Average Error: 33.4 → 32.0
Time: 7.5s
Precision: binary64
\[\frac{\left(2 \cdot a - 3 \cdot \sin a\right) + a \cdot \cos a}{\left(\left(\left(\left(2 \cdot a\right) \cdot a\right) \cdot a\right) \cdot a\right) \cdot a}\]
↓
\[\frac{\frac{\left(2 \cdot a - 3 \cdot \sin a\right) + a \cdot \cos a}{{a}^{4}}}{2 \cdot a}\]
\frac{\left(2 \cdot a - 3 \cdot \sin a\right) + a \cdot \cos a}{\left(\left(\left(\left(2 \cdot a\right) \cdot a\right) \cdot a\right) \cdot a\right) \cdot a}
↓
\frac{\frac{\left(2 \cdot a - 3 \cdot \sin a\right) + a \cdot \cos a}{{a}^{4}}}{2 \cdot a}
double code(double a) {
	return ((double) (((double) (((double) (((double) (2.0 * a)) - ((double) (3.0 * ((double) sin(a)))))) + ((double) (a * ((double) cos(a)))))) / ((double) (((double) (((double) (((double) (((double) (2.0 * a)) * a)) * a)) * a)) * a))));
}
↓
double code(double a) {
	return ((double) (((double) (((double) (((double) (((double) (2.0 * a)) - ((double) (3.0 * ((double) sin(a)))))) + ((double) (a * ((double) cos(a)))))) / ((double) pow(a, 4.0)))) / ((double) (2.0 * a))));
}

Error

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 33.4

    \[\frac{\left(2 \cdot a - 3 \cdot \sin a\right) + a \cdot \cos a}{\left(\left(\left(\left(2 \cdot a\right) \cdot a\right) \cdot a\right) \cdot a\right) \cdot a}\]

  2. Simplified32.0

    \[\leadsto \color{blue}{\frac{\frac{\left(2 \cdot a - 3 \cdot \sin a\right) + a \cdot \cos a}{{a}^{4}}}{2 \cdot a}}\]

  3. Final simplification32.0

    \[\leadsto \frac{\frac{\left(2 \cdot a - 3 \cdot \sin a\right) + a \cdot \cos a}{{a}^{4}}}{2 \cdot a}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (a)
  :name "(/ (+ (- (* 2 a) (* 3 (sin a))) (* a (cos a))) (* (* (* (* (* 2 a) a) a) a) a))"
  :precision binary64
  (/ (+ (- (* 2.0 a) (* 3.0 (sin a))) (* a (cos a))) (* (* (* (* (* 2.0 a) a) a) a) a)))