Average Error: 0.1 → 0.1
Time: 3.7s
Precision: binary64
\[\mathsf{max}\left(\frac{1}{\cos x + \frac{\sin^{-1} x}{2}} + \frac{4}{\sin y}, \frac{\pi}{e^{x}}\right)\]
↓
\[\mathsf{max}\left(\frac{1}{\cos x + \frac{\sin^{-1} x}{2}} + \frac{4}{\sin y}, \frac{\pi}{e^{x}}\right)\]
\mathsf{max}\left(\frac{1}{\cos x + \frac{\sin^{-1} x}{2}} + \frac{4}{\sin y}, \frac{\pi}{e^{x}}\right)
↓
\mathsf{max}\left(\frac{1}{\cos x + \frac{\sin^{-1} x}{2}} + \frac{4}{\sin y}, \frac{\pi}{e^{x}}\right)
double code(double x, double y) {
	return ((double) fmax(((double) (((double) (1.0 / ((double) (((double) cos(x)) + ((double) (((double) asin(x)) / 2.0)))))) + ((double) (4.0 / ((double) sin(y)))))), ((double) (((double) M_PI) / ((double) exp(x))))));
}
↓
double code(double x, double y) {
	return ((double) fmax(((double) (((double) (1.0 / ((double) (((double) cos(x)) + ((double) (((double) asin(x)) / 2.0)))))) + ((double) (4.0 / ((double) sin(y)))))), ((double) (((double) M_PI) / ((double) exp(x))))));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\mathsf{max}\left(\frac{1}{\cos x + \frac{\sin^{-1} x}{2}} + \frac{4}{\sin y}, \frac{\pi}{e^{x}}\right)\]

  2. Final simplification0.1

    \[\leadsto \mathsf{max}\left(\frac{1}{\cos x + \frac{\sin^{-1} x}{2}} + \frac{4}{\sin y}, \frac{\pi}{e^{x}}\right)\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x y)
  :name "(fmax (+ (/ 1 (+ (cos x) (/ (asin x) 2))) (/ 4 (sin y))) (/ PI (exp x)))"
  :precision binary64
  (fmax (+ (/ 1.0 (+ (cos x) (/ (asin x) 2.0))) (/ 4.0 (sin y))) (/ PI (exp x))))