Details

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
100%	100%	0%	0%	0%	0%	0%	1

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample2.3s (16%)

Results

1.1s	2202×	body	2048	valid
684.0ms	4485×	body	256	valid
378.0ms	1047×	body	1024	valid
131.0ms	522×	body	512	valid

Bogosity

preprocess80.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

922×	`rational_best-simplify-1`
654×	`rational_best-simplify-21`
654×	`rational_best-simplify-18`
646×	`rational_best-simplify-20`
408×	`rational_best-simplify-127`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	36	21
2	164	21
3	1005	21
4	7033	21
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Outputs
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify78.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

922×	`rational_best-simplify-1`
654×	`rational_best-simplify-21`
654×	`rational_best-simplify-18`
646×	`rational_best-simplify-20`
408×	`rational_best-simplify-127`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	36	21
2	164	21
3	1005	21
4	7033	21

Stop Event

1×	node limit

Counts

1 → 1

Calls

Call 1

Inputs
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Outputs
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

eval0.0ms (0%)

Compiler: Compiled 8 to 6 computations (25% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

15.7b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	15.7b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 8 to 6 computations (25% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(atan.f64 (+.f64 N 1))
✓	1.7b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 19 to 12 computations (36.8% saved)

series1.0ms (0%)

Counts

2 → 8

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	N	@	-inf	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
0.0ms	N	@	inf	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
0.0ms	N	@	0	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
0.0ms	N	@	-inf	(atan.f64 (+.f64 N 1))
0.0ms	N	@	0	(atan.f64 (+.f64 N 1))

rewrite88.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

922×	`rational_best-simplify-1`
654×	`rational_best-simplify-21`
654×	`rational_best-simplify-18`
646×	`rational_best-simplify-20`
408×	`rational_best-simplify-127`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	32
1	36	32
2	164	32
3	1005	32
4	7036	32

Stop Event

1×	node limit

Counts

2 → 37

Calls

Call 1

Inputs
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(atan.f64 (+.f64 N 1))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (atan.f64 N)) (atan.f64 (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (+.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (+.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) -4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (+.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 -2 (+.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (.f64 (+.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (+.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (-.f64 4 (.f64 -2 (+.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0) (/.f64 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (atan.f64 N) 0) (/.f64 (.f64 (atan.f64 N) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (atan.f64 N)) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (atan.f64 (+.f64 N 1)) 0) (/.f64 (.f64 (atan.f64 (+.f64 N 1)) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (neg.f64 (atan.f64 N)) 0) (/.f64 (.f64 (atan.f64 N) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (atan.f64 N)) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (neg.f64 (atan.f64 (+.f64 N 1))) 0) (/.f64 (.f64 (atan.f64 (+.f64 N 1)) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 0) (/.f64 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 -1 0) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 0 0) (/.f64 0 0) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (neg.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 0) (/.f64 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (*.f64 (atan.f64 N) (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 (+.f64 N 1)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (atan.f64 (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (atan.f64 (+.f64 N 1)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (neg.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (atan.f64 (+.f64 N 1))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (atan.f64 (+.f64 N 1))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan.f64 (+.f64 N 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (atan.f64 (+.f64 N 1))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (atan.f64 N)) (atan.f64 (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (+.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (+.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) -4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (+.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 -2 (+.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (*.f64 (+.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (+.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (-.f64 4 (*.f64 -2 (+.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (*.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (-.f64 (*.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (*.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0) (/.f64 (-.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (*.f64 (atan.f64 N) (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (atan.f64 N) 0) (/.f64 (*.f64 (atan.f64 N) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (atan.f64 N)) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (atan.f64 (+.f64 N 1)) 0) (/.f64 (*.f64 (atan.f64 (+.f64 N 1)) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (neg.f64 (atan.f64 N)) 0) (/.f64 (*.f64 (atan.f64 N) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (atan.f64 N)) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (neg.f64 (atan.f64 (+.f64 N 1))) 0) (/.f64 (*.f64 (atan.f64 (+.f64 N 1)) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 0) (/.f64 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 -1 0) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 0 0) (/.f64 0 0) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (neg.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 0) (/.f64 (-.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (*.f64 (atan.f64 N) (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 (+.f64 N 1)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (atan.f64 (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (atan.f64 (+.f64 N 1)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (neg.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (atan.f64 (+.f64 N 1))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (atan.f64 (+.f64 N 1))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan.f64 (+.f64 N 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (atan.f64 (+.f64 N 1))))))))

simplify60.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

928×	`rational_best-simplify-96`
892×	`rational_best-simplify-61`
882×	`rational_best-simplify-65`
602×	`rational_best-simplify-3`
522×	`rational_best-simplify-62`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	101	1085
1	470	815
2	2965	815

Stop Event

1×	node limit

Counts

45 → 41

Calls

Call 1

Inputs
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N)))
(+.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0)
(+.f64 (neg.f64 (atan.f64 N)) (atan.f64 (+.f64 N 1)))
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(*.f64 1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
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(/.f64 (+.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) -2)
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(/.f64 (+.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2)
(/.f64 (+.f64 (+.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (+.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) -4)
(/.f64 (+.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (+.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))
(/.f64 (-.f64 (.f64 -2 (+.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (.f64 (+.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (+.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (-.f64 4 (*.f64 -2 (+.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))))
(/.f64 (-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))))
(pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1)
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(if (!=.f64 (atan.f64 N) 0) (/.f64 (*.f64 (atan.f64 N) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (atan.f64 N)) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
(if (!=.f64 (atan.f64 (+.f64 N 1)) 0) (/.f64 (*.f64 (atan.f64 (+.f64 N 1)) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
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(if (!=.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 0) (/.f64 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
(if (!=.f64 -1 0) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
(if (!=.f64 0 0) (/.f64 0 0) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
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(/.f64 (neg.f64 (atan.f64 (+.f64 N 1))) -1)
(pow.f64 (atan.f64 (+.f64 N 1)) 1)
(neg.f64 (neg.f64 (atan.f64 (+.f64 N 1))))

Outputs
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(atan.f64 (+.f64 1 N))
(+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N)))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
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(+.f64 0 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
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(*.f64 1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
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(*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1)
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(*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) -1)
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
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(*.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))
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(/.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1)
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(/.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) -1)
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(/.f64 (+.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) -2)
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(/.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
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(/.f64 (+.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2)
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(/.f64 (+.f64 (+.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (+.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) -4)
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
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(/.f64 (+.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (+.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))
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(/.f64 (-.f64 (.f64 -2 (+.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (.f64 (+.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (+.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (-.f64 4 (*.f64 -2 (+.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))))
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(/.f64 (-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
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(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(if (!=.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0) (/.f64 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(if (!=.f64 (atan.f64 N) 0) (/.f64 (*.f64 (atan.f64 N) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (atan.f64 N)) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(if (!=.f64 (atan.f64 (+.f64 N 1)) 0) (/.f64 (*.f64 (atan.f64 (+.f64 N 1)) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
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(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
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(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
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(if (!=.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 0) (/.f64 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
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(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
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(if (!=.f64 0 0) (/.f64 0 0) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(if (!=.f64 (neg.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 0) (/.f64 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
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(-.f64 (atan.f64 (+.f64 N 1)) 0)
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(-.f64 0 (neg.f64 (atan.f64 (+.f64 N 1))))
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(*.f64 -1 (neg.f64 (atan.f64 (+.f64 N 1))))
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(*.f64 (neg.f64 (atan.f64 (+.f64 N 1))) -1)
(atan.f64 (-.f64 1 (*.f64 -1 N)))
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(/.f64 (neg.f64 (atan.f64 (+.f64 N 1))) -1)
(atan.f64 (-.f64 1 (*.f64 -1 N)))
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(pow.f64 (atan.f64 (+.f64 N 1)) 1)
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(atan.f64 (+.f64 1 N))
(neg.f64 (neg.f64 (atan.f64 (+.f64 N 1))))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
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eval13.0ms (0.1%)

Compiler: Compiled 819 to 535 computations (34.7% saved)

prune9.0ms (0.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	39	2	41
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	39	3	42

Error

15.7b

Counts

42 → 3

Alt Table

Click to see full alt table

Status	Error	Program
▶	15.7b	(if (!=.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0) (/.f64 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
▶	16.5b	(/.f64 (-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))))
✓	15.7b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Status

Error

Program

▶

15.7b

(if (!=.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0) (/.f64 (-.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (*.f64 (atan.f64 N) (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))

▶

16.5b

(/.f64 (-.f64 (*.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (*.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (-.f64 (*.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (*.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))))

✓

15.7b

(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 161 to 110 computations (31.7% saved)

localize116.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))
✓	0.5b	(-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))))
✓	0.5b	(-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))))
✓	1.7b	(-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))

Compiler

Compiled 357 to 239 computations (33.1% saved)

series9.0ms (0.1%)

Counts

4 → 40

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	N	@	-inf	(-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))))
2.0ms	N	@	0	(-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))))
2.0ms	N	@	inf	(-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))))
1.0ms	N	@	-inf	(-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))))
1.0ms	N	@	inf	(-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))))

rewrite170.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

1428×	`rational_best-simplify-61`
778×	`rational_best-simplify-53`
756×	`rational_best-simplify-56`
618×	`rational_best-simplify-1`
614×	`rational_best-simplify-52`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	450
1	115	392
2	653	340
3	4385	340

Stop Event

1×	node limit

Counts

4 → 117

Calls

Call 1

Inputs
(-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))
(-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))))
(-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))))
(.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 N) (neg.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (atan.f64 (+.f64 N 1))) (atan.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) (-.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (+.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 0) (/.f64 (-.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1)))) (+.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (atan.f64 (+.f64 N 1)) 0) (/.f64 (.f64 (atan.f64 (+.f64 N 1)) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (atan.f64 N) 0) (/.f64 (.f64 (atan.f64 N) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (atan.f64 N)) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 -1 0) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0) (/.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (-.f64 (neg.f64 (atan.f64 N)) (atan.f64 (+.f64 N 1))) 0) (/.f64 (-.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1)))) (+.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (neg.f64 (atan.f64 (+.f64 N 1))) 0) (/.f64 (.f64 (atan.f64 (+.f64 N 1)) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (neg.f64 (atan.f64 N)) 0) (/.f64 (.f64 (atan.f64 N) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (atan.f64 N)) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 0 0) (/.f64 (neg.f64 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0)) 0) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1)))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1)))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (.f64 (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1)))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1)))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) (.f64 (.f64 (-.f64 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simplify256.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

720×	`rational_best-simplify-113`
570×	`rational_best-simplify-124`
562×	`rational_best-simplify-126`
534×	`rational_best-simplify-61`
514×	`rational_best-simplify-65`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	295	25231
1	1496	24417

Stop Event

1×	node limit

Counts

157 → 191

Calls

Call 1

Inputs
(-.f64 (atan.f64 N) (atan.f64 (-.f64 1 (*.f64 -1 N))))
(-.f64 (atan.f64 N) (atan.f64 (-.f64 1 (*.f64 -1 N))))
(-.f64 (atan.f64 N) (atan.f64 (-.f64 1 (*.f64 -1 N))))
(-.f64 (atan.f64 N) (atan.f64 (-.f64 1 (*.f64 -1 N))))
(-.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))))) (*.f64 (pow.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 2) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2)))
(-.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))))) (*.f64 (pow.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 2) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2)))
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(-.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))))) (*.f64 (pow.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 2) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2)))
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(-.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (-.f64 1 (.f64 -1 N)))) (.f64 (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (-.f64 1 (.f64 -1 N)))) (-.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) (+.f64 1 (atan.f64 N))))) (.f64 (pow.f64 (-.f64 (atan.f64 N) (atan.f64 (-.f64 1 (.f64 -1 N)))) 2) (pow.f64 (-.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) (+.f64 1 (atan.f64 N))) 2)))
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(-.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (-.f64 1 (.f64 -1 N)))) (.f64 (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (-.f64 1 (.f64 -1 N)))) (-.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) (+.f64 1 (atan.f64 N))))) (.f64 (pow.f64 (-.f64 (atan.f64 N) (atan.f64 (-.f64 1 (.f64 -1 N)))) 2) (pow.f64 (-.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) (+.f64 1 (atan.f64 N))) 2)))
(-.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (-.f64 1 (.f64 -1 N)))) (.f64 (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (-.f64 1 (.f64 -1 N)))) (-.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) (+.f64 1 (atan.f64 N))))) (.f64 (pow.f64 (-.f64 (atan.f64 N) (atan.f64 (-.f64 1 (.f64 -1 N)))) 2) (pow.f64 (-.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) (+.f64 1 (atan.f64 N))) 2)))
(-.f64 (pow.f64 (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))) 2) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))))))
(-.f64 (pow.f64 (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))) 2) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))))))
(-.f64 (pow.f64 (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))) 2) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))))))
(-.f64 (pow.f64 (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))) 2) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))))))
(-.f64 (pow.f64 (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))) 2) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))))))
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(-.f64 (pow.f64 (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))) 2) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))))))
(-.f64 (pow.f64 (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))) 2) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))))))
(-.f64 (pow.f64 (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (-.f64 1 (.f64 -1 N)))) 2) (.f64 (-.f64 (atan.f64 N) (atan.f64 (-.f64 1 (.f64 -1 N)))) (.f64 (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (-.f64 1 (.f64 -1 N)))) (-.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) (+.f64 1 (atan.f64 N))))))
(-.f64 (pow.f64 (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (-.f64 1 (.f64 -1 N)))) 2) (.f64 (-.f64 (atan.f64 N) (atan.f64 (-.f64 1 (.f64 -1 N)))) (.f64 (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (-.f64 1 (.f64 -1 N)))) (-.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) (+.f64 1 (atan.f64 N))))))
(-.f64 (pow.f64 (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (-.f64 1 (.f64 -1 N)))) 2) (.f64 (-.f64 (atan.f64 N) (atan.f64 (-.f64 1 (.f64 -1 N)))) (.f64 (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (-.f64 1 (.f64 -1 N)))) (-.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) (+.f64 1 (atan.f64 N))))))
(-.f64 (pow.f64 (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (-.f64 1 (.f64 -1 N)))) 2) (.f64 (-.f64 (atan.f64 N) (atan.f64 (-.f64 1 (.f64 -1 N)))) (.f64 (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (-.f64 1 (.f64 -1 N)))) (-.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) (+.f64 1 (atan.f64 N))))))
(*.f64 (pow.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 2) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2))
(*.f64 (pow.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 2) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2))
(*.f64 (pow.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 2) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2))
(*.f64 (pow.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 2) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2))
(*.f64 (pow.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 2) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2))
(*.f64 (pow.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 2) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2))
(*.f64 (pow.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 2) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2))
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(.f64 (pow.f64 (-.f64 (atan.f64 N) (atan.f64 (-.f64 1 (.f64 -1 N)))) 2) (pow.f64 (-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (+.f64 1 (atan.f64 N))) 2))
(.f64 (pow.f64 (-.f64 (atan.f64 N) (atan.f64 (-.f64 1 (.f64 -1 N)))) 2) (pow.f64 (-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (+.f64 1 (atan.f64 N))) 2))
(.f64 (pow.f64 (-.f64 (atan.f64 N) (atan.f64 (-.f64 1 (.f64 -1 N)))) 2) (pow.f64 (-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (+.f64 1 (atan.f64 N))) 2))
(.f64 (pow.f64 (-.f64 (atan.f64 N) (atan.f64 (-.f64 1 (.f64 -1 N)))) 2) (pow.f64 (-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (+.f64 1 (atan.f64 N))) 2))
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(*.f64 -1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
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(/.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 1)
(/.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -1)
(/.f64 (+.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) -2)
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(if (!=.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) 0) (/.f64 (-.f64 (.f64 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1)))))) (.f64 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (.f64 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1)))))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1)))))))
(if (!=.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1)))))) 0) (/.f64 (-.f64 (.f64 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (.f64 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1)))))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1)))))))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1)))))))

Outputs
(-.f64 (atan.f64 N) (atan.f64 (-.f64 1 (*.f64 -1 N))))
(-.f64 (atan.f64 N) (atan.f64 (-.f64 1 (*.f64 N -1))))
(-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))
(-.f64 (atan.f64 N) (atan.f64 (-.f64 1 (*.f64 -1 N))))
(-.f64 (atan.f64 N) (atan.f64 (-.f64 1 (*.f64 N -1))))
(-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))
(-.f64 (atan.f64 N) (atan.f64 (-.f64 1 (*.f64 -1 N))))
(-.f64 (atan.f64 N) (atan.f64 (-.f64 1 (*.f64 N -1))))
(-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))
(-.f64 (atan.f64 N) (atan.f64 (-.f64 1 (*.f64 -1 N))))
(-.f64 (atan.f64 N) (atan.f64 (-.f64 1 (*.f64 N -1))))
(-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))
(-.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))))) (*.f64 (pow.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 2) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2)))
(-.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 (atan.f64 N) 1)) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (pow.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 (atan.f64 N) 1))) 2))
(-.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (pow.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))) 2))
(-.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))))) (*.f64 (pow.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 2) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2)))
(-.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 (atan.f64 N) 1)) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (pow.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 (atan.f64 N) 1))) 2))
(-.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (pow.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))) 2))
(-.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))))) (*.f64 (pow.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 2) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2)))
(-.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 (atan.f64 N) 1)) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (pow.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 (atan.f64 N) 1))) 2))
(-.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (pow.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))) 2))
(-.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))))) (*.f64 (pow.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 2) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2)))
(-.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 (atan.f64 N) 1)) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (pow.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 (atan.f64 N) 1))) 2))
(-.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (pow.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))) 2))
(-.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))))) (*.f64 (pow.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 2) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2)))
(-.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 (atan.f64 N) 1)) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (pow.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 (atan.f64 N) 1))) 2))
(-.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (pow.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))) 2))
(-.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))))) (*.f64 (pow.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 2) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2)))
(-.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 (atan.f64 N) 1)) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (pow.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 (atan.f64 N) 1))) 2))
(-.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (pow.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))) 2))
(-.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))))) (*.f64 (pow.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 2) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2)))
(-.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 (atan.f64 N) 1)) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (pow.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 (atan.f64 N) 1))) 2))
(-.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (pow.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))) 2))
(-.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))))) (*.f64 (pow.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 2) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2)))
(-.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 (atan.f64 N) 1)) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (pow.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 (atan.f64 N) 1))) 2))
(-.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (pow.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))) 2))
(-.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (-.f64 1 (.f64 -1 N)))) (.f64 (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (-.f64 1 (.f64 -1 N)))) (-.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) (+.f64 1 (atan.f64 N))))) (.f64 (pow.f64 (-.f64 (atan.f64 N) (atan.f64 (-.f64 1 (.f64 -1 N)))) 2) (pow.f64 (-.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) (+.f64 1 (atan.f64 N))) 2)))
(-.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 (atan.f64 N) 1)) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (pow.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 (atan.f64 N) 1))) 2))
(-.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (pow.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))) 2))
(-.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (-.f64 1 (.f64 -1 N)))) (.f64 (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (-.f64 1 (.f64 -1 N)))) (-.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) (+.f64 1 (atan.f64 N))))) (.f64 (pow.f64 (-.f64 (atan.f64 N) (atan.f64 (-.f64 1 (.f64 -1 N)))) 2) (pow.f64 (-.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) (+.f64 1 (atan.f64 N))) 2)))
(-.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 (atan.f64 N) 1)) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (pow.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 (atan.f64 N) 1))) 2))
(-.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (pow.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))) 2))
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(if (!=.f64 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1)))))) 0) (/.f64 (-.f64 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1)))))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1)))))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1)))) (.f64 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1)))))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1)))))))

localize45.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
✓	0.0b	(*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1)))
	1.7b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
✓	1.7b	(-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N)))

Compiler

Compiled 128 to 76 computations (40.6% saved)

series5.0ms (0%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	N	@	-inf	(-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N)))
1.0ms	N	@	0	(-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N)))
1.0ms	N	@	inf	(/.f64 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
1.0ms	N	@	-inf	(/.f64 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
1.0ms	N	@	inf	(-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N)))

rewrite117.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

936×	`rational_best-simplify-111`
812×	`rational_best-simplify-96`
704×	`rational_best-simplify-61`
678×	`rational_best-simplify-65`
600×	`rational_best-simplify-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	147
1	54	147
2	324	147
3	2142	147

Stop Event

1×	node limit

Counts

3 → 41

Calls

Call 1

Inputs

(-.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (*.f64 (atan.f64 N) (atan.f64 N)))

(*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1)))

(/.f64 (-.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (*.f64 (atan.f64 N) (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))

Outputs

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((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (neg.f64 (atan.f64 (+.f64 N 1))) 0) (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (*.f64 (atan.f64 (+.f64 N 1)) 0))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (*.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (neg.f64 (atan.f64 (+.f64 N 1))) 0) (*.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (atan.f64 (+.f64 N 1)) 0) (*.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 (+.f64 N 1)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1)))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 (+.f64 N 1)))) (*.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 (+.f64 N 1))))) (*.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (*.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (atan.f64 (+.f64 N 1)) (fabs.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (fabs.f64 (atan.f64 (+.f64 N 1))) (atan.f64 (+.f64 N 1))))))))

((#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (/.f64 (-.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (*.f64 (atan.f64 N) (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))))

simplify85.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1166×	`rational_best-simplify-61`
820×	`rational_best-simplify-3`
594×	`rational_best-simplify-62`
558×	`rational_best-simplify-53`
504×	`rational_best-simplify-1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	132	3407
1	679	2941
2	4585	2941

Stop Event

1×	node limit

Counts

77 → 52

Calls

Call 1

Inputs
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(pow.f64 (atan.f64 (+.f64 N 1)) 2)
(pow.f64 (atan.f64 (+.f64 N 1)) 2)
(pow.f64 (atan.f64 (+.f64 N 1)) 2)
(pow.f64 (atan.f64 (+.f64 N 1)) 2)
(pow.f64 (atan.f64 (+.f64 N 1)) 2)
(pow.f64 (atan.f64 (+.f64 N 1)) 2)
(pow.f64 (atan.f64 (+.f64 N 1)) 2)
(pow.f64 (atan.f64 (+.f64 N 1)) 2)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2)
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (-.f64 1 (.f64 -1 N)))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (-.f64 1 (.f64 -1 N)))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (-.f64 1 (.f64 -1 N)))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (-.f64 1 (.f64 -1 N)))))
(+.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (neg.f64 (atan.f64 N))))
(+.f64 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N))) 0)
(+.f64 (.f64 (atan.f64 N) (neg.f64 (atan.f64 N))) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))
(+.f64 0 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N))))
(.f64 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (*.f64 (atan.f64 N) (atan.f64 N))) 1)
(.f64 (-.f64 (.f64 (atan.f64 N) (atan.f64 N)) (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1)))) -1)
(.f64 -1 (-.f64 (.f64 (atan.f64 N) (atan.f64 N)) (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1)))))
(/.f64 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N))) 1)
(/.f64 (-.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1)))) -1)
(/.f64 (+.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (-.f64 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N))) (.f64 (atan.f64 N) (atan.f64 N)))) 2)
(/.f64 (+.f64 (-.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1)))) (-.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))) -2)
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Outputs
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(/.f64 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))

eval996.0ms (7.1%)

Compiler: Compiled 67519 to 45499 computations (32.6% saved)

prune140.0ms (1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	550	9	559
Fresh	0	0	0
Picked	1	0	1
Done	1	1	2
Total	552	10	562

Error

15.6b

Counts

562 → 10

Alt Table

Click to see full alt table

Status	Error	Program
▶	31.7b	(if (!=.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0) (/.f64 (if (!=.f64 (+.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N))) 0) (/.f64 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N)))) (+.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N)))) (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N)))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
▶	15.7b	(if (!=.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0) (/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
▶	16.2b	(if (!=.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0) (/.f64 (-.f64 (/.f64 (.f64 (.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 (+.f64 N 1)))) (.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 (+.f64 N 1))))) (.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1))))) (*.f64 (atan.f64 N) (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
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▶	17.2b	(/.f64 (-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (-.f64 (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (atan.f64 N)) (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (atan.f64 (+.f64 N 1))))) (-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))))
	16.5b	(/.f64 (-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (if (!=.f64 (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (+.f64 -1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) 0) (/.f64 (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (.f64 (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1)))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))))) (.f64 (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (+.f64 -1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 (atan.f64 N) 1)))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1)))))))
▶	32.3b	(/.f64 (-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (/.f64 (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))) (+.f64 (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))) -1)))
	15.8b	(/.f64 (-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (*.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))))
	16.7b	(/.f64 (.f64 (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1)))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) (-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))))
✓	15.7b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 2272 to 1564 computations (31.2% saved)

localize41.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
✓	0.0b	(pow.f64 (atan.f64 (+.f64 N 1)) 2)
	1.7b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
✓	1.7b	(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))

Compiler

Compiled 113 to 76 computations (32.7% saved)

series1.0ms (0%)

Counts

3 → 20

Calls

9 calls:

Time	Variable		Point	Expression
0.0ms	N	@	-inf	(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
0.0ms	N	@	inf	(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
0.0ms	N	@	0	(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
0.0ms	N	@	0	(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
0.0ms	N	@	inf	(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))

rewrite57.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

862×	`rational_best-simplify-111`
750×	`rational_best-simplify-113`
666×	`rational_best-simplify-96`
658×	`rational_best-simplify-61`
628×	`rational_best-simplify-65`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	109
1	53	109
2	309	109
3	2023	109

Stop Event

1×	node limit

Counts

3 → 32

Calls

Call 1

Inputs

(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))

(pow.f64 (atan.f64 (+.f64 N 1)) 2)

(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (neg.f64 (pow.f64 (atan.f64 N) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (pow.f64 (atan.f64 N) 2)) (pow.f64 (atan.f64 (+.f64 N 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (pow.f64 (atan.f64 N) 2)) (+.f64 0 (pow.f64 (atan.f64 (+.f64 N 1)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (pow.f64 (atan.f64 N) 2)) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (-.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (pow.f64 (atan.f64 N) 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)) (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)) (-.f64 -1 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)))) (+.f64 1 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (+.f64 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)) (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2))) (+.f64 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)) (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)))) -4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)) (-.f64 -1 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)))) (*.f64 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)) (-.f64 -1 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2))))) (+.f64 (+.f64 1 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2))) (+.f64 1 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) 0) (/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (pow.f64 (atan.f64 N) 2) 0) (/.f64 (-.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2) (pow.f64 (atan.f64 N) 4)) (pow.f64 (atan.f64 N) 2)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 0) (/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2)) (pow.f64 (atan.f64 (+.f64 N 1)) 2)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (-.f64 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2)) (pow.f64 (atan.f64 N) 2)) 0) (/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2)) 0) (/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2)) (pow.f64 (atan.f64 (+.f64 N 1)) 2)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)) 0) (/.f64 (*.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (neg.f64 (pow.f64 (atan.f64 N) 2)) 0) (/.f64 (-.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2) (pow.f64 (atan.f64 N) 4)) (pow.f64 (atan.f64 N) 2)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 0 0) (/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) 0)) 0) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2)))))))

()

simplify62.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

824×	`rational_best-simplify-96`
820×	`rational_best-simplify-61`
810×	`rational_best-simplify-65`
482×	`rational_best-simplify-3`
474×	`rational_best-simplify-62`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	100	2108
1	472	1868
2	3329	1868

Stop Event

1×	node limit

Counts

52 → 39

Calls

Call 1

Inputs
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2)
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (-.f64 1 (.f64 -1 N)))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (-.f64 1 (.f64 -1 N)))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (-.f64 1 (.f64 -1 N)))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (-.f64 1 (.f64 -1 N)))))
(+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (neg.f64 (pow.f64 (atan.f64 N) 2)))
(+.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) 0)
(+.f64 (neg.f64 (pow.f64 (atan.f64 N) 2)) (pow.f64 (atan.f64 (+.f64 N 1)) 2))
(+.f64 (neg.f64 (pow.f64 (atan.f64 N) 2)) (+.f64 0 (pow.f64 (atan.f64 (+.f64 N 1)) 2)))
(+.f64 (neg.f64 (pow.f64 (atan.f64 N) 2)) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 0))
(+.f64 0 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)))
(*.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) 1)
(*.f64 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)) -1)
(*.f64 -1 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) 1)
(/.f64 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)) -1)
(/.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (-.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (pow.f64 (atan.f64 N) 2))) 2)
(/.f64 (+.f64 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)) (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2))) -2)
(/.f64 (*.f64 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)) (-.f64 -1 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)))) (+.f64 1 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2))))
(/.f64 (+.f64 (+.f64 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)) (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2))) (+.f64 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)) (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)))) -4)
(/.f64 (+.f64 (.f64 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)) (-.f64 -1 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)))) (.f64 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)) (-.f64 -1 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2))))) (+.f64 (+.f64 1 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2))) (+.f64 1 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)))))
(pow.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) 1)
(neg.f64 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)))
(if (!=.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) 0) (/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)))
(if (!=.f64 (pow.f64 (atan.f64 N) 2) 0) (/.f64 (-.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2) (pow.f64 (atan.f64 N) 4)) (pow.f64 (atan.f64 N) 2)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)))
(if (!=.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 0) (/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2)) (pow.f64 (atan.f64 (+.f64 N 1)) 2)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)))
(if (!=.f64 (-.f64 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2)) (pow.f64 (atan.f64 N) 2)) 0) (/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)))
(if (!=.f64 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2)) 0) (/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2)) (pow.f64 (atan.f64 (+.f64 N 1)) 2)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)))
(if (!=.f64 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)) 0) (/.f64 (*.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)))
(if (!=.f64 (neg.f64 (pow.f64 (atan.f64 N) 2)) 0) (/.f64 (-.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2) (pow.f64 (atan.f64 N) 4)) (pow.f64 (atan.f64 N) 2)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)))
(if (!=.f64 0 0) (/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) 0)) 0) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 0)
(-.f64 0 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2)))
(*.f64 -1 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2)))
(*.f64 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2)) -1)
(/.f64 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2)) -1)
(neg.f64 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2)))

Outputs
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2) (pow.f64 (atan.f64 N) 2))
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2)
(pow.f64 (atan.f64 (+.f64 1 N)) 2)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2)
(pow.f64 (atan.f64 (+.f64 1 N)) 2)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2)
(pow.f64 (atan.f64 (+.f64 1 N)) 2)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2)
(pow.f64 (atan.f64 (+.f64 1 N)) 2)
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 1 N))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 1 N))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 1 N))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 1 N))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 1 N))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 1 N))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 1 N))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 1 N))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (-.f64 1 (.f64 -1 N)))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 1 N))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (-.f64 1 (.f64 -1 N)))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 1 N))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (-.f64 1 (.f64 -1 N)))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 1 N))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (-.f64 1 (.f64 -1 N)))))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 N) (atan.f64 (+.f64 1 N))))
(+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (neg.f64 (pow.f64 (atan.f64 N) 2)))
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(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2) (pow.f64 (atan.f64 N) 2))
(+.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) 0)
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(+.f64 (neg.f64 (pow.f64 (atan.f64 N) 2)) (pow.f64 (atan.f64 (+.f64 N 1)) 2))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2) (pow.f64 (atan.f64 N) 2))
(+.f64 (neg.f64 (pow.f64 (atan.f64 N) 2)) (+.f64 0 (pow.f64 (atan.f64 (+.f64 N 1)) 2)))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2) (pow.f64 (atan.f64 N) 2))
(+.f64 (neg.f64 (pow.f64 (atan.f64 N) 2)) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 0))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2) (pow.f64 (atan.f64 N) 2))
(+.f64 0 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2) (pow.f64 (atan.f64 N) 2))
(*.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) 1)
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2) (pow.f64 (atan.f64 N) 2))
(*.f64 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)) -1)
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2) (pow.f64 (atan.f64 N) 2))
(*.f64 -1 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2) (pow.f64 (atan.f64 N) 2))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) 1)
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(/.f64 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)) -1)
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(/.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (-.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (pow.f64 (atan.f64 N) 2))) 2)
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2) (pow.f64 (atan.f64 N) 2))
(/.f64 (+.f64 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)) (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2))) -2)
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
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(/.f64 (*.f64 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)) (-.f64 -1 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)))) (+.f64 1 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2))))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2) (pow.f64 (atan.f64 N) 2))
(/.f64 (+.f64 (+.f64 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)) (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2))) (+.f64 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)) (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)))) -4)
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
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(/.f64 (+.f64 (.f64 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)) (-.f64 -1 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)))) (.f64 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)) (-.f64 -1 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2))))) (+.f64 (+.f64 1 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2))) (+.f64 1 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)))))
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(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2) (pow.f64 (atan.f64 N) 2))
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(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2) (pow.f64 (atan.f64 N) 2))
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(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2) (pow.f64 (atan.f64 N) 2))
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(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2) (pow.f64 (atan.f64 N) 2))
(if (!=.f64 (-.f64 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2)) (pow.f64 (atan.f64 N) 2)) 0) (/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2) (pow.f64 (atan.f64 N) 2))
(if (!=.f64 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2)) 0) (/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2)) (pow.f64 (atan.f64 (+.f64 N 1)) 2)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2) (pow.f64 (atan.f64 N) 2))
(if (!=.f64 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2)) 0) (/.f64 (*.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2) (pow.f64 (atan.f64 N) 2))
(if (!=.f64 (neg.f64 (pow.f64 (atan.f64 N) 2)) 0) (/.f64 (-.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2) (pow.f64 (atan.f64 N) 4)) (pow.f64 (atan.f64 N) 2)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2) (pow.f64 (atan.f64 N) 2))
(if (!=.f64 0 0) (/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) 0)) 0) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 0)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2)
(pow.f64 (atan.f64 (+.f64 1 N)) 2)
(-.f64 0 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2)))
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2)
(pow.f64 (atan.f64 (+.f64 1 N)) 2)
(*.f64 -1 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2)))
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2)
(pow.f64 (atan.f64 (+.f64 1 N)) 2)
(*.f64 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2)) -1)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2)
(pow.f64 (atan.f64 (+.f64 1 N)) 2)
(/.f64 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2)) -1)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2)
(pow.f64 (atan.f64 (+.f64 1 N)) 2)
(neg.f64 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2)))
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2)
(pow.f64 (atan.f64 (+.f64 1 N)) 2)

localize106.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 (+.f64 N 1)))) (*.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 (+.f64 N 1)))))
✓	0.7b	(*.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1))))
	1.7b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
✓	17.6b	(-.f64 (/.f64 (.f64 (.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 (+.f64 N 1)))) (.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 (+.f64 N 1))))) (.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1))))) (*.f64 (atan.f64 N) (atan.f64 N)))

Compiler

Compiled 300 to 222 computations (26% saved)

series3.0ms (0%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
0.0ms	N	@	inf	(*.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1))))
0.0ms	N	@	-inf	(*.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1))))
0.0ms	N	@	-inf	(.f64 (.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 (+.f64 N 1)))) (*.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 (+.f64 N 1)))))
0.0ms	N	@	inf	(.f64 (.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 (+.f64 N 1)))) (*.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 (+.f64 N 1)))))
0.0ms	N	@	0	(.f64 (.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 (+.f64 N 1)))) (*.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 (+.f64 N 1)))))

rewrite81.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1084×	`rational_best-simplify-61`
1064×	`rational_best-simplify-65`
922×	`rational_best-simplify-3`
638×	`rational_best-simplify-93`
554×	`rational_best-simplify-53`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	17	245
1	87	245
2	474	157
3	3486	157

Stop Event

1×	node limit

Counts

3 → 48

Calls

Call 1

Inputs

(-.f64 (/.f64 (*.f64 (*.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 (+.f64 N 1)))) (*.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 (+.f64 N 1))))) (*.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1))))) (*.f64 (atan.f64 N) (atan.f64 N)))

(*.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1))))

(*.f64 (*.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 (+.f64 N 1)))) (*.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 (+.f64 N 1)))))

Outputs

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(atan.f64 (+.f64 N 1)))))) (*.f64 (atan.f64 (+.f64 N 1)) (*.f64 (atan.f64 (+.f64 N 1)) (*.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) (-.f64 -1 (atan.f64 (+.f64 N 1)))))))))))

simplify90.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1152×	`rational_best-simplify-3`
638×	`rational_best-simplify-53`
626×	`rational_best-simplify-1`
554×	`rational_best-simplify-56`
438×	`rational_best-simplify-47`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	153	4436
1	810	3604
2	5151	3604

Stop Event

1×	node limit

Counts

84 → 59

Calls

Call 1

Inputs
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2)
(pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2)
(pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2)
(pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2)
(pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2)
(pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2)
(pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2)
(pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2)
(pow.f64 (+.f64 1 (atan.f64 (-.f64 1 (*.f64 -1 N)))) 2)
(pow.f64 (+.f64 1 (atan.f64 (-.f64 1 (*.f64 -1 N)))) 2)
(pow.f64 (+.f64 1 (atan.f64 (-.f64 1 (*.f64 -1 N)))) 2)
(pow.f64 (+.f64 1 (atan.f64 (-.f64 1 (*.f64 -1 N)))) 2)
(*.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2))
(*.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2))
(*.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2))
(*.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2))
(*.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2))
(*.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2))
(*.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2))
(*.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2))
(.f64 (pow.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) 2) (pow.f64 (+.f64 1 (atan.f64 (-.f64 1 (*.f64 -1 N)))) 2))
(.f64 (pow.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) 2) (pow.f64 (+.f64 1 (atan.f64 (-.f64 1 (*.f64 -1 N)))) 2))
(.f64 (pow.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) 2) (pow.f64 (+.f64 1 (atan.f64 (-.f64 1 (*.f64 -1 N)))) 2))
(.f64 (pow.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) 2) (pow.f64 (+.f64 1 (atan.f64 (-.f64 1 (*.f64 -1 N)))) 2))
(+.f64 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N))) 0)
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(+.f64 0 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N))))
(.f64 -1 (-.f64 (.f64 (atan.f64 N) (atan.f64 N)) (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1)))))
(.f64 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (*.f64 (atan.f64 N) (atan.f64 N))) 1)
(.f64 (-.f64 (.f64 (atan.f64 N) (atan.f64 N)) (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1)))) -1)
(/.f64 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N))) 1)
(/.f64 (-.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1)))) -1)
(/.f64 (+.f64 (-.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1)))) (-.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))) -2)
(/.f64 (-.f64 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N))) (.f64 (-.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1)))) (-.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1)))))) (+.f64 1 (-.f64 (.f64 (atan.f64 N) (atan.f64 N)) (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))))
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(if (!=.f64 (.f64 (atan.f64 N) (atan.f64 N)) 0) (.f64 (+.f64 (atan.f64 N) (/.f64 0 (atan.f64 N))) (/.f64 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N))) (atan.f64 N))) (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N))))
(if (!=.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) 0) (/.f64 (.f64 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N))) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1)))) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1)))) (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N))))
(if (!=.f64 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 (+.f64 N 1)))) (.f64 (atan.f64 N) (atan.f64 N))) 0) (/.f64 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N)))) (+.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))) (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N))))
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Outputs
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
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(if (!=.f64 (+.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1))))) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 (+.f64 N 1))))))) 0) (/.f64 (-.f64 (.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1))))) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))))) (.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 (+.f64 N 1)))))) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 (+.f64 N 1)))))))) (+.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1))))) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 (+.f64 N 1)))))))) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (*.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) (-.f64 -1 (atan.f64 (+.f64 N 1)))))))
(+.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1))))) (.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1))))))
(.f64 (atan.f64 (+.f64 N 1)) (.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) (*.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 (+.f64 N 1))))))
(if (!=.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 (+.f64 N 1)))))) 0) (/.f64 (-.f64 (.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1))))) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 (+.f64 N 1))))))) (.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 (+.f64 N 1)))))) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 (+.f64 N 1)))))))) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 (+.f64 N 1))))))) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) (-.f64 -1 (atan.f64 (+.f64 N 1)))))))
(+.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1))))) (.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1))))))
(.f64 (atan.f64 (+.f64 N 1)) (.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) (*.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 (+.f64 N 1))))))
(if (!=.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1))))) 0) (/.f64 (-.f64 (.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1))))) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))))) (.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1))))) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 (+.f64 N 1)))))))) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))))) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) (-.f64 -1 (atan.f64 (+.f64 N 1)))))))
(+.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1))))) (.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1))))))
(.f64 (atan.f64 (+.f64 N 1)) (.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) (*.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 (+.f64 N 1))))))

localize143.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))
	1.7b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
	1.7b	(-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N)))
✓	29.9b	(-.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N))))

Compiler

Compiled 492 to 278 computations (43.5% saved)

series4.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	N	@	0	(-.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N))))
1.0ms	N	@	-inf	(-.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N))))
1.0ms	N	@	inf	(-.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N))))
0.0ms	N	@	inf	(.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))
0.0ms	N	@	-inf	(.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))

rewrite84.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1260×	`rational_best-simplify-113`
630×	`rational_best-simplify-96`
622×	`rational_best-simplify-117`
522×	`rational_best-simplify-65`
500×	`rational_best-simplify-61`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	142
1	52	142
2	243	142
3	1560	142

Stop Event

1×	node limit

Counts

2 → 48

Calls

Call 1

Inputs

(-.f64 (*.f64 (atan.f64 (+.f64 N 1)) (*.f64 (atan.f64 (+.f64 N 1)) (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))) (*.f64 (*.f64 (atan.f64 N) (atan.f64 N)) (*.f64 (atan.f64 N) (atan.f64 N))))

(*.f64 (atan.f64 (+.f64 N 1)) (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))

Outputs

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simplify85.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

496×	`rational_best-simplify-124`
490×	`rational_best-simplify-126`
490×	`rational_best-simplify-127`
464×	`rational_best-simplify-61`
460×	`rational_best-simplify-65`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	207	6134
1	1253	5924

Stop Event

1×	node limit

Counts

72 → 66

Calls

Call 1

Inputs
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(pow.f64 (atan.f64 (+.f64 N 1)) 3)
(pow.f64 (atan.f64 (+.f64 N 1)) 3)
(pow.f64 (atan.f64 (+.f64 N 1)) 3)
(pow.f64 (atan.f64 (+.f64 N 1)) 3)
(pow.f64 (atan.f64 (+.f64 N 1)) 3)
(pow.f64 (atan.f64 (+.f64 N 1)) 3)
(pow.f64 (atan.f64 (+.f64 N 1)) 3)
(pow.f64 (atan.f64 (+.f64 N 1)) 3)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 3)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 3)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 3)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 3)
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(+.f64 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N)))) 0)
(+.f64 (.f64 (atan.f64 N) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (neg.f64 (atan.f64 N)))) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))))
(+.f64 (.f64 (atan.f64 N) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (neg.f64 (atan.f64 N)))) (+.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))) 0))
(+.f64 (.f64 (atan.f64 N) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (neg.f64 (atan.f64 N)))) (+.f64 0 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1)))))))
(+.f64 0 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N)))))
(.f64 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (*.f64 (atan.f64 N) (atan.f64 N)))) 1)
(.f64 (-.f64 (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N))) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1)))))) -1)
(.f64 -1 (-.f64 (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N))) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1)))))))
(/.f64 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N)))) 1)
(/.f64 (-.f64 (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N))) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1)))))) -1)
(/.f64 (+.f64 (-.f64 (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N))) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1)))))) (-.f64 (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N))) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))))) -2)
(/.f64 (.f64 (-.f64 (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N))) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1)))))) (-.f64 -1 (-.f64 (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N))) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1)))))))) (-.f64 1 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (*.f64 (atan.f64 N) (atan.f64 N))))))
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Outputs
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(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))
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(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
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localize183.0ms (1.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (-.f64 (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (atan.f64 N)) (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (atan.f64 (+.f64 N 1)))))
✓	0.7b	(-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1)))
	1.7b	(-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))
✓	1.7b	(-.f64 (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (atan.f64 N)) (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (atan.f64 (+.f64 N 1))))

Compiler

Compiled 562 to 376 computations (33.1% saved)

series9.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
4.0ms	N	@	inf	(-.f64 (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (atan.f64 N)) (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (atan.f64 (+.f64 N 1))))
1.0ms	N	@	0	(-.f64 (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (atan.f64 N)) (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (atan.f64 (+.f64 N 1))))
1.0ms	N	@	-inf	(-.f64 (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (atan.f64 N)) (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (atan.f64 (+.f64 N 1))))
1.0ms	N	@	-inf	(-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (-.f64 (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (atan.f64 N)) (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (atan.f64 (+.f64 N 1)))))
1.0ms	N	@	inf	(-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (-.f64 (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (atan.f64 N)) (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (atan.f64 (+.f64 N 1)))))

rewrite132.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

876×	`rational_best-simplify-52`
822×	`rational_best-simplify-1`
608×	`rational_best-simplify-21`
606×	`rational_best-simplify-20`
604×	`rational_best-simplify-18`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	339
1	147	339
2	894	255
3	5844	255

Stop Event

1×	node limit

Counts

3 → 104

Calls

Call 1

Inputs

(-.f64 (*.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (*.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (atan.f64 N)) (*.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (*.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (atan.f64 (+.f64 N 1))))

(-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1)))

(-.f64 (*.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (-.f64 (*.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (*.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (atan.f64 N)) (*.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (*.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (atan.f64 (+.f64 N 1)))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (*.f64 (atan.f64 N) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))) (*.f64 (atan.f64 (+.f64 N 1)) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (atan.f64 (+.f64 N 1)) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) (*.f64 (-.f64 (atan.f64 N) (atan.f64 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(#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) (*.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 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simplify143.0ms (1%)

Algorithm

1×	egg-herbie

Rules

744×	`rational_best-simplify-113`
568×	`rational_best-simplify-124`
564×	`rational_best-simplify-126`
530×	`rational_best-simplify-65`
516×	`rational_best-simplify-61`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	298	23912
1	1560	19642

Stop Event

1×	node limit

Counts

140 → 150

Calls

Call 1

Inputs
(-.f64 (.f64 (atan.f64 N) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (pow.f64 (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))) 2))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 (+.f64 N 1)) (pow.f64 (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))) 2))))
(-.f64 (.f64 (atan.f64 N) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (pow.f64 (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))) 2))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 (+.f64 N 1)) (pow.f64 (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))) 2))))
(-.f64 (.f64 (atan.f64 N) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (pow.f64 (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))) 2))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 (+.f64 N 1)) (pow.f64 (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))) 2))))
(-.f64 (.f64 (atan.f64 N) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (pow.f64 (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))) 2))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 (+.f64 N 1)) (pow.f64 (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))) 2))))
(-.f64 (.f64 (atan.f64 N) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (pow.f64 (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))) 2))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 (+.f64 N 1)) (pow.f64 (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))) 2))))
(-.f64 (.f64 (atan.f64 N) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (pow.f64 (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))) 2))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 (+.f64 N 1)) (pow.f64 (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))) 2))))
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Outputs
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(-.f64 (.f64 (atan.f64 N) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (pow.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) 2))) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (pow.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) 2))))
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(-.f64 (.f64 (atan.f64 N) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (pow.f64 (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))) 2))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 (+.f64 N 1)) (pow.f64 (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1))) 2))))
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(if (!=.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) 0) (/.f64 (-.f64 (.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) 0) (.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))
(+.f64 0 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))
(.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (*.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))))
(if (!=.f64 0 0) (/.f64 (neg.f64 (.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) 0)) 0) (.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))
(+.f64 0 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))
(.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (*.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))))

localize234.0ms (1.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.7b	(-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1)))
	1.7b	(-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))
✓	17.3b	(+.f64 (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))) -1)
✓	17.7b	(-.f64 (.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))

Compiler

Compiled 768 to 526 computations (31.5% saved)

series4.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	N	@	-inf	(-.f64 (.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))
1.0ms	N	@	inf	(-.f64 (.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))
1.0ms	N	@	0	(-.f64 (.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))
0.0ms	N	@	-inf	(+.f64 (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))) -1)
0.0ms	N	@	inf	(+.f64 (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))) -1)

rewrite91.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1152×	`rational_best-simplify-61`
1112×	`rational_best-simplify-65`
984×	`rational_best-simplify-3`
696×	`rational_best-simplify-53`
614×	`rational_best-simplify-62`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	316
1	101	316
2	590	284
3	3715	284

Stop Event

1×	node limit

Counts

2 → 46

Calls

Call 1

Inputs

(-.f64 (*.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))) (*.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))

(+.f64 (*.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))) -1)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 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(-.f64 -1 (atan.f64 N))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 1 (-.f64 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simplify140.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1068×	`rational_best-simplify-3`
712×	`rational_best-simplify-53`
606×	`rational_best-simplify-1`
396×	`rational_best-simplify-21`
390×	`rational_best-simplify-47`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	148	12888
1	756	12216
2	5643	12164

Stop Event

1×	node limit

Counts

70 → 78

Calls

Call 1

Inputs
(-.f64 (*.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 4) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1)))) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2))
(-.f64 (*.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 4) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1)))) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2))
(-.f64 (*.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 4) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1)))) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2))
(-.f64 (*.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 4) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1)))) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2))
(-.f64 (*.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 4) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1)))) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2))
(-.f64 (*.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 4) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1)))) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2))
(-.f64 (*.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 4) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1)))) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2))
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(/.f64 (-.f64 (+.f64 -1 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (.f64 (+.f64 -1 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (+.f64 -1 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))))) (+.f64 1 (+.f64 1 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))))))
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(neg.f64 (.f64 (+.f64 1 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))) 1))
(if (!=.f64 -1 0) (+.f64 -1 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (+.f64 -1 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))))
(if (!=.f64 (+.f64 -1 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))) 0) (/.f64 (+.f64 1 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))))))) (+.f64 -1 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))))) (+.f64 -1 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))))
(if (!=.f64 (+.f64 1 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) 0) (/.f64 (+.f64 1 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))))))) (+.f64 -1 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))))) (+.f64 -1 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))))
(if (!=.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))) 0) (/.f64 (.f64 (+.f64 -1 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))) (+.f64 -1 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))))
(if (!=.f64 1 0) (+.f64 -1 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (+.f64 -1 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))))
(if (!=.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) 0) (/.f64 (.f64 (+.f64 -1 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))) (+.f64 -1 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))))

Outputs
(-.f64 (*.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 4) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1)))) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2))
(-.f64 (*.f64 (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1)))) (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2))
(-.f64 (*.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4)) (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2))
(-.f64 (*.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (pow.f64 (+.f64 -1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 4)) (pow.f64 (+.f64 -1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2))
(-.f64 (*.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 4) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1)))) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2))
(-.f64 (*.f64 (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1)))) (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2))
(-.f64 (*.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4)) (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2))
(-.f64 (*.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (pow.f64 (+.f64 -1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 4)) (pow.f64 (+.f64 -1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2))
(-.f64 (*.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 4) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1)))) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2))
(-.f64 (*.f64 (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1)))) (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2))
(-.f64 (*.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4)) (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2))
(-.f64 (*.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (pow.f64 (+.f64 -1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 4)) (pow.f64 (+.f64 -1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2))
(-.f64 (*.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 4) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1)))) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2))
(-.f64 (*.f64 (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1)))) (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2))
(-.f64 (*.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4)) (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2))
(-.f64 (*.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (pow.f64 (+.f64 -1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 4)) (pow.f64 (+.f64 -1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2))
(-.f64 (*.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 4) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1)))) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2))
(-.f64 (*.f64 (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1)))) (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2))
(-.f64 (*.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4)) (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2))
(-.f64 (*.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (pow.f64 (+.f64 -1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 4)) (pow.f64 (+.f64 -1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2))
(-.f64 (*.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 4) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1)))) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2))
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(-.f64 (*.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (pow.f64 (+.f64 -1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 4)) (pow.f64 (+.f64 -1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2))
(-.f64 (*.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 4) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1)))) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2))
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(-.f64 (*.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4)) (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2))
(-.f64 (*.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (pow.f64 (+.f64 -1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 4)) (pow.f64 (+.f64 -1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2))
(-.f64 (*.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 4) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1)))) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2))
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(-.f64 (*.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4)) (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2))
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(-.f64 (*.f64 (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1)))) (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2))
(-.f64 (*.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4)) (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2))
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(-.f64 (.f64 (pow.f64 (-.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) (+.f64 1 (atan.f64 N))) 4) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (-.f64 1 (.f64 -1 N))))) (pow.f64 (-.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) (+.f64 1 (atan.f64 N))) 2))
(-.f64 (*.f64 (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1)))) (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2))
(-.f64 (*.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4)) (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2))
(-.f64 (*.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (pow.f64 (+.f64 -1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 4)) (pow.f64 (+.f64 -1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2))
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(if (!=.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))) 0) (/.f64 (.f64 (+.f64 -1 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))) (+.f64 -1 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))))
(-.f64 -1 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))))
(+.f64 -1 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))))
(-.f64 -1 (.f64 (+.f64 -1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (.f64 (+.f64 -1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (+.f64 -1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))
(if (!=.f64 1 0) (+.f64 -1 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (+.f64 -1 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))))
(-.f64 -1 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))))
(+.f64 -1 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))))
(-.f64 -1 (.f64 (+.f64 -1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (.f64 (+.f64 -1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (+.f64 -1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))
(if (!=.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) 0) (/.f64 (.f64 (+.f64 -1 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))) (+.f64 -1 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))))
(-.f64 -1 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))))
(+.f64 -1 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))))
(-.f64 -1 (.f64 (+.f64 -1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (.f64 (+.f64 -1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (+.f64 -1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))

eval2.5s (17.6%)

Compiler: Compiled 196760 to 133502 computations (32.1% saved)

prune370.0ms (2.6%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	1219	14	1233
Fresh	2	2	4
Picked	1	0	1
Done	3	2	5
Total	1225	18	1243

Error

15.4b

Counts

1243 → 18

Alt Table

Click to see full alt table

Status	Error	Program
	31.7b	(if (!=.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0) (/.f64 (if (!=.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 0) (/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2)) (pow.f64 (atan.f64 (+.f64 N 1)) 2)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
	31.4b	(if (!=.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0) (/.f64 (if (!=.f64 (pow.f64 (atan.f64 N) 2) 0) (/.f64 (-.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2) (pow.f64 (atan.f64 N) 4)) (pow.f64 (atan.f64 N) 2)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
▶	16.2b	(if (!=.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0) (/.f64 (if (!=.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) 0) (/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
	16.2b	(if (!=.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0) (/.f64 (if (!=.f64 (+.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N))) 0) (/.f64 (if (!=.f64 (+.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N)))) 0) (/.f64 (-.f64 (.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))))) (.f64 (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N))) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N))))) (+.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N))))) (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N))))) (+.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N)))) (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N)))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
	31.7b	(if (!=.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0) (/.f64 (if (!=.f64 (+.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N))) 0) (/.f64 (if (!=.f64 (+.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N)))) 0) (/.f64 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1)))))))) (.f64 (atan.f64 N) (.f64 (atan.f64 N) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N))))))) (+.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N))))) (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N))))) (+.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N)))) (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N)))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
	31.7b	(if (!=.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0) (/.f64 (if (!=.f64 (+.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N))) 0) (/.f64 (if (!=.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))) 0) (.f64 (.f64 1 (/.f64 (.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N))))) (atan.f64 (+.f64 N 1)))) (/.f64 1 (atan.f64 (+.f64 N 1)))) (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N))))) (+.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N)))) (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (*.f64 (atan.f64 N) (atan.f64 N)))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
	31.7b	(if (!=.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0) (/.f64 (if (!=.f64 (+.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N))) 0) (/.f64 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (pow.f64 (atan.f64 (+.f64 N 1)) 3)) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N)))) (+.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N)))) (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N)))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
	24.4b	(if (!=.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0) (/.f64 (if (!=.f64 (+.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N))) 0) (/.f64 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (/.f64 (.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (/.f64 1 (atan.f64 (+.f64 N 1))))) (-.f64 (.f64 (.f64 1 (atan.f64 (+.f64 N 1))) 1) (/.f64 (/.f64 1 (atan.f64 (+.f64 N 1))) (atan.f64 (+.f64 N 1)))))) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N)))) (+.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N)))) (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (*.f64 (atan.f64 N) (atan.f64 N)))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
✓	15.7b	(if (!=.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0) (/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
▶	16.2b	(if (!=.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0) (/.f64 (-.f64 (/.f64 (pow.f64 (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2) (.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1))))) (*.f64 (atan.f64 N) (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
	22.6b	(if (!=.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0) (/.f64 (-.f64 (/.f64 (.f64 (.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 (+.f64 N 1)))) (.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 (+.f64 N 1))))) (-.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 (+.f64 N 1)))))) (*.f64 (atan.f64 N) (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
▶	33.8b	(/.f64 (-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (-.f64 (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (/.f64 (-.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))) (-.f64 1 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (atan.f64 N)) (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (atan.f64 (+.f64 N 1))))) (-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))))
	16.5b	(/.f64 (-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (if (!=.f64 (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (+.f64 -1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) 0) (/.f64 (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (.f64 (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1)))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))))) (.f64 (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (+.f64 -1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 (atan.f64 N) 1)))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1)))))))
	32.3b	(/.f64 (-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (/.f64 (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))) (.f64 (if (!=.f64 (-.f64 -1 (atan.f64 N)) 0) (/.f64 (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (+.f64 (atan.f64 N) 1)) (+.f64 (atan.f64 N) 1)) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1)))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))) (+.f64 (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))) -1)))
	32.3b	(/.f64 (-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (/.f64 (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))) (.f64 (if (!=.f64 (atan.f64 (+.f64 N 1)) 0) (/.f64 (.f64 (atan.f64 (+.f64 N 1)) (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1))))) (atan.f64 (+.f64 N 1))) (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1))))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))) (+.f64 (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))) -1)))
▶	32.3b	(/.f64 (-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (/.f64 (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))) (+.f64 (.f64 (/.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1)))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))) -1)))
▶	15.8b	(/.f64 (-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (*.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))))
✓	15.7b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 4657 to 3098 computations (33.5% saved)

localize105.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))
	0.5b	(-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))))
	0.7b	(-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1)))
	1.7b	(-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))

Compiler

Compiled 334 to 223 computations (33.2% saved)

localize79.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2)
	0.7b	(*.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1))))
	1.7b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
✓	17.6b	(-.f64 (/.f64 (pow.f64 (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2) (.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1))))) (*.f64 (atan.f64 N) (atan.f64 N)))

Compiler

Compiled 244 to 177 computations (27.5% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	N	@	-inf	(pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2)
1.0ms	N	@	inf	(pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2)
0.0ms	N	@	0	(pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2)
0.0ms	N	@	0	(-.f64 (/.f64 (pow.f64 (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2) (.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1))))) (*.f64 (atan.f64 N) (atan.f64 N)))
0.0ms	N	@	-inf	(-.f64 (/.f64 (pow.f64 (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2) (.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1))))) (*.f64 (atan.f64 N) (atan.f64 N)))

rewrite59.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

878×	`rational_best-simplify-96`
740×	`rational_best-simplify-65`
726×	`rational_best-simplify-61`
636×	`rational_best-simplify-111`
580×	`rational_best-simplify-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	142
1	64	142
2	326	142
3	2171	142

Stop Event

1×	node limit

Counts

2 → 34

Calls

Call 1

Inputs

(-.f64 (/.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2) (*.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1))))) (*.f64 (atan.f64 N) (atan.f64 N)))

(pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2) (*.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1))))) (*.f64 (atan.f64 N) (neg.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (/.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2) (*.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1))))) (*.f64 (atan.f64 N) (atan.f64 N))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (atan.f64 N) (neg.f64 (atan.f64 N))) (/.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2) (*.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 (/.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2) (*.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1))))) (*.f64 (atan.f64 N) (atan.f64 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(atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (atan.f64 N) (atan.f64 N)) (/.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2) (*.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1)))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (-.f64 (*.f64 (atan.f64 N) (atan.f64 N)) (/.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2) (*.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1)))))) (-.f64 (*.f64 (atan.f64 N) (atan.f64 N)) (/.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2) (*.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1))))))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (*.f64 (atan.f64 N) (atan.f64 N)) (/.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2) (*.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1)))))) (-.f64 -1 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((#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (neg.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2)) (neg.f64 (pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2)) (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2)))))))

simplify75.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

986×	`rational_best-simplify-96`
932×	`rational_best-simplify-61`
884×	`rational_best-simplify-65`
644×	`rational_best-simplify-3`
476×	`rational_best-simplify-62`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	112	3726
1	508	3726
2	3208	3726

Stop Event

1×	node limit

Counts

58 → 39

Calls

Call 1

Inputs
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(*.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2))
(*.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2))
(*.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2))
(*.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2))
(*.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2))
(*.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2))
(*.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2))
(*.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2))
(.f64 (pow.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) 2) (pow.f64 (+.f64 1 (atan.f64 (-.f64 1 (*.f64 -1 N)))) 2))
(.f64 (pow.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) 2) (pow.f64 (+.f64 1 (atan.f64 (-.f64 1 (*.f64 -1 N)))) 2))
(.f64 (pow.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) 2) (pow.f64 (+.f64 1 (atan.f64 (-.f64 1 (*.f64 -1 N)))) 2))
(.f64 (pow.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) 2) (pow.f64 (+.f64 1 (atan.f64 (-.f64 1 (*.f64 -1 N)))) 2))
(+.f64 (/.f64 (pow.f64 (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2) (.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1))))) (*.f64 (atan.f64 N) (neg.f64 (atan.f64 N))))
(+.f64 (-.f64 (/.f64 (pow.f64 (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2) (.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1))))) (*.f64 (atan.f64 N) (atan.f64 N))) 0)
(+.f64 (.f64 (atan.f64 N) (neg.f64 (atan.f64 N))) (/.f64 (pow.f64 (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2) (*.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1))))))
(+.f64 0 (-.f64 (/.f64 (pow.f64 (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2) (.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1))))) (*.f64 (atan.f64 N) (atan.f64 N))))
(.f64 (-.f64 (/.f64 (pow.f64 (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2) (.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1))))) (.f64 (atan.f64 N) (atan.f64 N))) 1)
(.f64 -1 (-.f64 (.f64 (atan.f64 N) (atan.f64 N)) (/.f64 (pow.f64 (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2) (.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1)))))))
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(/.f64 (-.f64 (/.f64 (pow.f64 (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2) (.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1))))) (*.f64 (atan.f64 N) (atan.f64 N))) 1)
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(-.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2) 0)
(-.f64 0 (neg.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2)))
(.f64 -1 (neg.f64 (pow.f64 (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2)))
(*.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2))
(*.f64 (pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2))
(.f64 (neg.f64 (pow.f64 (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2)) -1)
(*.f64 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2)) (neg.f64 (pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2)))
(*.f64 (neg.f64 (pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2)) (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2)))
(/.f64 (neg.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2)) -1)
(neg.f64 (neg.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2)))

Outputs
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) (pow.f64 (atan.f64 N) 2))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))
(*.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2))
(pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2)
(*.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2))
(pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2)
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(pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2)
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(*.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2))
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(.f64 (pow.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) 2) (pow.f64 (+.f64 1 (atan.f64 (-.f64 1 (*.f64 -1 N)))) 2))
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(if (!=.f64 (-.f64 (.f64 (atan.f64 N) (atan.f64 N)) (/.f64 (pow.f64 (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2) (.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1)))))) 0) (/.f64 (.f64 (-.f64 (.f64 (atan.f64 N) (atan.f64 N)) (/.f64 (pow.f64 (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2) (.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1)))))) (-.f64 (/.f64 (pow.f64 (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2) (.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1))))) (.f64 (atan.f64 N) (atan.f64 N)))) (-.f64 (.f64 (atan.f64 N) (atan.f64 N)) (/.f64 (pow.f64 (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2) (.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1))))))) (-.f64 (/.f64 (pow.f64 (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2) (.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1))))) (.f64 (atan.f64 N) (atan.f64 N))))
(-.f64 (/.f64 (pow.f64 (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2) (.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1))))) (*.f64 (atan.f64 N) (atan.f64 N)))
(if (!=.f64 0 0) (/.f64 (neg.f64 (.f64 (-.f64 (.f64 (atan.f64 N) (atan.f64 N)) (/.f64 (pow.f64 (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2) (.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1)))))) 0)) 0) (-.f64 (/.f64 (pow.f64 (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2) (.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1))))) (*.f64 (atan.f64 N) (atan.f64 N))))
(-.f64 (/.f64 (pow.f64 (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2) (.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 (+.f64 N 1))))) (*.f64 (atan.f64 N) (atan.f64 N)))
(-.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2) 0)
(pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2)
(-.f64 0 (neg.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2)))
(pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2)
(.f64 -1 (neg.f64 (pow.f64 (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2)))
(pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2)
(*.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2))
(pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2)
(*.f64 (pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2) (pow.f64 (atan.f64 (+.f64 N 1)) 2))
(pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2)
(.f64 (neg.f64 (pow.f64 (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2)) -1)
(pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2)
(*.f64 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2)) (neg.f64 (pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2)))
(pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2)
(*.f64 (neg.f64 (pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2)) (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2)))
(pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2)
(/.f64 (neg.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2)) -1)
(pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2)
(neg.f64 (neg.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2)))
(pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2)

localize91.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.5b	(pow.f64 (atan.f64 (+.f64 N 1)) 4)
✓	1.7b	(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))
	1.7b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
	1.7b	(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))

Compiler

Compiled 304 to 219 computations (28% saved)

series0.0ms (0%)

Counts

2 → 8

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	N	@	0	(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))
0.0ms	N	@	-inf	(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))
0.0ms	N	@	inf	(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))
0.0ms	N	@	0	(pow.f64 (atan.f64 (+.f64 N 1)) 4)
0.0ms	N	@	-inf	(pow.f64 (atan.f64 (+.f64 N 1)) 4)

rewrite85.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

878×	`rational_best-simplify-1`
630×	`rational_best-simplify-21`
630×	`rational_best-simplify-18`
622×	`rational_best-simplify-20`
392×	`rational_best-simplify-127`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	50
1	39	50
2	177	50
3	1066	50
4	6849	50

Stop Event

1×	node limit

Counts

2 → 36

Calls

Call 1

Inputs
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))
(pow.f64 (atan.f64 (+.f64 N 1)) 4)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (neg.f64 (pow.f64 (atan.f64 N) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (pow.f64 (atan.f64 N) 4)) (pow.f64 (atan.f64 (+.f64 N 1)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 -1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)))) (+.f64 1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (+.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4))) (+.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)))) -4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 -1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)))) (*.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 -1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4))))) (+.f64 (+.f64 1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4))) (+.f64 1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 -2 (+.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)))) (*.f64 (+.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4))) (+.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4))))) (-.f64 4 (*.f64 -2 (+.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (+.f64 1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4))) (*.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 -1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4))))) (*.f64 (*.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 -1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)))) (*.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 -1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)))))) (-.f64 (*.f64 (+.f64 1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4))) (+.f64 1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)))) (*.f64 (+.f64 1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4))) (*.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 -1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)) 0) (/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 8) (pow.f64 (atan.f64 N) 8)) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (pow.f64 (atan.f64 N) 4) 0) (/.f64 (-.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 4) (pow.f64 (atan.f64 N) 8)) (pow.f64 (atan.f64 N) 4)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) 0) (/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 8) (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 4)) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (neg.f64 (pow.f64 (atan.f64 N) 4)) 0) (/.f64 (-.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 4) (pow.f64 (atan.f64 N) 8)) (pow.f64 (atan.f64 N) 4)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4)) 0) (/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 8) (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 4)) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) 0) (/.f64 (*.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 -1 0) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 0 0) (/.f64 0 0) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x if (!=.f64 (-.f64 (neg.f64 (pow.f64 (atan.f64 N) 4)) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) 0) (/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 8) (pow.f64 (atan.f64 N) 8)) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (atan.f64 (+.f64 N 1)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4)))))))

simplify60.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1000×	`rational_best-simplify-96`
964×	`rational_best-simplify-61`
950×	`rational_best-simplify-65`
624×	`rational_best-simplify-3`
570×	`rational_best-simplify-62`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	106	1524
1	527	1260
2	3490	1260

Stop Event

1×	node limit

Counts

44 → 40

Calls

Call 1

Inputs
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4)
(+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (neg.f64 (pow.f64 (atan.f64 N) 4)))
(+.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)) 0)
(+.f64 (neg.f64 (pow.f64 (atan.f64 N) 4)) (pow.f64 (atan.f64 (+.f64 N 1)) 4))
(+.f64 0 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)))
(*.f64 1 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)))
(*.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)) 1)
(*.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) -1)
(*.f64 -1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)) 1)
(/.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) -1)
(/.f64 (+.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4))) -2)
(/.f64 (*.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 -1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)))) (+.f64 1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4))))
(/.f64 (+.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))) 2)
(/.f64 (+.f64 (+.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4))) (+.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)))) -4)
(/.f64 (+.f64 (.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 -1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)))) (.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 -1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4))))) (+.f64 (+.f64 1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4))) (+.f64 1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)))))
(/.f64 (-.f64 (.f64 -2 (+.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)))) (.f64 (+.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4))) (+.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4))))) (-.f64 4 (*.f64 -2 (+.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4))))))
(/.f64 (-.f64 (.f64 (+.f64 1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4))) (.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 -1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4))))) (.f64 (.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 -1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)))) (.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 -1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)))))) (-.f64 (.f64 (+.f64 1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4))) (+.f64 1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)))) (.f64 (+.f64 1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4))) (.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 -1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)))))))
(pow.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)) 1)
(neg.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)))
(if (!=.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)) 0) (/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 8) (pow.f64 (atan.f64 N) 8)) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)))
(if (!=.f64 (pow.f64 (atan.f64 N) 4) 0) (/.f64 (-.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 4) (pow.f64 (atan.f64 N) 8)) (pow.f64 (atan.f64 N) 4)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)))
(if (!=.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) 0) (/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 8) (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 4)) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)))
(if (!=.f64 (neg.f64 (pow.f64 (atan.f64 N) 4)) 0) (/.f64 (-.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 4) (pow.f64 (atan.f64 N) 8)) (pow.f64 (atan.f64 N) 4)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)))
(if (!=.f64 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4)) 0) (/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 8) (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 4)) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)))
(if (!=.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) 0) (/.f64 (*.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)))
(if (!=.f64 -1 0) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)))
(if (!=.f64 0 0) (/.f64 0 0) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)))
(if (!=.f64 (-.f64 (neg.f64 (pow.f64 (atan.f64 N) 4)) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) 0) (/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 8) (pow.f64 (atan.f64 N) 8)) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)))
(+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) 0)
(+.f64 0 (pow.f64 (atan.f64 (+.f64 N 1)) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) 0)
(-.f64 0 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4)))
(*.f64 -1 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4)))
(*.f64 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4)) -1)
(/.f64 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4)) -1)
(neg.f64 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4)))

Outputs
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 4) (pow.f64 (atan.f64 N) 4))
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4)
(pow.f64 (atan.f64 (+.f64 1 N)) 4)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4)
(pow.f64 (atan.f64 (+.f64 1 N)) 4)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4)
(pow.f64 (atan.f64 (+.f64 1 N)) 4)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4)
(pow.f64 (atan.f64 (+.f64 1 N)) 4)
(+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (neg.f64 (pow.f64 (atan.f64 N) 4)))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 4) (pow.f64 (atan.f64 N) 4))
(+.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)) 0)
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 4) (pow.f64 (atan.f64 N) 4))
(+.f64 (neg.f64 (pow.f64 (atan.f64 N) 4)) (pow.f64 (atan.f64 (+.f64 N 1)) 4))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 4) (pow.f64 (atan.f64 N) 4))
(+.f64 0 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 4) (pow.f64 (atan.f64 N) 4))
(*.f64 1 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 4) (pow.f64 (atan.f64 N) 4))
(*.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)) 1)
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 4) (pow.f64 (atan.f64 N) 4))
(*.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) -1)
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 4) (pow.f64 (atan.f64 N) 4))
(*.f64 -1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 4) (pow.f64 (atan.f64 N) 4))
(/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)) 1)
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 4) (pow.f64 (atan.f64 N) 4))
(/.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) -1)
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 4) (pow.f64 (atan.f64 N) 4))
(/.f64 (+.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4))) -2)
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 4) (pow.f64 (atan.f64 N) 4))
(/.f64 (*.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 -1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)))) (+.f64 1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4))))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 4) (pow.f64 (atan.f64 N) 4))
(/.f64 (+.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))) 2)
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 4) (pow.f64 (atan.f64 N) 4))
(/.f64 (+.f64 (+.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4))) (+.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)))) -4)
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 4) (pow.f64 (atan.f64 N) 4))
(/.f64 (+.f64 (.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 -1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)))) (.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 -1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4))))) (+.f64 (+.f64 1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4))) (+.f64 1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)))))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 4) (pow.f64 (atan.f64 N) 4))
(/.f64 (-.f64 (.f64 -2 (+.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)))) (.f64 (+.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4))) (+.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4))))) (-.f64 4 (*.f64 -2 (+.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4))))))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 4) (pow.f64 (atan.f64 N) 4))
(/.f64 (-.f64 (.f64 (+.f64 1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4))) (.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 -1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4))))) (.f64 (.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 -1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)))) (.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 -1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)))))) (-.f64 (.f64 (+.f64 1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4))) (+.f64 1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)))) (.f64 (+.f64 1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4))) (.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 -1 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)))))))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 4) (pow.f64 (atan.f64 N) 4))
(pow.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)) 1)
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 4) (pow.f64 (atan.f64 N) 4))
(neg.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 4) (pow.f64 (atan.f64 N) 4))
(if (!=.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)) 0) (/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 8) (pow.f64 (atan.f64 N) 8)) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 4) (pow.f64 (atan.f64 N) 4))
(if (!=.f64 (pow.f64 (atan.f64 N) 4) 0) (/.f64 (-.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 4) (pow.f64 (atan.f64 N) 8)) (pow.f64 (atan.f64 N) 4)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 4) (pow.f64 (atan.f64 N) 4))
(if (!=.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) 0) (/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 8) (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 4)) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 4) (pow.f64 (atan.f64 N) 4))
(if (!=.f64 (neg.f64 (pow.f64 (atan.f64 N) 4)) 0) (/.f64 (-.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 4) (pow.f64 (atan.f64 N) 8)) (pow.f64 (atan.f64 N) 4)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 4) (pow.f64 (atan.f64 N) 4))
(if (!=.f64 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4)) 0) (/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 8) (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 4)) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 4) (pow.f64 (atan.f64 N) 4))
(if (!=.f64 (-.f64 (pow.f64 (atan.f64 N) 4) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) 0) (/.f64 (*.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 4) (pow.f64 (atan.f64 N) 4))
(if (!=.f64 -1 0) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 4) (pow.f64 (atan.f64 N) 4))
(if (!=.f64 0 0) (/.f64 0 0) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 4) (pow.f64 (atan.f64 N) 4))
(if (!=.f64 (-.f64 (neg.f64 (pow.f64 (atan.f64 N) 4)) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) 0) (/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 8) (pow.f64 (atan.f64 N) 8)) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)))
(-.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4) (pow.f64 (atan.f64 N) 4))
(-.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 4) (pow.f64 (atan.f64 N) 4))
(+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) 0)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4)
(pow.f64 (atan.f64 (+.f64 1 N)) 4)
(+.f64 0 (pow.f64 (atan.f64 (+.f64 N 1)) 4))
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4)
(pow.f64 (atan.f64 (+.f64 1 N)) 4)
(-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) 0)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4)
(pow.f64 (atan.f64 (+.f64 1 N)) 4)
(-.f64 0 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4)))
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4)
(pow.f64 (atan.f64 (+.f64 1 N)) 4)
(*.f64 -1 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4)))
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4)
(pow.f64 (atan.f64 (+.f64 1 N)) 4)
(*.f64 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4)) -1)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4)
(pow.f64 (atan.f64 (+.f64 1 N)) 4)
(/.f64 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4)) -1)
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4)
(pow.f64 (atan.f64 (+.f64 1 N)) 4)
(neg.f64 (neg.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4)))
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 4)
(pow.f64 (atan.f64 (+.f64 1 N)) 4)

localize272.0ms (1.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.4b	(-.f64 (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (/.f64 (-.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))) (-.f64 1 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (atan.f64 N)) (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (*.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (atan.f64 (+.f64 N 1))))
	1.7b	(-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))
✓	14.9b	(-.f64 1 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))))
✓	30.7b	(-.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))

Compiler

Compiled 928 to 634 computations (31.7% saved)

series7.0ms (0%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	N	@	-inf	(-.f64 (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (/.f64 (-.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))) (-.f64 1 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (atan.f64 N)) (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (*.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (atan.f64 (+.f64 N 1))))
2.0ms	N	@	inf	(-.f64 (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (/.f64 (-.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))) (-.f64 1 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (atan.f64 N)) (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (*.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (atan.f64 (+.f64 N 1))))
2.0ms	N	@	0	(-.f64 (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (/.f64 (-.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))) (-.f64 1 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (atan.f64 N)) (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (*.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (atan.f64 (+.f64 N 1))))
1.0ms	N	@	-inf	(-.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))
0.0ms	N	@	0	(-.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))

rewrite78.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

502×	`rational_best-simplify-111`
498×	`rational_best-simplify-127`
488×	`rational_best-simplify-126`
482×	`rational_best-simplify-124`
428×	`rational_best-simplify-61`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	27	427
1	195	427
2	1304	197

Stop Event

1×	node limit

Counts

3 → 106

Calls

Call 1

Inputs

(-.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))

(-.f64 1 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))))

(-.f64 (*.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (*.f64 (/.f64 (-.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))) (-.f64 1 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (atan.f64 N)) (*.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (*.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (atan.f64 (+.f64 N 1))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 N) (+.f64 (-.f64 1 (atan.f64 (+.f64 N 1))) (*.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 N) (+.f64 (*.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))) (-.f64 1 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (*.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 (atan.f64 N) (*.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 (*.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (*.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (+.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (+.f64 1 (*.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (atan.f64 N) 1) (+.f64 (neg.f64 (atan.f64 (+.f64 N 1))) (*.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (atan.f64 N) 1) (+.f64 (*.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))) (neg.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (atan.f64 (+.f64 N 1))) (+.f64 (+.f64 (atan.f64 N) 1) (*.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (atan.f64 (+.f64 N 1))) (+.f64 (*.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))) (+.f64 (atan.f64 N) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))) (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (+.f64 (-.f64 (atan.f64 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simplify120.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

718×	`rational_best-simplify-124`
680×	`rational_best-simplify-65`
638×	`rational_best-simplify-113`
606×	`rational_best-simplify-61`
536×	`rational_best-simplify-117`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	327	17194
1	1749	14100

Stop Event

1×	node limit

Counts

142 → 148

Calls

Call 1

Inputs
(-.f64 (+.f64 1 (atan.f64 N)) (+.f64 (atan.f64 (+.f64 N 1)) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2)))
(-.f64 (+.f64 1 (atan.f64 N)) (+.f64 (atan.f64 (+.f64 N 1)) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2)))
(-.f64 (+.f64 1 (atan.f64 N)) (+.f64 (atan.f64 (+.f64 N 1)) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2)))
(-.f64 (+.f64 1 (atan.f64 N)) (+.f64 (atan.f64 (+.f64 N 1)) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2)))
(-.f64 (+.f64 1 (atan.f64 N)) (+.f64 (atan.f64 (+.f64 N 1)) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2)))
(-.f64 (+.f64 1 (atan.f64 N)) (+.f64 (atan.f64 (+.f64 N 1)) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2)))
(-.f64 (+.f64 1 (atan.f64 N)) (+.f64 (atan.f64 (+.f64 N 1)) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2)))
(-.f64 (+.f64 1 (atan.f64 N)) (+.f64 (atan.f64 (+.f64 N 1)) (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2)))
(-.f64 (+.f64 1 (atan.f64 N)) (+.f64 (pow.f64 (-.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) (+.f64 1 (atan.f64 N))) 2) (atan.f64 (-.f64 1 (.f64 -1 N)))))
(-.f64 (+.f64 1 (atan.f64 N)) (+.f64 (pow.f64 (-.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) (+.f64 1 (atan.f64 N))) 2) (atan.f64 (-.f64 1 (.f64 -1 N)))))
(-.f64 (+.f64 1 (atan.f64 N)) (+.f64 (pow.f64 (-.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) (+.f64 1 (atan.f64 N))) 2) (atan.f64 (-.f64 1 (.f64 -1 N)))))
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Outputs
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(+.f64 (.f64 (atan.f64 N) (.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 1 N)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 1 N))) (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 1 N))))))) (.f64 (atan.f64 (+.f64 1 N)) (.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 1 N)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 1 N))) (+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -1 (atan.f64 N)))))))
(.f64 (.f64 (+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -1 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))) (*.f64 (+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -1 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))))
(if (!=.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))) 0) (/.f64 (-.f64 (.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))))) (.f64 (.f64 (atan.f64 N) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))))) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (*.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))))
(if (!=.f64 (.f64 (atan.f64 (+.f64 1 N)) (.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 1 N)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 1 N))) (+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -1 (atan.f64 N)))))) 0) (/.f64 (-.f64 (.f64 (.f64 (atan.f64 (+.f64 1 N)) (.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 1 N)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 1 N))) (+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -1 (atan.f64 N)))))) (.f64 (atan.f64 (+.f64 1 N)) (.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 1 N)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 1 N))) (+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -1 (atan.f64 N))))))) (.f64 (.f64 (atan.f64 (+.f64 1 N)) (.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 1 N)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 1 N))) (+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -1 (atan.f64 N)))))) (.f64 (atan.f64 N) (.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 1 N)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 1 N))) (+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -1 (atan.f64 N)))))))) (.f64 (atan.f64 (+.f64 1 N)) (.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 1 N)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 1 N))) (+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -1 (atan.f64 N))))))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 1 N))) (.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 1 N)))) (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 1 N))) (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 1 N))))))))
(if (!=.f64 (.f64 (atan.f64 (+.f64 1 N)) (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 1 N)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 1 N))) (+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -1 (atan.f64 N)))))) 0) (/.f64 (.f64 (.f64 (atan.f64 (+.f64 1 N)) (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 1 N)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 1 N))) (+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -1 (atan.f64 N)))))) (.f64 (.f64 (+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -1 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -1 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))))) (.f64 (atan.f64 (+.f64 1 N)) (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 1 N)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 1 N))) (+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -1 (atan.f64 N))))))) (.f64 (.f64 (+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -1 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))) (.f64 (+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -1 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)))))
(if (!=.f64 0 0) (/.f64 (-.f64 0 (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))) 0)) 0) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (*.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))))
(+.f64 (.f64 (atan.f64 N) (.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 1 N)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 1 N))) (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 1 N))))))) (.f64 (atan.f64 (+.f64 1 N)) (.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 1 N)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 1 N))) (+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -1 (atan.f64 N)))))))
(.f64 (.f64 (+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -1 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))) (*.f64 (+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -1 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))))

localize262.0ms (1.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.7b	(-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1)))
✓	1.6b	(+.f64 (.f64 (/.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1)))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))) -1)
	1.7b	(-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))
	17.7b	(-.f64 (.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))

Compiler

Compiled 903 to 613 computations (32.1% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time

Variable

Point

Expression

0.0ms

(+.f64 (*.f64 (/.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1)))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))) -1)

0.0ms

-inf

(+.f64 (*.f64 (/.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1)))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))) -1)

0.0ms

inf

(+.f64 (*.f64 (/.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1)))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))) -1)

rewrite74.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1142×	`rational_best-simplify-3`
864×	`rational_best-simplify-53`
808×	`rational_best-simplify-56`
666×	`rational_best-simplify-1`
512×	`rational_best-simplify-60`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	149
1	108	149
2	679	149
3	4338	149

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

Inputs

(+.f64 (*.f64 (/.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1)))) (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))) -1)

Outputs

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simplify72.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

874×	`rational_best-simplify-65`
868×	`rational_best-simplify-96`
828×	`rational_best-simplify-61`
638×	`rational_best-simplify-3`
500×	`rational_best-simplify-62`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	87	3981
1	505	3981
2	3541	3981

Stop Event

1×	node limit

Counts

33 → 27

Calls

Call 1

Inputs
(-.f64 (*.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1)))) 1)
(-.f64 (*.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1)))) 1)
(-.f64 (*.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1)))) 1)
(-.f64 (*.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1)))) 1)
(-.f64 (*.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1)))) 1)
(-.f64 (*.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1)))) 1)
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Outputs
(-.f64 (*.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1)))) 1)
(+.f64 (*.f64 (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1)))) -1)
(+.f64 (*.f64 (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) -1)
(-.f64 (*.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 N))) 2) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1)))) 1)
(+.f64 (*.f64 (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2) (-.f64 (+.f64 1 (atan.f64 N)) (atan.f64 (+.f64 N 1)))) -1)
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eval2.9s (20.8%)

Compiler: Compiled 238702 to 163857 computations (31.4% saved)

prune509.0ms (3.6%)

Pruning

24 alts after pruning (21 fresh and 3 done)

	Pruned	Kept	Total
New	1466	12	1478
Fresh	2	9	11
Picked	1	0	1
Done	3	3	6
Total	1472	24	1496

Error

15.4b

Counts

1496 → 24

Alt Table

Click to see full alt table

Status	Error	Program
	31.7b	(if (!=.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0) (/.f64 (if (!=.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 0) (/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2)) (pow.f64 (atan.f64 (+.f64 N 1)) 2)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
	31.4b	(if (!=.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0) (/.f64 (if (!=.f64 (pow.f64 (atan.f64 N) 2) 0) (/.f64 (-.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2) (pow.f64 (atan.f64 N) 4)) (pow.f64 (atan.f64 N) 2)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
	31.7b	(if (!=.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0) (/.f64 (if (!=.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) 0) (/.f64 (if (!=.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) 0) (/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 8) (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 4)) (pow.f64 (atan.f64 (+.f64 N 1)) 4)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
	31.8b	(if (!=.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0) (/.f64 (if (!=.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) 0) (/.f64 (if (!=.f64 (pow.f64 (atan.f64 N) 4) 0) (/.f64 (-.f64 (pow.f64 (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 4) (pow.f64 (atan.f64 N) 8)) (pow.f64 (atan.f64 N) 4)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
	16.2b	(if (!=.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0) (/.f64 (if (!=.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) 0) (/.f64 (if (!=.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)) 0) (/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 8) (pow.f64 (atan.f64 N) 8)) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4))) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
✓	16.2b	(if (!=.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0) (/.f64 (if (!=.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) 0) (/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 4) (pow.f64 (atan.f64 N) 4)) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
	16.2b	(if (!=.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0) (/.f64 (if (!=.f64 (+.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N))) 0) (/.f64 (if (!=.f64 (+.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N)))) 0) (/.f64 (-.f64 (.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))))) (.f64 (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N))) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N))))) (+.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N))))) (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N))))) (+.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N)))) (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N)))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
	31.7b	(if (!=.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0) (/.f64 (if (!=.f64 (+.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N))) 0) (/.f64 (if (!=.f64 (+.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N)))) 0) (/.f64 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1)))))))) (.f64 (atan.f64 N) (.f64 (atan.f64 N) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N))))))) (+.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N))))) (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N))))) (+.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N)))) (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N)))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
	31.7b	(if (!=.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0) (/.f64 (if (!=.f64 (+.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N))) 0) (/.f64 (if (!=.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))) 0) (.f64 (.f64 1 (/.f64 (.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N))))) (atan.f64 (+.f64 N 1)))) (/.f64 1 (atan.f64 (+.f64 N 1)))) (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))))) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N))))) (+.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N)))) (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (*.f64 (atan.f64 N) (atan.f64 N)))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
	31.7b	(if (!=.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0) (/.f64 (if (!=.f64 (+.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N))) 0) (/.f64 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (pow.f64 (atan.f64 (+.f64 N 1)) 3)) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N)))) (+.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N)))) (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N)))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
	24.4b	(if (!=.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0) (/.f64 (if (!=.f64 (+.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N))) 0) (/.f64 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (/.f64 (.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (/.f64 1 (atan.f64 (+.f64 N 1))))) (-.f64 (.f64 (.f64 1 (atan.f64 (+.f64 N 1))) 1) (/.f64 (/.f64 1 (atan.f64 (+.f64 N 1))) (atan.f64 (+.f64 N 1)))))) (.f64 (.f64 (atan.f64 N) (atan.f64 N)) (.f64 (atan.f64 N) (atan.f64 N)))) (+.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 N) (atan.f64 N)))) (-.f64 (.f64 (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1))) (*.f64 (atan.f64 N) (atan.f64 N)))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
✓	15.7b	(if (!=.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0) (/.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
	16.2b	(if (!=.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0) (/.f64 (-.f64 (/.f64 (pow.f64 (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2) (pow.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2)) (.f64 (atan.f64 N) (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
	22.6b	(if (!=.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0) (/.f64 (-.f64 (/.f64 (pow.f64 (.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (atan.f64 (+.f64 N 1)))) 2) (-.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 (+.f64 N 1)))))) (*.f64 (atan.f64 N) (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
	16.2b	(/.f64 (if (!=.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1)))))) 0) (/.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (.f64 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))))) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))))
	15.8b	(/.f64 (-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (pow.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 (atan.f64 N) 1))) 2)) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (*.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))))
	33.8b	(/.f64 (-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (-.f64 (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (/.f64 (-.f64 (+.f64 (atan.f64 N) (-.f64 1 (atan.f64 (+.f64 N 1)))) (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (atan.f64 N)) (.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (.f64 (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))) (-.f64 (+.f64 (atan.f64 N) 1) (atan.f64 (+.f64 N 1))))) (atan.f64 (+.f64 N 1))))) (-.f64 (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) (.f64 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))) (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (-.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))))
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✓	15.7b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 2995 to 2020 computations (32.6% saved)

regimes103.0ms (0.7%)

Accuracy

Total -18.6b remaining (-118.5%)

Threshold costs -18.6b (-118.5%)

Counts

38 → 1

Calls

Call 1

Inputs
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Outputs
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Calls

2 calls:

14.0ms	N
4.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Results

Error	Segments	Branch
15.7b	1	`N`
15.7b	1	`(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))`

Compiler

Compiled 4713 to 3144 computations (33.3% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Outputs
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 8 to 6 computations (25% saved)

soundness0.0ms (0%)

end11.0ms (0.1%)

Compiler: Compiled 8 to 6 computations (25% saved)

Details

analyze0.0ms (0%)

sample2.3s (16%)

preprocess80.0ms (0.6%)

simplify78.0ms (0.6%)

eval0.0ms (0%)

prune1.0ms (0%)

localize9.0ms (0.1%)

series1.0ms (0%)

rewrite88.0ms (0.6%)

simplify60.0ms (0.4%)

eval13.0ms (0.1%)

prune9.0ms (0.1%)

localize116.0ms (0.8%)

series9.0ms (0.1%)

rewrite170.0ms (1.2%)

simplify256.0ms (1.8%)

localize45.0ms (0.3%)

series5.0ms (0%)

rewrite117.0ms (0.8%)

simplify85.0ms (0.6%)

eval996.0ms (7.1%)

prune140.0ms (1%)

localize41.0ms (0.3%)

series1.0ms (0%)

rewrite57.0ms (0.4%)

simplify62.0ms (0.4%)

localize106.0ms (0.8%)

series3.0ms (0%)

rewrite81.0ms (0.6%)

simplify90.0ms (0.6%)

localize143.0ms (1%)

series4.0ms (0%)

rewrite84.0ms (0.6%)

simplify85.0ms (0.6%)

localize183.0ms (1.3%)

series9.0ms (0.1%)

rewrite132.0ms (0.9%)

simplify143.0ms (1%)

localize234.0ms (1.7%)

series4.0ms (0%)

rewrite91.0ms (0.6%)

simplify140.0ms (1%)

eval2.5s (17.6%)

prune370.0ms (2.6%)

localize105.0ms (0.7%)

localize79.0ms (0.6%)

series2.0ms (0%)

rewrite59.0ms (0.4%)

simplify75.0ms (0.5%)

localize91.0ms (0.6%)

series0.0ms (0%)

rewrite85.0ms (0.6%)

simplify60.0ms (0.4%)

localize272.0ms (1.9%)

series7.0ms (0%)

rewrite78.0ms (0.6%)

simplify120.0ms (0.9%)

localize262.0ms (1.9%)

series1.0ms (0%)

rewrite74.0ms (0.5%)

simplify72.0ms (0.5%)

eval2.9s (20.8%)

prune509.0ms (3.6%)

regimes103.0ms (0.7%)

simplify1.0ms (0%)

soundness0.0ms (0%)

end11.0ms (0.1%)

Profiling