Average Error: 40.4 → 40.4
Time: 3.2s
Precision: binary64
\[\tan \left(\tan^{-1} x + z \cdot \left(\tan^{-1} y - \tan^{-1} x\right)\right)\]
↓
\[\tan \left(\tan^{-1} x + z \cdot \left(\tan^{-1} y - \tan^{-1} x\right)\right)\]
\tan \left(\tan^{-1} x + z \cdot \left(\tan^{-1} y - \tan^{-1} x\right)\right)
↓
\tan \left(\tan^{-1} x + z \cdot \left(\tan^{-1} y - \tan^{-1} x\right)\right)
double code(double x, double z, double y) {
	return ((double) tan(((double) (((double) atan(x)) + ((double) (z * ((double) (((double) atan(y)) - ((double) atan(x))))))))));
}
↓
double code(double x, double z, double y) {
	return ((double) tan(((double) (((double) atan(x)) + ((double) (z * ((double) (((double) atan(y)) - ((double) atan(x))))))))));
}

Error

Bits error versus x

Bits error versus z

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 40.4

    \[\tan \left(\tan^{-1} x + z \cdot \left(\tan^{-1} y - \tan^{-1} x\right)\right)\]

  2. Final simplification40.4

    \[\leadsto \tan \left(\tan^{-1} x + z \cdot \left(\tan^{-1} y - \tan^{-1} x\right)\right)\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x z y)
  :name "(tan (+ (atan x) (* z (- (atan y) (atan x)))))"
  :precision binary64
  (tan (+ (atan x) (* z (- (atan y) (atan x))))))