Average Error: 30.8 → 30.8
Time: 1.9s
Precision: binary64
\[\sqrt{\left(\left({\left(\left(e^{1} \cdot x\right) \cdot 8\right)}^{2} + {\left(\frac{e^{1} \cdot x}{8}\right)}^{2}\right) + {\left(\left(e^{1} \cdot x\right) \cdot 4\right)}^{2}\right) + {\left(\frac{e^{1} \cdot x}{4}\right)}^{2}}\]
↓
\[\sqrt{\left(\left({\left(\left(e^{1} \cdot x\right) \cdot 8\right)}^{2} + {\left(\frac{e^{1} \cdot x}{8}\right)}^{2}\right) + {\left(\left(e^{1} \cdot x\right) \cdot 4\right)}^{2}\right) + {\left(\frac{e^{1} \cdot x}{4}\right)}^{2}}\]
\sqrt{\left(\left({\left(\left(e^{1} \cdot x\right) \cdot 8\right)}^{2} + {\left(\frac{e^{1} \cdot x}{8}\right)}^{2}\right) + {\left(\left(e^{1} \cdot x\right) \cdot 4\right)}^{2}\right) + {\left(\frac{e^{1} \cdot x}{4}\right)}^{2}}
↓
\sqrt{\left(\left({\left(\left(e^{1} \cdot x\right) \cdot 8\right)}^{2} + {\left(\frac{e^{1} \cdot x}{8}\right)}^{2}\right) + {\left(\left(e^{1} \cdot x\right) \cdot 4\right)}^{2}\right) + {\left(\frac{e^{1} \cdot x}{4}\right)}^{2}}
double code(double x) {
	return ((double) sqrt(((double) (((double) (((double) (((double) pow(((double) (((double) (((double) exp(1.0)) * x)) * 8.0)), 2.0)) + ((double) pow(((double) (((double) (((double) exp(1.0)) * x)) / 8.0)), 2.0)))) + ((double) pow(((double) (((double) (((double) exp(1.0)) * x)) * 4.0)), 2.0)))) + ((double) pow(((double) (((double) (((double) exp(1.0)) * x)) / 4.0)), 2.0))))));
}
↓
double code(double x) {
	return ((double) sqrt(((double) (((double) (((double) (((double) pow(((double) (((double) (((double) exp(1.0)) * x)) * 8.0)), 2.0)) + ((double) pow(((double) (((double) (((double) exp(1.0)) * x)) / 8.0)), 2.0)))) + ((double) pow(((double) (((double) (((double) exp(1.0)) * x)) * 4.0)), 2.0)))) + ((double) pow(((double) (((double) (((double) exp(1.0)) * x)) / 4.0)), 2.0))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 30.8

    \[\sqrt{\left(\left({\left(\left(e^{1} \cdot x\right) \cdot 8\right)}^{2} + {\left(\frac{e^{1} \cdot x}{8}\right)}^{2}\right) + {\left(\left(e^{1} \cdot x\right) \cdot 4\right)}^{2}\right) + {\left(\frac{e^{1} \cdot x}{4}\right)}^{2}}\]

  2. Final simplification30.8

    \[\leadsto \sqrt{\left(\left({\left(\left(e^{1} \cdot x\right) \cdot 8\right)}^{2} + {\left(\frac{e^{1} \cdot x}{8}\right)}^{2}\right) + {\left(\left(e^{1} \cdot x\right) \cdot 4\right)}^{2}\right) + {\left(\frac{e^{1} \cdot x}{4}\right)}^{2}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(sqrt (+ (+ (+ (pow (* (* (exp 1) x) 8) 2) (pow (/ (* (exp 1) x) 8) 2)) (pow (* (* (exp 1) x) 4) 2)) (pow (/ (* (exp 1) x) 4) 2)))"
  :precision binary64
  (sqrt (+ (+ (+ (pow (* (* (exp 1.0) x) 8.0) 2.0) (pow (/ (* (exp 1.0) x) 8.0) 2.0)) (pow (* (* (exp 1.0) x) 4.0) 2.0)) (pow (/ (* (exp 1.0) x) 4.0) 2.0))))