Average Error: 15.1 → 15.1
Time: 1.3s
Precision: binary64
\[\tan^{-1} \left(x + y\right) - \tan^{-1} \left(x - y\right)\]
↓
\[\tan^{-1} \left(x + y\right) - \tan^{-1} \left(x - y\right)\]
\tan^{-1} \left(x + y\right) - \tan^{-1} \left(x - y\right)
↓
\tan^{-1} \left(x + y\right) - \tan^{-1} \left(x - y\right)
double code(double x, double y) {
	return ((double) (((double) atan(((double) (x + y)))) - ((double) atan(((double) (x - y))))));
}
↓
double code(double x, double y) {
	return ((double) (((double) atan(((double) (x + y)))) - ((double) atan(((double) (x - y))))));
}

Error

Bits error versus x

Bits error versus y

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Results

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Derivation

  1. Initial program 15.1

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

  2. Final simplification15.1

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

Reproduce

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