\leadsto 0.70711 \cdot \left(\frac{2.30753 + x \cdot 0.27061}{\color{blue}{\sqrt[3]{\left(\left(1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)\right) \cdot \left(1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)\right)\right) \cdot \left(1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)\right)}}} - x\right)\]

  4. Applied add-cbrt-cube21.3

    \[\leadsto 0.70711 \cdot \left(\frac{\color{blue}{\sqrt[3]{\left(\left(2.30753 + x \cdot 0.27061\right) \cdot \left(2.30753 + x \cdot 0.27061\right)\right) \cdot \left(2.30753 + x \cdot 0.27061\right)}}}{\sqrt[3]{\left(\left(1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)\right) \cdot \left(1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)\right)\right) \cdot \left(1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)\right)}} - x\right)\]

  5. Applied cbrt-undiv21.3

    \[\leadsto 0.70711 \cdot \left(\color{blue}{\sqrt[3]{\frac{\left(\left(2.30753 + x \cdot 0.27061\right) \cdot \left(2.30753 + x \cdot 0.27061\right)\right) \cdot \left(2.30753 + x \cdot 0.27061\right)}{\left(\left(1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)\right) \cdot \left(1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)\right)\right) \cdot \left(1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)\right)}}} - x\right)\]

  6. Simplified0.0

    \[\leadsto 0.70711 \cdot \left(\sqrt[3]{\color{blue}{{\left(\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}\right)}^{3}}} - x\right)\]

  7. Final simplification0.0

    \[\leadsto 0.70711 \cdot \left(\sqrt[3]{{\left(\frac{2.30753 + x \cdot 0.27061}{1 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}\right)}^{3}} - x\right)\]

Reproduce

herbie shell --seed 2020198 
(FPCore (x)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, B"
  :precision binary64
  (* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x)))