Average Error: 3.8 → 2.9
Time: 13.2s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double kx, double ky, double th) {
	return ((double) (((double) (((double) sin(ky)) / ((double) sqrt(((double) (((double) pow(((double) sin(kx)), 2.0)) + ((double) pow(((double) sin(ky)), 2.0)))))))) * ((double) sin(th))));
}

↓
double code(double kx, double ky, double th) {
	double VAR;
	if ((((double) (((double) sin(ky)) / ((double) sqrt(((double) (((double) pow(((double) sin(kx)), 2.0)) + ((double) pow(((double) sin(ky)), 2.0)))))))) <= 0.9999999999719434)) {
		VAR = ((double) (((double) (1.0 / ((double) (((double) sqrt(((double) (((double) pow(((double) sin(kx)), 2.0)) + ((double) pow(((double) sin(ky)), 2.0)))))) / ((double) sin(ky)))))) * ((double) sin(th))));
	} else {
		VAR = ((double) (((double) sin(th)) * ((double) (1.0 + ((double) (kx * ((double) (kx * -0.16666666666666666))))))));
	}
	return VAR;
}

Error
Bits error versus kx
Bits error versus ky
Bits error versus th
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Derivation
  1. Split input into 2 regimes
  2. if  (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))  < 0.999999999971943443
    1. Initial program 2.5
      \[\]
    2. Using strategy rm
    3. Applied clear-num2.5
      \[\leadsto \]
    if 0.999999999971943443 <  (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) 
    1. Initial program 9.0
      \[\]
    2. Using strategy rm
    3. Applied clear-num9.0
      \[\leadsto \]
    4. Taylor expanded around 0 4.3
      \[\leadsto \]
    5. Simplified4.3
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification2.9
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(FPCore (kx ky th)
  :name "Toniolo and Linder, Equation (3b), real"
  :precision binary64
  (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th)))