Average Error: 15.4 → 15.4
Time: 1.5s
Precision: binary64
\[\frac{a2 + a2 \cdot a2}{\left({\left(\left(nh \cdot a2 - nh\right) \cdot nh + 1\right)}^{2} \cdot \left(\left(lh \cdot lh\right) \cdot 3 + lh\right)\right) \cdot \left(nh \cdot 0.75 + 0.25\right)}\]
↓
\[\frac{a2 + a2 \cdot a2}{\left({\left(\left(nh \cdot a2 - nh\right) \cdot nh + 1\right)}^{2} \cdot \left(\left(lh \cdot lh\right) \cdot 3 + lh\right)\right) \cdot \left(nh \cdot 0.75 + 0.25\right)}\]
\frac{a2 + a2 \cdot a2}{\left({\left(\left(nh \cdot a2 - nh\right) \cdot nh + 1\right)}^{2} \cdot \left(\left(lh \cdot lh\right) \cdot 3 + lh\right)\right) \cdot \left(nh \cdot 0.75 + 0.25\right)}
↓
\frac{a2 + a2 \cdot a2}{\left({\left(\left(nh \cdot a2 - nh\right) \cdot nh + 1\right)}^{2} \cdot \left(\left(lh \cdot lh\right) \cdot 3 + lh\right)\right) \cdot \left(nh \cdot 0.75 + 0.25\right)}
double code(double a2, double nh, double lh) {
	return ((double) (((double) (a2 + ((double) (a2 * a2)))) / ((double) (((double) (((double) pow(((double) (((double) (((double) (((double) (nh * a2)) - nh)) * nh)) + 1.0)), 2.0)) * ((double) (((double) (((double) (lh * lh)) * 3.0)) + lh)))) * ((double) (((double) (nh * 0.75)) + 0.25))))));
}
↓
double code(double a2, double nh, double lh) {
	return ((double) (((double) (a2 + ((double) (a2 * a2)))) / ((double) (((double) (((double) pow(((double) (((double) (((double) (((double) (nh * a2)) - nh)) * nh)) + 1.0)), 2.0)) * ((double) (((double) (((double) (lh * lh)) * 3.0)) + lh)))) * ((double) (((double) (nh * 0.75)) + 0.25))))));
}

Error

Bits error versus a2

Bits error versus nh

Bits error versus lh

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.4

    \[\frac{a2 + a2 \cdot a2}{\left({\left(\left(nh \cdot a2 - nh\right) \cdot nh + 1\right)}^{2} \cdot \left(\left(lh \cdot lh\right) \cdot 3 + lh\right)\right) \cdot \left(nh \cdot 0.75 + 0.25\right)}\]

  2. Final simplification15.4

    \[\leadsto \frac{a2 + a2 \cdot a2}{\left({\left(\left(nh \cdot a2 - nh\right) \cdot nh + 1\right)}^{2} \cdot \left(\left(lh \cdot lh\right) \cdot 3 + lh\right)\right) \cdot \left(nh \cdot 0.75 + 0.25\right)}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (a2 nh lh)
  :name "(/ (+ a2 (* a2 a2)) (* (* (pow (+ (* (- (* nh a2) nh) nh) 1) 2) (+ (* (* lh lh) 3) lh)) (+ (* nh 0.75) 0.25)))"
  :precision binary64
  (/ (+ a2 (* a2 a2)) (* (* (pow (+ (* (- (* nh a2) nh) nh) 1.0) 2.0) (+ (* (* lh lh) 3.0) lh)) (+ (* nh 0.75) 0.25))))