Average Error: 34.7 → 34.7
Time: 8.8s
Precision: binary64
\[\frac{{d}^{2} \cdot \left(theta - \sin theta\right)}{8 \cdot {\left(\sin \left(\frac{theta}{2}\right)\right)}^{2}}\]
↓
\[\frac{{d}^{2} \cdot \left(theta - \sin theta\right)}{8 \cdot {\left(\sin \left(\frac{theta}{2}\right)\right)}^{2}}\]
\frac{{d}^{2} \cdot \left(theta - \sin theta\right)}{8 \cdot {\left(\sin \left(\frac{theta}{2}\right)\right)}^{2}}
↓
\frac{{d}^{2} \cdot \left(theta - \sin theta\right)}{8 \cdot {\left(\sin \left(\frac{theta}{2}\right)\right)}^{2}}
double code(double d, double theta) {
	return ((double) (((double) (((double) pow(d, 2.0)) * ((double) (theta - ((double) sin(theta)))))) / ((double) (8.0 * ((double) pow(((double) sin(((double) (theta / 2.0)))), 2.0))))));
}
↓
double code(double d, double theta) {
	return ((double) (((double) (((double) pow(d, 2.0)) * ((double) (theta - ((double) sin(theta)))))) / ((double) (8.0 * ((double) pow(((double) sin(((double) (theta / 2.0)))), 2.0))))));
}

Error

Bits error versus d

Bits error versus theta

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 34.7

    \[\frac{{d}^{2} \cdot \left(theta - \sin theta\right)}{8 \cdot {\left(\sin \left(\frac{theta}{2}\right)\right)}^{2}}\]

  2. Final simplification34.7

    \[\leadsto \frac{{d}^{2} \cdot \left(theta - \sin theta\right)}{8 \cdot {\left(\sin \left(\frac{theta}{2}\right)\right)}^{2}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (d theta)
  :name "(/ (* (pow d 2) (- theta (sin theta))) (* 8 (pow (sin (/ theta 2)) 2)))"
  :precision binary64
  (/ (* (pow d 2.0) (- theta (sin theta))) (* 8.0 (pow (sin (/ theta 2.0)) 2.0))))