Average Error: 1.5 → 1.5
Time: 1.9s
Precision: binary64
\[\frac{\cos^{-1} \left(\frac{x - 1}{2}\right)}{2 \cdot \sin \left(\cos^{-1} \left(\frac{x - 1}{2}\right)\right)}\]
↓
\[\frac{\cos^{-1} \left(\frac{x - 1}{2}\right)}{2 \cdot \sin \left(\cos^{-1} \left(\frac{x - 1}{2}\right)\right)}\]
\frac{\cos^{-1} \left(\frac{x - 1}{2}\right)}{2 \cdot \sin \left(\cos^{-1} \left(\frac{x - 1}{2}\right)\right)}
↓
\frac{\cos^{-1} \left(\frac{x - 1}{2}\right)}{2 \cdot \sin \left(\cos^{-1} \left(\frac{x - 1}{2}\right)\right)}
double code(double x) {
	return ((double) (((double) acos(((double) (((double) (x - 1.0)) / 2.0)))) / ((double) (2.0 * ((double) sin(((double) acos(((double) (((double) (x - 1.0)) / 2.0))))))))));
}
↓
double code(double x) {
	return ((double) (((double) acos(((double) (((double) (x - 1.0)) / 2.0)))) / ((double) (2.0 * ((double) sin(((double) acos(((double) (((double) (x - 1.0)) / 2.0))))))))));
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.5

    \[\frac{\cos^{-1} \left(\frac{x - 1}{2}\right)}{2 \cdot \sin \left(\cos^{-1} \left(\frac{x - 1}{2}\right)\right)}\]

  2. Final simplification1.5

    \[\leadsto \frac{\cos^{-1} \left(\frac{x - 1}{2}\right)}{2 \cdot \sin \left(\cos^{-1} \left(\frac{x - 1}{2}\right)\right)}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(/ (acos (/ (- x 1) 2)) (* 2 (sin (acos (/ (- x 1) 2)))))"
  :precision binary64
  (/ (acos (/ (- x 1.0) 2.0)) (* 2.0 (sin (acos (/ (- x 1.0) 2.0))))))