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)

sample10.4s (59.9%)

Results

9.1s	2200×	body	2048	valid
927.0ms	4544×	body	256	valid
313.0ms	1021×	body	1024	valid
75.0ms	491×	body	512	valid

Bogosity

preprocess3.0ms (0%)

Algorithm

2×	egg-herbie

Rules

2×	`rational.json-simplify-17`
2×	`rational.json-simplify-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	10	21
2	12	21
0	1	1

Stop Event

1×	saturated
1×	saturated

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)

simplify116.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

2×	`rational.json-simplify-17`
2×	`rational.json-simplify-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	10	21
2	12	21

Stop Event

1×

saturated

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

15.4b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	15.4b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 8 to 6 computations (25% saved)

localize10.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 19 to 12 computations (36.8% saved)

series1.0ms (0%)

Counts

1 → 4

Calls

3 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))

rewrite185.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1318×	`rational.json-simplify-35`
1312×	`exponential.json-3`
1312×	`rational.json-1`
1312×	`rational.json-2`
1312×	`rational.json-4`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	66	21
2	145	21
3	282	21
4	526	21
5	1165	21
6	2731	21
7	4446	21
8	6304	21

Stop Event

1×	node limit

Counts

1 → 52

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))))) (#(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 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)) (-.f64 1 (atan.f64 N))))))) (#(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 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (atan.f64 (+.f64 N 1)) 1/2) (-.f64 (.f64 (atan.f64 (+.f64 N 1)) 1/2) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2) (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 1 (atan.f64 N)) (+.f64 (atan.f64 (+.f64 N 1)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -2 (+.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (-.f64 -1 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (atan.f64 (+.f64 N 1)) -1) (-.f64 1 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2)) (+.f64 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2) -1) (+.f64 1 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 -1 (atan.f64 N)) (+.f64 1 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) 1/2) (atan.f64 N)) (.f64 (atan.f64 (+.f64 N 1)) 1/2))))) (#(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 2 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2))))) (#(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 4 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2) 1/2)))) (#(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 (+.f64 N 1)) (atan.f64 N)) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 8) 1/8)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -2) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/4 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -2 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 1/2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/8 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 8))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1/2 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -2))))) (#(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)) 2) 2)))) (#(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 (+.f64 N 1)) (atan.f64 N)) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -4) -4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -8) -8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 8)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -8)) -16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 8))))) 128)))) (#(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))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))))) (#(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 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)) (-.f64 1 (atan.f64 N))))))) (#(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 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (atan.f64 (+.f64 N 1)) 1/2) (-.f64 (*.f64 (atan.f64 (+.f64 N 1)) 1/2) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2) (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 1 (atan.f64 N)) (+.f64 (atan.f64 (+.f64 N 1)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -2 (+.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (-.f64 -1 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (atan.f64 (+.f64 N 1)) -1) (-.f64 1 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2)) (+.f64 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2) -1) (+.f64 1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 -1 (atan.f64 N)) (+.f64 1 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (*.f64 (atan.f64 (+.f64 N 1)) 1/2) (atan.f64 N)) (*.f64 (atan.f64 (+.f64 N 1)) 1/2))))) (#(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 2 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2))))) (#(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 4 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2) 1/2)))) (#(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 (+.f64 N 1)) (atan.f64 N)) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 8) 1/8)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -2) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -2 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 1/2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/8 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/2 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -2))))) (#(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)) 2) 2)))) (#(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 (+.f64 N 1)) (atan.f64 N)) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -4) -4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -8) -8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 8)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -8)) -16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 8))))) 128)))) (#(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))))))))

simplify216.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1828×	`rational.json-simplify-35`
1126×	`rational.json-simplify-2`
1090×	`rational.json-simplify-1`
906×	`rational.json-simplify-51`
890×	`rational.json-simplify-52`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	109	1556
1	231	1448
2	819	1448
3	1735	1232
4	3019	1232
5	3866	1232
6	4647	1232
7	6702	1232
8	7372	1232
9	7784	1232

Stop Event

1×	node limit

Counts

56 → 56

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

eval11.0ms (0.1%)

Compiler: Compiled 650 to 470 computations (27.7% saved)

prune101.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	53	3	56
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	53	4	57

Error

15.4b

Counts

57 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	15.4b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
▶	15.4b	(+.f64 (+.f64 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2) -1) (+.f64 1 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2)))
▶	15.4b	(+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) -1)
▶	15.4b	(+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1)

Compiler

Compiled 56 to 45 computations (19.6% saved)

localize384.0ms (2.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(-.f64 -1 (atan.f64 N))
✓	0.8b	(+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))
✓	14.2b	(+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1)

Compiler

Compiled 37 to 25 computations (32.4% saved)

series1.0ms (0%)

Counts

3 → 36

Calls

9 calls:

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

rewrite120.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1732×	`rational.json-simplify-35`
1528×	`exponential.json-3`
1528×	`rational.json-1`
1528×	`rational.json-2`
1528×	`rational.json-4`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	12	71
1	87	71
2	178	71
3	357	65
4	745	63
5	1872	63
6	3831	63
7	5450	63
8	7107	63

Stop Event

1×	node limit

Counts

3 → 89

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (+.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)) (neg.f64 (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 4 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/4 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 8)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 8)))) (.f64 2 (.f64 2 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 8))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 1)))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (-.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 4 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (+.f64 (.f64 (-.f64 -1 (atan.f64 N)) 2) (.f64 (atan.f64 (+.f64 N 1)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (+.f64 (.f64 (atan.f64 (+.f64 N 1)) 2) (.f64 (-.f64 -1 (atan.f64 N)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/4 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (.f64 (-.f64 -1 (atan.f64 N)) 2) (.f64 (atan.f64 (+.f64 N 1)) 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (.f64 (atan.f64 (+.f64 N 1)) 2) (.f64 (-.f64 -1 (atan.f64 N)) 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 8)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 8)))) (.f64 2 (.f64 2 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 8))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1)))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (-.f64 -2 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (neg.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 -1 (atan.f64 N)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 -1 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (atan.f64 N)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (-.f64 -1 (atan.f64 N)) 1/2) (.f64 (-.f64 -1 (atan.f64 N)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -2 (-.f64 1 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 -2 (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (.f64 (-.f64 -1 (atan.f64 N)) 1/2) -1) (+.f64 1 (.f64 (-.f64 -1 (atan.f64 N)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (-.f64 -1 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (+.f64 1 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 -1 (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (.f64 (-.f64 -1 (atan.f64 N)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 4 (/.f64 (-.f64 -1 (atan.f64 N)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (-.f64 -1 (atan.f64 N)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 1 (atan.f64 N)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (-.f64 -1 (atan.f64 N)) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (.f64 (-.f64 -1 (atan.f64 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/4 (.f64 (-.f64 -1 (atan.f64 N)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (-.f64 -1 (atan.f64 N)) 1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (+.f64 1 (atan.f64 N)) 2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (-.f64 -1 (atan.f64 N)) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 -1 (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 -1 (atan.f64 N)) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (atan.f64 N)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 -1 (atan.f64 N)) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (+.f64 1 (atan.f64 N))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 -1 (atan.f64 N)) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 4 (+.f64 1 (atan.f64 N))) -4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (-.f64 -1 (atan.f64 N)) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 (-.f64 -1 (atan.f64 N)) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 4 (+.f64 1 (atan.f64 N)))) -8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 4 (+.f64 1 (atan.f64 N)))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 4 (+.f64 1 (atan.f64 N))))) -16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (-.f64 -1 (atan.f64 N)) 8)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (neg.f64 (.f64 4 (+.f64 1 (atan.f64 N))))) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (-.f64 -1 (atan.f64 N)) 8)))) (.f64 2 (.f64 2 (.f64 2 (.f64 (-.f64 -1 (atan.f64 N)) 8))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 2 (neg.f64 (.f64 4 (+.f64 1 (atan.f64 N))))) (.f64 2 (neg.f64 (*.f64 4 (+.f64 1 (atan.f64 N)))))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 -1 (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (+.f64 1 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (-.f64 0 (-.f64 -1 (atan.f64 N))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.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)) (neg.f64 (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 8)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 8)))) (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 8))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 1)))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (-.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (+.f64 (*.f64 (-.f64 -1 (atan.f64 N)) 2) (*.f64 (atan.f64 (+.f64 N 1)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (+.f64 (*.f64 (atan.f64 (+.f64 N 1)) 2) (*.f64 (-.f64 -1 (atan.f64 N)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 (-.f64 -1 (atan.f64 N)) 2) (*.f64 (atan.f64 (+.f64 N 1)) 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 (atan.f64 (+.f64 N 1)) 2) (*.f64 (-.f64 -1 (atan.f64 N)) 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 8)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 8)))) (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 8))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1)))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (-.f64 -2 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (neg.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 -1 (atan.f64 N)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 -1 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (atan.f64 N)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (-.f64 -1 (atan.f64 N)) 1/2) (*.f64 (-.f64 -1 (atan.f64 N)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -2 (-.f64 1 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 -2 (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (*.f64 (-.f64 -1 (atan.f64 N)) 1/2) -1) (+.f64 1 (*.f64 (-.f64 -1 (atan.f64 N)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 -1 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (+.f64 1 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 -1 (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 (-.f64 -1 (atan.f64 N)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (/.f64 (-.f64 -1 (atan.f64 N)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 -1 (atan.f64 N)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (atan.f64 N)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 -1 (atan.f64 N)) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 (-.f64 -1 (atan.f64 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (-.f64 -1 (atan.f64 N)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 -1 (atan.f64 N)) 1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 1 (atan.f64 N)) 2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 -1 (atan.f64 N)) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 -1 (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 -1 (atan.f64 N)) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (atan.f64 N)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 -1 (atan.f64 N)) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (+.f64 1 (atan.f64 N))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 -1 (atan.f64 N)) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 4 (+.f64 1 (atan.f64 N))) -4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (-.f64 -1 (atan.f64 N)) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (-.f64 -1 (atan.f64 N)) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 4 (+.f64 1 (atan.f64 N)))) -8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 4 (+.f64 1 (atan.f64 N)))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 4 (+.f64 1 (atan.f64 N))))) -16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (-.f64 -1 (atan.f64 N)) 8)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (neg.f64 (*.f64 4 (+.f64 1 (atan.f64 N))))) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (-.f64 -1 (atan.f64 N)) 8)))) (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (-.f64 -1 (atan.f64 N)) 8))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (neg.f64 (*.f64 4 (+.f64 1 (atan.f64 N))))) (*.f64 2 (neg.f64 (*.f64 4 (+.f64 1 (atan.f64 N)))))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 -1 (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (+.f64 1 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (-.f64 0 (-.f64 -1 (atan.f64 N))))))))

simplify448.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

1904×	`rational.json-simplify-2`
1888×	`rational.json-simplify-35`
1394×	`rational.json-simplify-51`
1048×	`rational.json-simplify-45`
1032×	`rational.json-simplify-1`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	169	2543
1	361	2543
2	939	2335
3	2087	2335
4	3656	2335
5	4831	2335
6	5840	2335
7	6476	2335
8	7291	2335
9	7598	2335
10	7812	2335

Stop Event

1×	node limit

Counts

125 → 98

Calls

Call 1

Inputs
(-.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 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))
(-.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 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 1 (atan.f64 N)))
(-.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 1 (atan.f64 N)))
(-.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 1 (*.f64 -1 N))) (+.f64 1 (atan.f64 N)))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (+.f64 1 (atan.f64 N)))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (+.f64 1 (atan.f64 N)))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (+.f64 1 (atan.f64 N)))
(*.f64 -1 (+.f64 1 (atan.f64 N)))
(*.f64 -1 (+.f64 1 (atan.f64 N)))
(*.f64 -1 (+.f64 1 (atan.f64 N)))
(*.f64 -1 (+.f64 1 (atan.f64 N)))
(*.f64 -1 (+.f64 1 (atan.f64 N)))
(*.f64 -1 (+.f64 1 (atan.f64 N)))
(*.f64 -1 (+.f64 1 (atan.f64 N)))
(*.f64 -1 (+.f64 1 (atan.f64 N)))
(*.f64 -1 (+.f64 1 (atan.f64 N)))
(*.f64 -1 (+.f64 1 (atan.f64 N)))
(*.f64 -1 (+.f64 1 (atan.f64 N)))
(*.f64 -1 (+.f64 1 (atan.f64 N)))
(-.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) -1)
(-.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 0)
(-.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) 1)
(*.f64 1 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))))
(*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 1)
(.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 1/2))
(*.f64 4 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4))
(.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 2) 1/2)
(.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4) 1/4)
(.f64 1/2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 2))
(.f64 1/4 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4))
(.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 1/2) 2)
(*.f64 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4) 4)
(/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 1)
(/.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 2) 2)
(/.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4) 4)
(/.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 8) 8)
(/.f64 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 8)) 16)
(/.f64 (.f64 2 (.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 8))) 32)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 8)))) 64)
(/.f64 (+.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 8)))) (.f64 2 (.f64 2 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 8))))) 128)
(pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 1)
(-.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 0)
(-.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 1)
(-.f64 (-.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1) -1)
(*.f64 1 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))
(*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1)
(.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1/2))
(.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2) 1/2)
(*.f64 4 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4))
(.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4) 1/4)
(.f64 1/2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2))
(.f64 1/2 (+.f64 (.f64 (-.f64 -1 (atan.f64 N)) 2) (*.f64 (atan.f64 (+.f64 N 1)) 2)))
(.f64 1/2 (+.f64 (.f64 (atan.f64 (+.f64 N 1)) 2) (*.f64 (-.f64 -1 (atan.f64 N)) 2)))
(.f64 1/4 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4))
(.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1/2) 2)
(*.f64 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4) 4)
(.f64 (+.f64 (.f64 (-.f64 -1 (atan.f64 N)) 2) (*.f64 (atan.f64 (+.f64 N 1)) 2)) 1/2)
(.f64 (+.f64 (.f64 (atan.f64 (+.f64 N 1)) 2) (*.f64 (-.f64 -1 (atan.f64 N)) 2)) 1/2)
(/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1)
(/.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2) 2)
(/.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4) 4)
(/.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 8) 8)
(/.f64 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 8)) 16)
(/.f64 (.f64 2 (.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 8))) 32)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 8)))) 64)
(/.f64 (+.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 8)))) (.f64 2 (.f64 2 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 8))))) 128)
(pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1)
(+.f64 1 (-.f64 -2 (atan.f64 N)))
(+.f64 -1 (neg.f64 (atan.f64 N)))
(+.f64 (-.f64 -1 (atan.f64 N)) 0)
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(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(*.f64 4 (/.f64 (-.f64 -1 (atan.f64 N)) 4))
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(.f64 (.f64 (-.f64 -1 (atan.f64 N)) 2) 1/2)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(*.f64 (+.f64 1 (atan.f64 N)) -1)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(.f64 (.f64 (-.f64 -1 (atan.f64 N)) 4) 1/4)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(.f64 1/2 (.f64 (-.f64 -1 (atan.f64 N)) 2))
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(.f64 1/4 (.f64 (-.f64 -1 (atan.f64 N)) 4))
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(.f64 (.f64 (-.f64 -1 (atan.f64 N)) 1/2) 2)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(*.f64 (/.f64 (+.f64 1 (atan.f64 N)) 2) -2)
(*.f64 -2 (/.f64 (+.f64 1 (atan.f64 N)) 2))
(.f64 -2 (.f64 (-.f64 -1 (atan.f64 N)) -1/2))
(.f64 -2 (.f64 (+.f64 1 (atan.f64 N)) 1/2))
(*.f64 (/.f64 (-.f64 -1 (atan.f64 N)) 4) 4)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(/.f64 (-.f64 -1 (atan.f64 N)) 1)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(/.f64 (*.f64 (-.f64 -1 (atan.f64 N)) 2) 2)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(/.f64 (+.f64 1 (atan.f64 N)) -1)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(/.f64 (*.f64 (-.f64 -1 (atan.f64 N)) 4) 4)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(/.f64 (*.f64 2 (+.f64 1 (atan.f64 N))) -2)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(/.f64 (*.f64 (-.f64 -1 (atan.f64 N)) 8) 8)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(/.f64 (*.f64 4 (+.f64 1 (atan.f64 N))) -4)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(/.f64 (.f64 2 (.f64 (-.f64 -1 (atan.f64 N)) 8)) 16)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(/.f64 (.f64 2 (.f64 2 (*.f64 (-.f64 -1 (atan.f64 N)) 8))) 32)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(/.f64 (.f64 2 (.f64 4 (+.f64 1 (atan.f64 N)))) -8)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(/.f64 (neg.f64 (*.f64 4 (+.f64 1 (atan.f64 N)))) 4)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(/.f64 (.f64 2 (.f64 2 (*.f64 4 (+.f64 1 (atan.f64 N))))) -16)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (-.f64 -1 (atan.f64 N)) 8)))) 64)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(/.f64 (.f64 2 (neg.f64 (.f64 4 (+.f64 1 (atan.f64 N))))) 8)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(/.f64 (+.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (-.f64 -1 (atan.f64 N)) 8)))) (.f64 2 (.f64 2 (.f64 2 (.f64 (-.f64 -1 (atan.f64 N)) 8))))) 128)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(/.f64 (+.f64 (.f64 2 (neg.f64 (.f64 4 (+.f64 1 (atan.f64 N))))) (.f64 2 (neg.f64 (.f64 4 (+.f64 1 (atan.f64 N)))))) 16)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(pow.f64 (-.f64 -1 (atan.f64 N)) 1)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(neg.f64 (-.f64 0 (-.f64 -1 (atan.f64 N))))
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))

localize17.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(-.f64 1 (atan.f64 N))
✓	0.2b	(+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N)))
✓	16.9b	(+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) -1)

Compiler

Compiled 37 to 25 computations (32.4% saved)

series1.0ms (0%)

Counts

3 → 24

Calls

9 calls:

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

rewrite123.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1804×	`rational.json-simplify-35`
1576×	`rational.json-1`
1576×	`rational.json-2`
1576×	`rational.json-4`
1576×	`rational.json-3`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	71
1	88	71
2	183	65
3	374	63
4	751	63
5	1882	63
6	3874	63
7	5574	63
8	7321	63

Stop Event

1×	node limit

Counts

3 → 86

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) -1) (neg.f64 (+.f64 (atan.f64 N) -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.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)) (neg.f64 (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 8)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 8)))) (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 8))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 1)))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (+.f64 (atan.f64 N) -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (+.f64 (*.f64 (-.f64 1 (atan.f64 N)) 2) (*.f64 (atan.f64 (+.f64 N 1)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (+.f64 (*.f64 (atan.f64 (+.f64 N 1)) 2) (*.f64 (-.f64 1 (atan.f64 N)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) 1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 (-.f64 1 (atan.f64 N)) 2) (*.f64 (atan.f64 (+.f64 N 1)) 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 (atan.f64 (+.f64 N 1)) 2) (*.f64 (-.f64 1 (atan.f64 N)) 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) 8)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) 8)))) (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) 8))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) 1)))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 1 (atan.f64 N)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (neg.f64 (+.f64 (atan.f64 N) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 1 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (+.f64 (atan.f64 N) -2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -2 (-.f64 1 (+.f64 (atan.f64 N) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (-.f64 1 (atan.f64 N)) 1/2) (*.f64 (-.f64 1 (atan.f64 N)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (*.f64 (-.f64 1 (atan.f64 N)) 1/2) -1) (-.f64 1 (/.f64 (+.f64 (atan.f64 N) -1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 1 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (+.f64 (atan.f64 N) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 (-.f64 1 (atan.f64 N)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 1 (atan.f64 N)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (/.f64 (+.f64 (atan.f64 N) -1) -4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (atan.f64 N) -1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 1 (atan.f64 N)) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 (-.f64 1 (atan.f64 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 1 (atan.f64 N)) 1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (-.f64 1 (atan.f64 N)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 (atan.f64 N) -1) 2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 (atan.f64 N) -1) -4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (atan.f64 N)) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (atan.f64 N) -1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (atan.f64 N)) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (+.f64 (atan.f64 N) -1)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (atan.f64 N)) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (-.f64 1 (atan.f64 N)) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 4 (+.f64 (atan.f64 N) -1)) -4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 4 (+.f64 (atan.f64 N) -1))) -8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (-.f64 1 (atan.f64 N)) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 4 (+.f64 (atan.f64 N) -1))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 4 (+.f64 (atan.f64 N) -1)))) -16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (-.f64 1 (atan.f64 N)) 8)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (neg.f64 (*.f64 4 (+.f64 (atan.f64 N) -1)))) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (-.f64 1 (atan.f64 N)) 8)))) (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (-.f64 1 (atan.f64 N)) 8))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (neg.f64 (*.f64 4 (+.f64 (atan.f64 N) -1)))) (*.f64 2 (neg.f64 (*.f64 4 (+.f64 (atan.f64 N) -1))))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (+.f64 (atan.f64 N) -1))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (-.f64 0 (-.f64 1 (atan.f64 N))))))))

simplify390.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

1942×	`rational.json-simplify-1`
1894×	`rational.json-simplify-35`
1688×	`rational.json-simplify-2`
1284×	`rational.json-simplify-51`
1056×	`rational.json-simplify-52`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	170	2142
1	365	2142
2	924	2142
3	1931	2142
4	3808	2142
5	4470	2142
6	5046	2142
7	5572	2142
8	5903	2142
9	6221	2142
10	7473	2142

Stop Event

1×	node limit

Counts

110 → 93

Calls

Call 1

Inputs
(-.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 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))
(-.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 (+.f64 1 (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (+.f64 1 (atan.f64 (-.f64 1 (*.f64 -1 N)))) (atan.f64 N))
(-.f64 (+.f64 1 (atan.f64 (-.f64 1 (*.f64 -1 N)))) (atan.f64 N))
(-.f64 (+.f64 1 (atan.f64 (-.f64 1 (*.f64 -1 N)))) (atan.f64 N))
(-.f64 (+.f64 1 (atan.f64 (-.f64 1 (*.f64 -1 N)))) (atan.f64 N))
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(.f64 1/2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 2))
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Outputs
(-.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))
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(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
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(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
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(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
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(/.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) 2) 2)
(+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N)))
(+.f64 1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
(/.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) 4) 4)
(+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N)))
(+.f64 1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
(/.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) 8) 8)
(+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N)))
(+.f64 1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
(/.f64 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) 8)) 16)
(+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N)))
(+.f64 1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
(/.f64 (.f64 2 (.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) 8))) 32)
(+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N)))
(+.f64 1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) 8)))) 64)
(+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N)))
(+.f64 1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
(/.f64 (+.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) 8)))) (.f64 2 (.f64 2 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) 8))))) 128)
(+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N)))
(+.f64 1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
(pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) 1)
(+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N)))
(+.f64 1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
(+.f64 (-.f64 1 (atan.f64 N)) 0)
(-.f64 1 (atan.f64 N))
(+.f64 -1 (neg.f64 (+.f64 (atan.f64 N) -2)))
(-.f64 1 (atan.f64 N))
(+.f64 0 (-.f64 1 (atan.f64 N)))
(-.f64 1 (atan.f64 N))
(+.f64 (neg.f64 (+.f64 (atan.f64 N) -2)) -1)
(-.f64 1 (atan.f64 N))
(+.f64 -2 (-.f64 1 (+.f64 (atan.f64 N) -2)))
(-.f64 1 (atan.f64 N))
(+.f64 (.f64 (-.f64 1 (atan.f64 N)) 1/2) (.f64 (-.f64 1 (atan.f64 N)) 1/2))
(-.f64 1 (atan.f64 N))
(+.f64 (+.f64 (*.f64 (-.f64 1 (atan.f64 N)) 1/2) -1) (-.f64 1 (/.f64 (+.f64 (atan.f64 N) -1) 2)))
(-.f64 1 (atan.f64 N))
(*.f64 1 (-.f64 1 (atan.f64 N)))
(-.f64 1 (atan.f64 N))
(*.f64 (-.f64 1 (atan.f64 N)) 1)
(-.f64 1 (atan.f64 N))
(*.f64 -1 (+.f64 (atan.f64 N) -1))
(-.f64 1 (atan.f64 N))
(.f64 2 (.f64 (-.f64 1 (atan.f64 N)) 1/2))
(-.f64 1 (atan.f64 N))
(.f64 (.f64 (-.f64 1 (atan.f64 N)) 2) 1/2)
(-.f64 1 (atan.f64 N))
(*.f64 4 (/.f64 (+.f64 (atan.f64 N) -1) -4))
(-.f64 1 (atan.f64 N))
(*.f64 (+.f64 (atan.f64 N) -1) -1)
(-.f64 1 (atan.f64 N))
(.f64 (.f64 (-.f64 1 (atan.f64 N)) 4) 1/4)
(-.f64 1 (atan.f64 N))
(.f64 1/2 (.f64 (-.f64 1 (atan.f64 N)) 2))
(-.f64 1 (atan.f64 N))
(.f64 (.f64 (-.f64 1 (atan.f64 N)) 1/2) 2)
(-.f64 1 (atan.f64 N))
(.f64 1/4 (.f64 (-.f64 1 (atan.f64 N)) 4))
(-.f64 1 (atan.f64 N))
(*.f64 (/.f64 (+.f64 (atan.f64 N) -1) 2) -2)
(-.f64 1 (atan.f64 N))
(*.f64 (/.f64 (+.f64 (atan.f64 N) -1) -4) 4)
(-.f64 1 (atan.f64 N))
(/.f64 (-.f64 1 (atan.f64 N)) 1)
(-.f64 1 (atan.f64 N))
(/.f64 (*.f64 (-.f64 1 (atan.f64 N)) 2) 2)
(-.f64 1 (atan.f64 N))
(/.f64 (+.f64 (atan.f64 N) -1) -1)
(-.f64 1 (atan.f64 N))
(/.f64 (*.f64 (-.f64 1 (atan.f64 N)) 4) 4)
(-.f64 1 (atan.f64 N))
(/.f64 (*.f64 2 (+.f64 (atan.f64 N) -1)) -2)
(-.f64 1 (atan.f64 N))
(/.f64 (*.f64 (-.f64 1 (atan.f64 N)) 8) 8)
(-.f64 1 (atan.f64 N))
(/.f64 (.f64 2 (.f64 (-.f64 1 (atan.f64 N)) 8)) 16)
(-.f64 1 (atan.f64 N))
(/.f64 (*.f64 4 (+.f64 (atan.f64 N) -1)) -4)
(-.f64 1 (atan.f64 N))
(/.f64 (.f64 2 (.f64 4 (+.f64 (atan.f64 N) -1))) -8)
(-.f64 1 (atan.f64 N))
(/.f64 (.f64 2 (.f64 2 (*.f64 (-.f64 1 (atan.f64 N)) 8))) 32)
(-.f64 1 (atan.f64 N))
(/.f64 (neg.f64 (*.f64 4 (+.f64 (atan.f64 N) -1))) 4)
(-.f64 1 (atan.f64 N))
(/.f64 (.f64 2 (.f64 2 (*.f64 4 (+.f64 (atan.f64 N) -1)))) -16)
(-.f64 1 (atan.f64 N))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (-.f64 1 (atan.f64 N)) 8)))) 64)
(-.f64 1 (atan.f64 N))
(/.f64 (.f64 2 (neg.f64 (.f64 4 (+.f64 (atan.f64 N) -1)))) 8)
(-.f64 1 (atan.f64 N))
(/.f64 (+.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (-.f64 1 (atan.f64 N)) 8)))) (.f64 2 (.f64 2 (.f64 2 (.f64 (-.f64 1 (atan.f64 N)) 8))))) 128)
(-.f64 1 (atan.f64 N))
(/.f64 (+.f64 (.f64 2 (neg.f64 (.f64 4 (+.f64 (atan.f64 N) -1)))) (.f64 2 (neg.f64 (.f64 4 (+.f64 (atan.f64 N) -1))))) 16)
(-.f64 1 (atan.f64 N))
(pow.f64 (-.f64 1 (atan.f64 N)) 1)
(-.f64 1 (atan.f64 N))
(neg.f64 (+.f64 (atan.f64 N) -1))
(-.f64 1 (atan.f64 N))
(neg.f64 (-.f64 0 (-.f64 1 (atan.f64 N))))
(-.f64 1 (atan.f64 N))

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 75 to 53 computations (29.3% saved)

series5.0ms (0%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	N	@	inf	(+.f64 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2) -1)
1.0ms	N	@	inf	(+.f64 (+.f64 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2) -1) (+.f64 1 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2)))
1.0ms	N	@	0	(+.f64 (+.f64 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2) -1) (+.f64 1 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2)))
0.0ms	N	@	-inf	(+.f64 (+.f64 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2) -1) (+.f64 1 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2)))
0.0ms	N	@	-inf	(+.f64 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2) -1)

rewrite100.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1336×	`exponential.json-3`
1336×	`rational.json-1`
1336×	`rational.json-2`
1336×	`rational.json-4`
1336×	`rational.json-3`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	137
1	111	137
2	224	87
3	472	87
4	948	87
5	1921	87
6	3509	87
7	6101	87

Stop Event

1×	node limit

Counts

3 → 95

Calls

Call 1

Inputs

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

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

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 1 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (+.f64 (atan.f64 N) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (/.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 -1 (+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1)))))))) (#(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 0 (-.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))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (-.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))) (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (atan.f64 (+.f64 N 1)) -1) (+.f64 (atan.f64 N) -1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3/4) (/.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -4))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 (atan.f64 (+.f64 N 1)) -1)) (atan.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (-.f64 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) -1) -1) -2) (atan.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (+.f64 (-.f64 (atan.f64 (+.f64 N 1)) -2) -1) -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 1/2 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2)))) (#(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 2 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (+.f64 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))) 4) (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (-.f64 (/.f64 (atan.f64 (+.f64 N 1)) 4) (/.f64 (atan.f64 N) 4)))))) (#(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 (+.f64 N 1)) (atan.f64 N)) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -2) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))) 4) (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 4)) 2)))) (#(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)) 2) 2)))) (#(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 (+.f64 N 1)) (atan.f64 N)) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -4) -4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -4)) -8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 8)))) 64)))) (#(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 -.f64 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) -1) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) -2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/4) -1) (/.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N)))) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 8) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N)))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 4) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 4)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 4))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 4)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) -1) 1)))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 1 (/.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 1 (*.f64 2 (/.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -4)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) -1) -2)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/4)) (/.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))) 8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N)))) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))) 4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))) 8) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N)))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))) 4) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))) 4)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))) 4))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))) 4)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N)))) 1)))))

simplify754.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

3032×	`rational.json-simplify-35`
1580×	`rational.json-simplify-2`
1146×	`rational.json-simplify-1`
914×	`rational.json-simplify-51`
854×	`rational.json-simplify-49`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	186	3733
1	413	3733
2	977	3733
3	2873	3733
4	4753	3733
5	5713	3733
6	6249	3733
7	6425	3733
8	6592	3733
9	6753	3733
10	7136	3733
11	7159	3733
12	7273	3733
13	7304	3733
14	7311	3733
15	7486	3733
16	7654	3733
17	7824	3733
18	7989	3733

Stop Event

1×	node limit

Counts

131 → 103

Calls

Call 1

Inputs
(-.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 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))
(-.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 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 1)
(-.f64 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 1)
(-.f64 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 1)
(-.f64 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 1)
(-.f64 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 1)
(-.f64 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 1)
(-.f64 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 1)
(-.f64 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 1)
(-.f64 (.f64 1/2 (-.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) (atan.f64 N))) 1)
(-.f64 (.f64 1/2 (-.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) (atan.f64 N))) 1)
(-.f64 (.f64 1/2 (-.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) (atan.f64 N))) 1)
(-.f64 (.f64 1/2 (-.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) (atan.f64 N))) 1)
(+.f64 1 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))
(+.f64 1 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))
(+.f64 1 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))
(+.f64 1 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))
(+.f64 1 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))
(+.f64 1 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))
(+.f64 1 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))
(+.f64 1 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))
(+.f64 1 (.f64 1/2 (-.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) (atan.f64 N))))
(+.f64 1 (.f64 1/2 (-.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) (atan.f64 N))))
(+.f64 1 (.f64 1/2 (-.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) (atan.f64 N))))
(+.f64 1 (.f64 1/2 (-.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) (atan.f64 N))))
(-.f64 1 (+.f64 1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (+.f64 1 (+.f64 (atan.f64 N) -1)))
(-.f64 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (/.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -2))
(-.f64 -1 (+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1)))))
(-.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0)
(-.f64 0 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))
(-.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) -1)
(-.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))) 2)
(-.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) -2)
(-.f64 (+.f64 1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 1)
(-.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -2))
(-.f64 (+.f64 (atan.f64 (+.f64 N 1)) -1) (+.f64 (atan.f64 N) -1))
(-.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (+.f64 1 (atan.f64 N)))
(-.f64 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3/4) (/.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -4))
(-.f64 (+.f64 1 (+.f64 (atan.f64 (+.f64 N 1)) -1)) (atan.f64 N))
(-.f64 (-.f64 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) -1) -1) -2) (atan.f64 N))
(-.f64 (+.f64 (+.f64 (-.f64 (atan.f64 (+.f64 N 1)) -2) -1) -1) (atan.f64 N))
(*.f64 1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
(.f64 1/2 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2))
(.f64 (.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2)
(*.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))
(*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1)
(.f64 2 (.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))
(*.f64 2 (+.f64 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))) 4) (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 4)))
(.f64 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2) 1/2)
(.f64 4 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/4))
(*.f64 4 (-.f64 (/.f64 (atan.f64 (+.f64 N 1)) 4) (/.f64 (atan.f64 N) 4)))
(*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) -1)
(.f64 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 4) 1/4)
(.f64 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -2) -1/2)
(.f64 1/4 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 4))
(.f64 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/4) 4)
(*.f64 (/.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -2) -2)
(*.f64 (+.f64 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))) 4) (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 4)) 2)
(/.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1)
(/.f64 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2) 2)
(/.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) -1)
(/.f64 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 4) 4)
(/.f64 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 8) 8)
(/.f64 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -2) -2)
(/.f64 (.f64 2 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 8)) 16)
(/.f64 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -4) -4)
(/.f64 (.f64 2 (.f64 2 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 8))) 32)
(/.f64 (.f64 2 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -4)) -8)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 8)))) 64)
(pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1)
(neg.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))
(-.f64 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 1)
(-.f64 (+.f64 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) -1) 0)
(-.f64 (+.f64 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) -2) -1)
(-.f64 (+.f64 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/4) -1) (/.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -4))
(.f64 1 (+.f64 (.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) -1))
(*.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))))
(.f64 (+.f64 (.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) -1) 1)
(*.f64 2 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 4))
(*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 1/2)
(*.f64 4 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 8))
(.f64 (.f64 2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N)))) 1/4)
(.f64 1/4 (.f64 2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N)))))
(*.f64 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 4) 2)
(*.f64 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 8) 4)
(/.f64 (+.f64 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) -1) 1)
(/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 2)
(/.f64 (*.f64 2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N)))) 4)
(/.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 4) 8)
(/.f64 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 4)) 16)
(/.f64 (.f64 2 (.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 4))) 32)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 4)))) 64)
(pow.f64 (+.f64 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) -1) 1)
(-.f64 1 (/.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -2))
(-.f64 1 (*.f64 2 (/.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -4)))
(-.f64 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) -1)
(-.f64 (+.f64 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) -1) -2)
(-.f64 (*.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N)))) 0)
(-.f64 (+.f64 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2) 1)
(-.f64 (+.f64 1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/4)) (/.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -4))
(.f64 1 (.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N)))))
(*.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))))
(.f64 (.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N)))) 1)
(*.f64 2 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))) 4))
(*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))) 1/2)
(*.f64 4 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))) 8))
(.f64 (.f64 2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N)))) 1/4)
(*.f64 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))) 4) 2)
(.f64 1/4 (.f64 2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N)))))
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(-.f64 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) -1)
(+.f64 1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2))
(-.f64 (+.f64 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) -1) -2)
(+.f64 1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2))
(-.f64 (*.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N)))) 0)
(*.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))))
(-.f64 (+.f64 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2) 1)
(+.f64 1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2))
(-.f64 (+.f64 1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/4)) (/.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -4))
(+.f64 1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2))
(.f64 1 (.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N)))))
(*.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))))
(*.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))))
(.f64 (.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N)))) 1)
(*.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))))
(*.f64 2 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))) 4))
(*.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))))
(*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))) 1/2)
(*.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))))
(*.f64 4 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))) 8))
(*.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))))
(.f64 (.f64 2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N)))) 1/4)
(*.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))))
(*.f64 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))) 4) 2)
(*.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))))
(.f64 1/4 (.f64 2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N)))))
(*.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))))
(*.f64 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))) 8) 4)
(*.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))))
(/.f64 (*.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N)))) 1)
(*.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))))
(/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))) 2)
(*.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))))
(/.f64 (*.f64 2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N)))) 4)
(*.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))))
(/.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))) 4) 8)
(*.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))))
(/.f64 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))) 4)) 16)
(*.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))))
(/.f64 (.f64 2 (.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))) 4))) 32)
(*.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))) 4)))) 64)
(*.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))))
(pow.f64 (*.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N)))) 1)
(*.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 2 (atan.f64 N))))

eval477.0ms (2.7%)

Compiler: Compiled 7903 to 6066 computations (23.2% saved)

prune566.0ms (3.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	404	2	406
Fresh	0	0	0
Picked	1	0	1
Done	0	3	3
Total	405	5	410

Error

15.4b

Counts

410 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	15.4b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
▶	15.4b	(+.f64 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 2) (+.f64 1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2)))
✓	15.4b	(+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) -1)
✓	15.4b	(+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1)
▶	15.4b	(+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (+.f64 (+.f64 (.f64 (-.f64 -1 (atan.f64 N)) 1/2) -1) (+.f64 1 (.f64 (-.f64 -1 (atan.f64 N)) 1/2)))) 1)

Compiler

Compiled 81 to 66 computations (18.5% saved)

localize61.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(-.f64 -1 (atan.f64 N))
✓	0.3b	(+.f64 (+.f64 (.f64 (-.f64 -1 (atan.f64 N)) 1/2) -1) (+.f64 1 (.f64 (-.f64 -1 (atan.f64 N)) 1/2)))
✓	0.8b	(+.f64 (atan.f64 (+.f64 N 1)) (+.f64 (+.f64 (.f64 (-.f64 -1 (atan.f64 N)) 1/2) -1) (+.f64 1 (.f64 (-.f64 -1 (atan.f64 N)) 1/2))))
✓	14.5b	(+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (+.f64 (+.f64 (.f64 (-.f64 -1 (atan.f64 N)) 1/2) -1) (+.f64 1 (.f64 (-.f64 -1 (atan.f64 N)) 1/2)))) 1)

Compiler

Compiled 103 to 77 computations (25.2% saved)

series3.0ms (0%)

Counts

3 → 36

Calls

9 calls:

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

rewrite137.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1566×	`rational.json-1`
1430×	`rational.json-simplify-35`
1400×	`exponential.json-3`
1400×	`rational.json-2`
1400×	`rational.json-4`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	17	191
1	127	191
2	268	71
3	626	65
4	1598	63
5	3469	63
6	4882	63
7	6456	63
8	7953	63

Stop Event

1×	node limit

Counts

3 → 91

Calls

Call 1

Inputs

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

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

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4)))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4))))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 1)))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (+.f64 (*.f64 (atan.f64 (+.f64 N 1)) 2) (-.f64 (*.f64 (atan.f64 N) -2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 (atan.f64 (+.f64 N 1)) 2) (-.f64 (*.f64 (atan.f64 N) -2) 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4)))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4))))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1)))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 1 (+.f64 1 (+.f64 1 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 1 (-.f64 (atan.f64 N) -2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 -1 (atan.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 -1 (+.f64 1 (+.f64 (atan.f64 N) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 1/2 (-.f64 -1 (atan.f64 N))) (/.f64 (+.f64 1 (atan.f64 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (-.f64 -1 (atan.f64 N)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (+.f64 1 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (+.f64 1 (+.f64 1 (+.f64 (atan.f64 N) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (-.f64 1 (neg.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (-.f64 (+.f64 (atan.f64 N) -1) -2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (-.f64 (+.f64 1 (+.f64 1 (atan.f64 N))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (-.f64 (-.f64 (atan.f64 N) -2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (-.f64 -2 (atan.f64 N)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (neg.f64 (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 -2 (+.f64 (atan.f64 N) -1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (-.f64 (/.f64 (+.f64 1 (atan.f64 N)) -4) (/.f64 (+.f64 1 (atan.f64 N)) 2)) (/.f64 (+.f64 1 (atan.f64 N)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 -1 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (+.f64 1 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (-.f64 (*.f64 (atan.f64 N) -2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (-.f64 -1 (atan.f64 N))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 -1 (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 1/2 (-.f64 -1 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 (atan.f64 N) -2) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (/.f64 (+.f64 1 (atan.f64 N)) -4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (atan.f64 N)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 -1 (atan.f64 N)) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (-.f64 -1 (atan.f64 N)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 1 (atan.f64 N)) -4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 1 (atan.f64 N)) 2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 -1 (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (atan.f64 N) -2) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (atan.f64 N)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 -1 (atan.f64 N)) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (-.f64 -1 (atan.f64 N)) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (+.f64 1 (atan.f64 N))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (-.f64 -1 (atan.f64 N)) 4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (+.f64 1 (atan.f64 N)))) -4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (-.f64 -1 (atan.f64 N)) 4)))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (+.f64 1 (atan.f64 N))))) -8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 2 (*.f64 2 (+.f64 1 (atan.f64 N))))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (-.f64 -1 (atan.f64 N)) 4))))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (neg.f64 (*.f64 2 (*.f64 2 (+.f64 1 (atan.f64 N)))))) 8)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 -1 (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (+.f64 1 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (+.f64 1 (+.f64 1 (+.f64 (atan.f64 N) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (-.f64 1 (neg.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (-.f64 (+.f64 (atan.f64 N) -1) -2))))))

simplify223.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

2348×	`rational.json-simplify-2`
1476×	`rational.json-simplify-35`
1286×	`rational.json-simplify-51`
1152×	`rational.json-simplify-52`
1102×	`rational.json-simplify-1`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	171	3219
1	384	2719
2	891	2455
3	2528	2455
4	4456	2455
5	5541	2455
6	5951	2455
7	6422	2455
8	6828	2455
9	7485	2455

Stop Event

1×	node limit

Counts

127 → 102

Calls

Call 1

Inputs
(+.f64 1 (+.f64 (*.f64 -1 (+.f64 1 (atan.f64 N))) (atan.f64 (+.f64 N 1))))
(+.f64 1 (+.f64 (*.f64 -1 (+.f64 1 (atan.f64 N))) (atan.f64 (+.f64 N 1))))
(+.f64 1 (+.f64 (*.f64 -1 (+.f64 1 (atan.f64 N))) (atan.f64 (+.f64 N 1))))
(+.f64 1 (+.f64 (*.f64 -1 (+.f64 1 (atan.f64 N))) (atan.f64 (+.f64 N 1))))
(+.f64 1 (+.f64 (*.f64 -1 (+.f64 1 (atan.f64 N))) (atan.f64 (+.f64 N 1))))
(+.f64 1 (+.f64 (*.f64 -1 (+.f64 1 (atan.f64 N))) (atan.f64 (+.f64 N 1))))
(+.f64 1 (+.f64 (*.f64 -1 (+.f64 1 (atan.f64 N))) (atan.f64 (+.f64 N 1))))
(+.f64 1 (+.f64 (*.f64 -1 (+.f64 1 (atan.f64 N))) (atan.f64 (+.f64 N 1))))
(+.f64 1 (+.f64 (.f64 -1 (+.f64 1 (atan.f64 N))) (atan.f64 (-.f64 1 (.f64 -1 N)))))
(+.f64 1 (+.f64 (.f64 -1 (+.f64 1 (atan.f64 N))) (atan.f64 (-.f64 1 (.f64 -1 N)))))
(+.f64 1 (+.f64 (.f64 -1 (+.f64 1 (atan.f64 N))) (atan.f64 (-.f64 1 (.f64 -1 N)))))
(+.f64 1 (+.f64 (.f64 -1 (+.f64 1 (atan.f64 N))) (atan.f64 (-.f64 1 (.f64 -1 N)))))
(+.f64 (*.f64 -1 (+.f64 1 (atan.f64 N))) (atan.f64 (+.f64 N 1)))
(+.f64 (*.f64 -1 (+.f64 1 (atan.f64 N))) (atan.f64 (+.f64 N 1)))
(+.f64 (*.f64 -1 (+.f64 1 (atan.f64 N))) (atan.f64 (+.f64 N 1)))
(+.f64 (*.f64 -1 (+.f64 1 (atan.f64 N))) (atan.f64 (+.f64 N 1)))
(+.f64 (*.f64 -1 (+.f64 1 (atan.f64 N))) (atan.f64 (+.f64 N 1)))
(+.f64 (*.f64 -1 (+.f64 1 (atan.f64 N))) (atan.f64 (+.f64 N 1)))
(+.f64 (*.f64 -1 (+.f64 1 (atan.f64 N))) (atan.f64 (+.f64 N 1)))
(+.f64 (*.f64 -1 (+.f64 1 (atan.f64 N))) (atan.f64 (+.f64 N 1)))
(+.f64 (.f64 -1 (+.f64 1 (atan.f64 N))) (atan.f64 (-.f64 1 (.f64 -1 N))))
(+.f64 (.f64 -1 (+.f64 1 (atan.f64 N))) (atan.f64 (-.f64 1 (.f64 -1 N))))
(+.f64 (.f64 -1 (+.f64 1 (atan.f64 N))) (atan.f64 (-.f64 1 (.f64 -1 N))))
(+.f64 (.f64 -1 (+.f64 1 (atan.f64 N))) (atan.f64 (-.f64 1 (.f64 -1 N))))
(*.f64 -1 (+.f64 1 (atan.f64 N)))
(*.f64 -1 (+.f64 1 (atan.f64 N)))
(*.f64 -1 (+.f64 1 (atan.f64 N)))
(*.f64 -1 (+.f64 1 (atan.f64 N)))
(*.f64 -1 (+.f64 1 (atan.f64 N)))
(*.f64 -1 (+.f64 1 (atan.f64 N)))
(*.f64 -1 (+.f64 1 (atan.f64 N)))
(*.f64 -1 (+.f64 1 (atan.f64 N)))
(*.f64 -1 (+.f64 1 (atan.f64 N)))
(*.f64 -1 (+.f64 1 (atan.f64 N)))
(*.f64 -1 (+.f64 1 (atan.f64 N)))
(*.f64 -1 (+.f64 1 (atan.f64 N)))
(-.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) -1)
(-.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 0)
(-.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) 1)
(*.f64 1 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))))
(.f64 1/2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 2))
(*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 1)
(.f64 2 (.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N)))))
(*.f64 4 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4))
(.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 2) 1/2)
(.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4) 1/4)
(.f64 (.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N)))) 2)
(.f64 1/4 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4))
(*.f64 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4) 4)
(/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 1)
(/.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 2) 2)
(/.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4) 4)
(/.f64 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4)) 8)
(/.f64 (.f64 2 (.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4))) 16)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4)))) 32)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 4))))) 64)
(pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 1)
(-.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 0)
(-.f64 (+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))) 1)
(-.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) -1)
(*.f64 1 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))
(.f64 1/2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2))
(.f64 1/2 (+.f64 (.f64 (atan.f64 (+.f64 N 1)) 2) (-.f64 (*.f64 (atan.f64 N) -2) 2)))
(*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1)
(.f64 2 (.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))))
(*.f64 4 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4))
(.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2) 1/2)
(.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4) 1/4)
(.f64 1/4 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4))
(.f64 (.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))) 2)
(*.f64 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4) 4)
(.f64 (+.f64 (.f64 (atan.f64 (+.f64 N 1)) 2) (-.f64 (*.f64 (atan.f64 N) -2) 2)) 1/2)
(/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1)
(/.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2) 2)
(/.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4) 4)
(/.f64 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4)) 8)
(/.f64 (.f64 2 (.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4))) 16)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4)))) 32)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4))))) 64)
(pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1)
(-.f64 1 (+.f64 1 (+.f64 1 (atan.f64 N))))
(-.f64 1 (-.f64 (atan.f64 N) -2))
(-.f64 -1 (atan.f64 N))
(-.f64 -1 (+.f64 1 (+.f64 (atan.f64 N) -1)))
(-.f64 (*.f64 1/2 (-.f64 -1 (atan.f64 N))) (/.f64 (+.f64 1 (atan.f64 N)) 2))
(-.f64 (-.f64 -1 (atan.f64 N)) 0)
(-.f64 0 (+.f64 1 (atan.f64 N)))
(-.f64 0 (+.f64 1 (+.f64 1 (+.f64 (atan.f64 N) -1))))
(-.f64 0 (-.f64 1 (neg.f64 (atan.f64 N))))
(-.f64 0 (-.f64 (+.f64 (atan.f64 N) -1) -2))
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(.f64 1/2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2))
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(.f64 1/2 (+.f64 (.f64 (atan.f64 (+.f64 1 N)) 2) (-.f64 (*.f64 (atan.f64 N) -2) 2)))
(.f64 1/2 (+.f64 (.f64 (atan.f64 (+.f64 1 N)) 2) (+.f64 -2 (*.f64 (atan.f64 N) -2))))
(*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1)
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(*.f64 4 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4))
(+.f64 (neg.f64 (+.f64 1 (atan.f64 N))) (atan.f64 (+.f64 1 N)))
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(.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2) 1/2)
(+.f64 (neg.f64 (+.f64 1 (atan.f64 N))) (atan.f64 (+.f64 1 N)))
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(.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4) 1/4)
(+.f64 (neg.f64 (+.f64 1 (atan.f64 N))) (atan.f64 (+.f64 1 N)))
(+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -1 (atan.f64 N)))
(.f64 1/4 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4))
(+.f64 (neg.f64 (+.f64 1 (atan.f64 N))) (atan.f64 (+.f64 1 N)))
(+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -1 (atan.f64 N)))
(.f64 (.f64 1/2 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))) 2)
(+.f64 (neg.f64 (+.f64 1 (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 N 1)) (-.f64 -1 (atan.f64 N))) 4) 4)
(+.f64 (neg.f64 (+.f64 1 (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 N 1)) 2) (-.f64 (*.f64 (atan.f64 N) -2) 2)) 1/2)
(.f64 1/2 (+.f64 (.f64 (atan.f64 (+.f64 1 N)) 2) (-.f64 (*.f64 (atan.f64 N) -2) 2)))
(.f64 1/2 (+.f64 (.f64 (atan.f64 (+.f64 1 N)) 2) (+.f64 -2 (*.f64 (atan.f64 N) -2))))
(/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1)
(+.f64 (neg.f64 (+.f64 1 (atan.f64 N))) (atan.f64 (+.f64 1 N)))
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(/.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 2) 2)
(+.f64 (neg.f64 (+.f64 1 (atan.f64 N))) (atan.f64 (+.f64 1 N)))
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(/.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4) 4)
(+.f64 (neg.f64 (+.f64 1 (atan.f64 N))) (atan.f64 (+.f64 1 N)))
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(/.f64 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4)) 8)
(+.f64 (neg.f64 (+.f64 1 (atan.f64 N))) (atan.f64 (+.f64 1 N)))
(+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -1 (atan.f64 N)))
(/.f64 (.f64 2 (.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4))) 16)
(+.f64 (neg.f64 (+.f64 1 (atan.f64 N))) (atan.f64 (+.f64 1 N)))
(+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -1 (atan.f64 N)))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4)))) 32)
(+.f64 (neg.f64 (+.f64 1 (atan.f64 N))) (atan.f64 (+.f64 1 N)))
(+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -1 (atan.f64 N)))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 4))))) 64)
(+.f64 (neg.f64 (+.f64 1 (atan.f64 N))) (atan.f64 (+.f64 1 N)))
(+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -1 (atan.f64 N)))
(pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1)
(+.f64 (neg.f64 (+.f64 1 (atan.f64 N))) (atan.f64 (+.f64 1 N)))
(+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -1 (atan.f64 N)))
(-.f64 1 (+.f64 1 (+.f64 1 (atan.f64 N))))
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(-.f64 1 (-.f64 (atan.f64 N) -2))
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(-.f64 -1 (atan.f64 N))
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (+.f64 1 (+.f64 (atan.f64 N) -1)))
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(-.f64 (*.f64 1/2 (-.f64 -1 (atan.f64 N))) (/.f64 (+.f64 1 (atan.f64 N)) 2))
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(-.f64 (-.f64 -1 (atan.f64 N)) 0)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(-.f64 0 (+.f64 1 (atan.f64 N)))
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(-.f64 0 (+.f64 1 (+.f64 1 (+.f64 (atan.f64 N) -1))))
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(-.f64 0 (-.f64 1 (neg.f64 (atan.f64 N))))
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(-.f64 0 (-.f64 (+.f64 (atan.f64 N) -1) -2))
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(-.f64 0 (-.f64 (+.f64 1 (+.f64 1 (atan.f64 N))) 1))
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(-.f64 0 (-.f64 (-.f64 (atan.f64 N) -2) 1))
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(-.f64 (-.f64 -2 (atan.f64 N)) -1)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(-.f64 (neg.f64 (atan.f64 N)) 1)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(-.f64 -2 (+.f64 (atan.f64 N) -1))
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(-.f64 (-.f64 (/.f64 (+.f64 1 (atan.f64 N)) -4) (/.f64 (+.f64 1 (atan.f64 N)) 2)) (/.f64 (+.f64 1 (atan.f64 N)) 4))
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(*.f64 1 (-.f64 -1 (atan.f64 N)))
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(*.f64 -1 (+.f64 1 (atan.f64 N)))
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(.f64 1/2 (-.f64 (.f64 (atan.f64 N) -2) 2))
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(.f64 (.f64 1/2 (-.f64 -1 (atan.f64 N))) 2)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(*.f64 (-.f64 -1 (atan.f64 N)) 1)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(.f64 2 (.f64 1/2 (-.f64 -1 (atan.f64 N))))
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(.f64 (-.f64 (.f64 (atan.f64 N) -2) 2) 1/2)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(*.f64 4 (/.f64 (+.f64 1 (atan.f64 N)) -4))
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(*.f64 (+.f64 1 (atan.f64 N)) -1)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(.f64 (.f64 (-.f64 -1 (atan.f64 N)) 4) 1/4)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(.f64 1/4 (.f64 (-.f64 -1 (atan.f64 N)) 4))
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(*.f64 (/.f64 (+.f64 1 (atan.f64 N)) -4) 4)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(*.f64 (/.f64 (+.f64 1 (atan.f64 N)) 2) -2)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(/.f64 (-.f64 -1 (atan.f64 N)) 1)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(/.f64 (-.f64 (*.f64 (atan.f64 N) -2) 2) 2)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(/.f64 (+.f64 1 (atan.f64 N)) -1)
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(-.f64 -1 (atan.f64 N))
(/.f64 (*.f64 (-.f64 -1 (atan.f64 N)) 4) 4)
(neg.f64 (+.f64 1 (atan.f64 N)))
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(/.f64 (.f64 2 (.f64 (-.f64 -1 (atan.f64 N)) 4)) 8)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(/.f64 (*.f64 2 (+.f64 1 (atan.f64 N))) -2)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(/.f64 (.f64 2 (.f64 2 (*.f64 (-.f64 -1 (atan.f64 N)) 4))) 16)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(/.f64 (.f64 2 (.f64 2 (+.f64 1 (atan.f64 N)))) -4)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (-.f64 -1 (atan.f64 N)) 4)))) 32)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(/.f64 (.f64 2 (.f64 2 (*.f64 2 (+.f64 1 (atan.f64 N))))) -8)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(/.f64 (neg.f64 (.f64 2 (.f64 2 (+.f64 1 (atan.f64 N))))) 4)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (*.f64 (-.f64 -1 (atan.f64 N)) 4))))) 64)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(/.f64 (.f64 2 (neg.f64 (.f64 2 (*.f64 2 (+.f64 1 (atan.f64 N)))))) 8)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(pow.f64 (-.f64 -1 (atan.f64 N)) 1)
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(neg.f64 (+.f64 1 (+.f64 1 (+.f64 (atan.f64 N) -1))))
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(neg.f64 (-.f64 1 (neg.f64 (atan.f64 N))))
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))
(neg.f64 (-.f64 (+.f64 (atan.f64 N) -1) -2))
(neg.f64 (+.f64 1 (atan.f64 N)))
(-.f64 -1 (atan.f64 N))

localize103.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N)))
✓	0.3b	(-.f64 -2 (atan.f64 N))
	1.7b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
✓	14.2b	(+.f64 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 2) (+.f64 1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2)))

Compiler

Compiled 89 to 62 computations (30.3% saved)

series2.0ms (0%)

Counts

3 → 36

Calls

9 calls:

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

rewrite143.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1370×	`exponential.json-3`
1370×	`rational.json-1`
1370×	`rational.json-2`
1370×	`rational.json-4`
1370×	`rational.json-3`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	109
1	131	109
2	269	103
3	539	103
4	1117	103
5	2365	103
6	3833	103
7	5428	103
8	6939	103

Stop Event

1×	node limit

Counts

3 → 84

Calls

Call 1

Inputs

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

(-.f64 -2 (atan.f64 N))

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 1/2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 1/2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1 (*.f64 1/2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (/.f64 (+.f64 2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (+.f64 2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (+.f64 2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (*.f64 1/2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (/.f64 (+.f64 2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) 8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (+.f64 2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 2 (+.f64 2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) 4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) 8) 4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (+.f64 2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (*.f64 1/2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (+.f64 2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (+.f64 2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (+.f64 2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (+.f64 2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (+.f64 2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (*.f64 1/2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) 1)))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 -2 (-.f64 1 (+.f64 1 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 -2 (atan.f64 N)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 -2 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (neg.f64 (+.f64 1 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (-.f64 1 (neg.f64 (-.f64 -2 (atan.f64 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (+.f64 1 (atan.f64 N))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (-.f64 -2 (atan.f64 N)) 1/2) (*.f64 (-.f64 -2 (atan.f64 N)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 -1 (/.f64 (+.f64 (atan.f64 N) 2) 2)) (-.f64 1 (/.f64 (+.f64 (atan.f64 N) 2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 -2 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 -2 (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 (-.f64 -2 (atan.f64 N)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 -2 (+.f64 (atan.f64 N) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (+.f64 (atan.f64 N) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (/.f64 (-.f64 -2 (atan.f64 N)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 -2 (+.f64 (atan.f64 N) 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (atan.f64 N) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 -2 (atan.f64 N)) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (-.f64 -2 (atan.f64 N)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 -2 (atan.f64 N)) 1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 (atan.f64 N) 2) 2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 -2 (atan.f64 N)) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (-.f64 -2 (atan.f64 N))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 -2 (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -2 (+.f64 (atan.f64 N) 2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (atan.f64 N) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 -2 (atan.f64 N)) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (+.f64 (atan.f64 N) 2)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (-.f64 -2 (atan.f64 N)) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (+.f64 (atan.f64 N) 2))) -4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (-.f64 -2 (atan.f64 N)) 4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (-.f64 -2 (atan.f64 N)) 4)))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (+.f64 (atan.f64 N) 2)))) -8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 2 (*.f64 2 (+.f64 (atan.f64 N) 2)))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (-.f64 -2 (atan.f64 N)) 4))))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (neg.f64 (*.f64 2 (*.f64 2 (+.f64 (atan.f64 N) 2))))) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 -2 (atan.f64 N))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 -2 (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (+.f64 (atan.f64 N) 2))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (-.f64 -2 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (+.f64 1 (+.f64 1 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (-.f64 (+.f64 (atan.f64 N) -1) -3))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 8) 1/8)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 1/4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/8 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 8))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 8)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 1)))))

simplify410.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

2102×	`rational.json-simplify-52`
1918×	`rational.json-simplify-35`
1646×	`rational.json-simplify-2`
1230×	`rational.json-simplify-51`
922×	`rational.json-simplify-1`

Iterations

Useful iterations: 10 (0.0ms)

Iter	Nodes	Cost
0	172	4100
1	371	3896
2	966	3684
3	2266	3684
4	4035	3684
5	5362	3684
6	5945	3684
7	6239	3684
8	6424	3684
9	6618	3684
10	7250	3276

Stop Event

1×	node limit

Counts

120 → 97

Calls

Call 1

Inputs
(+.f64 1 (+.f64 (.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 2 (atan.f64 N))))))
(+.f64 1 (+.f64 (.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 2 (atan.f64 N))))))
(+.f64 1 (+.f64 (.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 2 (atan.f64 N))))))
(+.f64 1 (+.f64 (.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 2 (atan.f64 N))))))
(+.f64 1 (+.f64 (.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 2 (atan.f64 N))))))
(+.f64 1 (+.f64 (.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 2 (atan.f64 N))))))
(+.f64 1 (+.f64 (.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 2 (atan.f64 N))))))
(+.f64 1 (+.f64 (.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (.f64 1/2 (-.f64 (atan.f64 (+.f64 N 1)) (+.f64 2 (atan.f64 N))))))
(+.f64 1 (+.f64 (.f64 1/2 (-.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) (atan.f64 N))) (.f64 1/2 (-.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) (+.f64 2 (atan.f64 N))))))
(+.f64 1 (+.f64 (.f64 1/2 (-.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) (atan.f64 N))) (.f64 1/2 (-.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) (+.f64 2 (atan.f64 N))))))
(+.f64 1 (+.f64 (.f64 1/2 (-.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) (atan.f64 N))) (.f64 1/2 (-.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) (+.f64 2 (atan.f64 N))))))
(+.f64 1 (+.f64 (.f64 1/2 (-.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) (atan.f64 N))) (.f64 1/2 (-.f64 (atan.f64 (-.f64 1 (.f64 -1 N))) (+.f64 2 (atan.f64 N))))))
(*.f64 -1 (+.f64 2 (atan.f64 N)))
(*.f64 -1 (+.f64 2 (atan.f64 N)))
(*.f64 -1 (+.f64 2 (atan.f64 N)))
(*.f64 -1 (+.f64 2 (atan.f64 N)))
(*.f64 -1 (+.f64 2 (atan.f64 N)))
(*.f64 -1 (+.f64 2 (atan.f64 N)))
(*.f64 -1 (+.f64 2 (atan.f64 N)))
(*.f64 -1 (+.f64 2 (atan.f64 N)))
(*.f64 -1 (+.f64 2 (atan.f64 N)))
(*.f64 -1 (+.f64 2 (atan.f64 N)))
(*.f64 -1 (+.f64 2 (atan.f64 N)))
(*.f64 -1 (+.f64 2 (atan.f64 N)))
(-.f64 (atan.f64 (+.f64 N 1)) (+.f64 2 (atan.f64 N)))
(-.f64 (atan.f64 (+.f64 N 1)) (+.f64 2 (atan.f64 N)))
(-.f64 (atan.f64 (+.f64 N 1)) (+.f64 2 (atan.f64 N)))
(-.f64 (atan.f64 (+.f64 N 1)) (+.f64 2 (atan.f64 N)))
(-.f64 (atan.f64 (+.f64 N 1)) (+.f64 2 (atan.f64 N)))
(-.f64 (atan.f64 (+.f64 N 1)) (+.f64 2 (atan.f64 N)))
(-.f64 (atan.f64 (+.f64 N 1)) (+.f64 2 (atan.f64 N)))
(-.f64 (atan.f64 (+.f64 N 1)) (+.f64 2 (atan.f64 N)))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (+.f64 2 (atan.f64 N)))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (+.f64 2 (atan.f64 N)))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (+.f64 2 (atan.f64 N)))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (+.f64 2 (atan.f64 N)))
(-.f64 (+.f64 1 (*.f64 1/2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) 0)
(-.f64 (*.f64 1/2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) -1)
(.f64 1 (+.f64 1 (.f64 1/2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))
(*.f64 2 (/.f64 (+.f64 2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) 4))
(*.f64 1/2 (+.f64 2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))
(*.f64 1/2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (+.f64 2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))
(.f64 (+.f64 1 (.f64 1/2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) 1)
(*.f64 4 (/.f64 (+.f64 2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) 8))
(*.f64 (+.f64 2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) 1/2)
(.f64 (.f64 2 (+.f64 2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) 1/4)
(.f64 1/4 (.f64 2 (+.f64 2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))
(*.f64 (/.f64 (+.f64 2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) 4) 2)
(*.f64 (/.f64 (+.f64 2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) 8) 4)
(*.f64 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (+.f64 2 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) 1/2)
(/.f64 (+.f64 1 (*.f64 1/2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) 1)
(/.f64 (+.f64 2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) 2)
(/.f64 (*.f64 2 (+.f64 2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) 4)
(/.f64 (.f64 2 (.f64 2 (+.f64 2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) 8)
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(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (+.f64 2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))))) 32)
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(pow.f64 (+.f64 1 (*.f64 1/2 (+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) 1)
(+.f64 -2 (-.f64 1 (+.f64 1 (atan.f64 N))))
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(*.f64 1 (-.f64 -2 (atan.f64 N)))
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(.f64 2 (.f64 (-.f64 -2 (atan.f64 N)) 1/2))
(.f64 1/2 (.f64 -2 (+.f64 (atan.f64 N) 2)))
(*.f64 -1 (+.f64 (atan.f64 N) 2))
(*.f64 4 (/.f64 (-.f64 -2 (atan.f64 N)) 4))
(.f64 (.f64 -2 (+.f64 (atan.f64 N) 2)) 1/2)
(*.f64 (+.f64 (atan.f64 N) 2) -1)
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(*.f64 (/.f64 (+.f64 (atan.f64 N) 2) 2) -2)
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(/.f64 (.f64 2 (.f64 2 (+.f64 (atan.f64 N) 2))) -4)
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(/.f64 (neg.f64 (-.f64 -2 (atan.f64 N))) -1)
(pow.f64 (-.f64 -2 (atan.f64 N)) 1)
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(.f64 1/2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 2))
(.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 2) 1/2)
(.f64 4 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 1/4))
(.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 4) 1/4)
(.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 8) 1/8)
(.f64 1/4 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 4))
(.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 1/4) 4)
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(pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 1)

Outputs
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(*.f64 1/2 (+.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))))
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(*.f64 1/2 (+.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))))
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(*.f64 (-.f64 -2 (atan.f64 N)) 1)
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(.f64 2 (.f64 (-.f64 -2 (atan.f64 N)) 1/2))
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(-.f64 -2 (atan.f64 N))
(.f64 1/2 (.f64 -2 (+.f64 (atan.f64 N) 2)))
(neg.f64 (+.f64 (atan.f64 N) 2))
(-.f64 -2 (atan.f64 N))
(*.f64 -1 (+.f64 (atan.f64 N) 2))
(neg.f64 (+.f64 (atan.f64 N) 2))
(-.f64 -2 (atan.f64 N))
(*.f64 4 (/.f64 (-.f64 -2 (atan.f64 N)) 4))
(neg.f64 (+.f64 (atan.f64 N) 2))
(-.f64 -2 (atan.f64 N))
(.f64 (.f64 -2 (+.f64 (atan.f64 N) 2)) 1/2)
(neg.f64 (+.f64 (atan.f64 N) 2))
(-.f64 -2 (atan.f64 N))
(*.f64 (+.f64 (atan.f64 N) 2) -1)
(neg.f64 (+.f64 (atan.f64 N) 2))
(-.f64 -2 (atan.f64 N))
(.f64 (.f64 (-.f64 -2 (atan.f64 N)) 4) 1/4)
(neg.f64 (+.f64 (atan.f64 N) 2))
(-.f64 -2 (atan.f64 N))
(.f64 1/4 (.f64 (-.f64 -2 (atan.f64 N)) 4))
(neg.f64 (+.f64 (atan.f64 N) 2))
(-.f64 -2 (atan.f64 N))
(.f64 (.f64 (-.f64 -2 (atan.f64 N)) 1/2) 2)
(neg.f64 (+.f64 (atan.f64 N) 2))
(-.f64 -2 (atan.f64 N))
(*.f64 (/.f64 (+.f64 (atan.f64 N) 2) 2) -2)
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(-.f64 -2 (atan.f64 N))
(*.f64 (/.f64 (-.f64 -2 (atan.f64 N)) 4) 4)
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(*.f64 (neg.f64 (-.f64 -2 (atan.f64 N))) -1)
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(/.f64 (-.f64 -2 (atan.f64 N)) 1)
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(/.f64 (*.f64 -2 (+.f64 (atan.f64 N) 2)) 2)
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(/.f64 (+.f64 (atan.f64 N) 2) -1)
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(/.f64 (*.f64 (-.f64 -2 (atan.f64 N)) 4) 4)
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(/.f64 (*.f64 2 (+.f64 (atan.f64 N) 2)) -2)
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(/.f64 (.f64 2 (.f64 (-.f64 -2 (atan.f64 N)) 4)) 8)
(neg.f64 (+.f64 (atan.f64 N) 2))
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(/.f64 (.f64 2 (.f64 2 (+.f64 (atan.f64 N) 2))) -4)
(neg.f64 (+.f64 (atan.f64 N) 2))
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(/.f64 (.f64 2 (.f64 2 (*.f64 (-.f64 -2 (atan.f64 N)) 4))) 16)
(neg.f64 (+.f64 (atan.f64 N) 2))
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(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (-.f64 -2 (atan.f64 N)) 4)))) 32)
(neg.f64 (+.f64 (atan.f64 N) 2))
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(/.f64 (.f64 2 (.f64 2 (*.f64 2 (+.f64 (atan.f64 N) 2)))) -8)
(neg.f64 (+.f64 (atan.f64 N) 2))
(-.f64 -2 (atan.f64 N))
(/.f64 (neg.f64 (.f64 2 (.f64 2 (+.f64 (atan.f64 N) 2)))) 4)
(neg.f64 (+.f64 (atan.f64 N) 2))
(-.f64 -2 (atan.f64 N))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (*.f64 (-.f64 -2 (atan.f64 N)) 4))))) 64)
(neg.f64 (+.f64 (atan.f64 N) 2))
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(/.f64 (.f64 2 (neg.f64 (.f64 2 (*.f64 2 (+.f64 (atan.f64 N) 2))))) 8)
(neg.f64 (+.f64 (atan.f64 N) 2))
(-.f64 -2 (atan.f64 N))
(/.f64 (neg.f64 (-.f64 -2 (atan.f64 N))) -1)
(neg.f64 (+.f64 (atan.f64 N) 2))
(-.f64 -2 (atan.f64 N))
(pow.f64 (-.f64 -2 (atan.f64 N)) 1)
(neg.f64 (+.f64 (atan.f64 N) 2))
(-.f64 -2 (atan.f64 N))
(neg.f64 (+.f64 (atan.f64 N) 2))
(-.f64 -2 (atan.f64 N))
(neg.f64 (neg.f64 (-.f64 -2 (atan.f64 N))))
(neg.f64 (+.f64 (atan.f64 N) 2))
(-.f64 -2 (atan.f64 N))
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(-.f64 -2 (atan.f64 N))
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(-.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 0)
(-.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 N) 2))
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(*.f64 1 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))))
(-.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 N) 2))
(+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -2 (atan.f64 N)))
(*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 1)
(-.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 N) 2))
(+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -2 (atan.f64 N)))
(.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 1/2))
(-.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 N) 2))
(+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -2 (atan.f64 N)))
(.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 1/2) 2)
(-.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 N) 2))
(+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -2 (atan.f64 N)))
(.f64 1/2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 2))
(-.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 N) 2))
(+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -2 (atan.f64 N)))
(.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 2) 1/2)
(-.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 N) 2))
(+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -2 (atan.f64 N)))
(.f64 4 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 1/4))
(-.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 N) 2))
(+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -2 (atan.f64 N)))
(.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 4) 1/4)
(-.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 N) 2))
(+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -2 (atan.f64 N)))
(.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 8) 1/8)
(-.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 N) 2))
(+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -2 (atan.f64 N)))
(.f64 1/4 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 4))
(-.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 N) 2))
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(.f64 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 1/4) 4)
(-.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 N) 2))
(+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -2 (atan.f64 N)))
(.f64 1/8 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 8))
(-.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 N) 2))
(+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -2 (atan.f64 N)))
(/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 1)
(-.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 N) 2))
(+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -2 (atan.f64 N)))
(/.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 2) 2)
(-.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 N) 2))
(+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -2 (atan.f64 N)))
(/.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 4) 4)
(-.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 N) 2))
(+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -2 (atan.f64 N)))
(/.f64 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 8) 8)
(-.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 N) 2))
(+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -2 (atan.f64 N)))
(/.f64 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 8)) 16)
(-.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 N) 2))
(+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -2 (atan.f64 N)))
(/.f64 (.f64 2 (.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 8))) 32)
(-.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 N) 2))
(+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -2 (atan.f64 N)))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 8)))) 64)
(-.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 N) 2))
(+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -2 (atan.f64 N)))
(pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -2 (atan.f64 N))) 1)
(-.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 N) 2))
(+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -2 (atan.f64 N)))

eval456.0ms (2.6%)

Compiler: Compiled 8112 to 6372 computations (21.4% saved)

prune367.0ms (2.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	344	1	345
Fresh	0	0	0
Picked	1	0	1
Done	0	4	4
Total	345	5	350

Error

15.4b

Counts

350 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	15.4b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
✓	15.4b	(+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) -1)
✓	15.4b	(+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1)
✓	15.4b	(+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (+.f64 (+.f64 (.f64 (-.f64 -1 (atan.f64 N)) 1/2) -1) (+.f64 1 (.f64 (-.f64 -1 (atan.f64 N)) 1/2)))) 1)
▶	15.4b	(+.f64 1 (*.f64 1/2 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) (-.f64 -2 (atan.f64 N))))))

Compiler

Compiled 79 to 64 computations (19% saved)

localize100.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(-.f64 -2 (atan.f64 N))
✓	0.5b	(+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) (-.f64 -2 (atan.f64 N))))
✓	1.7b	(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
✓	14.2b	(+.f64 1 (*.f64 1/2 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) (-.f64 -2 (atan.f64 N))))))

Compiler

Compiled 94 to 62 computations (34% saved)

series4.0ms (0%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	N	@	inf	(+.f64 1 (*.f64 1/2 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) (-.f64 -2 (atan.f64 N))))))
1.0ms	N	@	-inf	(+.f64 1 (*.f64 1/2 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) (-.f64 -2 (atan.f64 N))))))
1.0ms	N	@	0	(+.f64 1 (*.f64 1/2 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) (-.f64 -2 (atan.f64 N))))))
0.0ms	N	@	-inf	(+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) (-.f64 -2 (atan.f64 N))))
0.0ms	N	@	0	(+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) (-.f64 -2 (atan.f64 N))))

rewrite159.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1572×	`rational.json-1`
1572×	`rational.json-2`
1458×	`exponential.json-3`
1458×	`rational.json-4`
1458×	`rational.json-3`

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	16	139
1	117	139
2	234	139
3	462	139
4	957	139
5	2027	139
6	3746	139
7	5621	139
8	6951	131
9	7909	131

Stop Event

1×	node limit

Counts

3 → 82

Calls

Call 1

Inputs

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

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

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 1/2 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N)))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 1/2 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1 (*.f64 1/2 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (+.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (*.f64 1/2 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (/.f64 (+.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))) 2) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (/.f64 (+.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))) 2) 8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (+.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))) 2)) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 2 (+.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))) 2) 4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))) 2) 8) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (*.f64 1/2 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (+.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))) 2)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 4 (+.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))) 2)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 4 (+.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))) 2))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 4 (+.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))) 2)))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 4 (+.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))) 2))))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (*.f64 1/2 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))))) 1)))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 (+.f64 1 N)) (neg.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -2 (-.f64 (atan.f64 (+.f64 1 N)) (-.f64 (atan.f64 N) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (+.f64 1 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (atan.f64 N)) (atan.f64 (+.f64 1 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))) (*.f64 1/2 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 -1 (/.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) -2)) (-.f64 1 (/.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (-.f64 (atan.f64 N) (atan.f64 (+.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (/.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (-.f64 (/.f64 (atan.f64 (+.f64 1 N)) 4) (/.f64 (atan.f64 N) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 1 N))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) -2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 1 N))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) -2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) -4) -4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) -8) -8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) 8)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 1 N))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (+.f64 (*.f64 (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N)))) 2) (*.f64 (atan.f64 (+.f64 1 N)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (+.f64 (*.f64 (+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -2 (atan.f64 N))) 2) (*.f64 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (+.f64 (*.f64 (atan.f64 (+.f64 1 N)) 2) (*.f64 (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N)))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N)))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 1/2 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (+.f64 (*.f64 1/2 (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))) (*.f64 1/2 (atan.f64 (+.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (+.f64 (*.f64 1/2 (atan.f64 (+.f64 1 N))) (*.f64 1/2 (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (+.f64 (*.f64 1/2 (-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))) (/.f64 (+.f64 (atan.f64 (+.f64 1 N)) (-.f64 -2 (atan.f64 N))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (*.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))) 1/4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))) 8)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))) 1)))))

simplify531.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

2082×	`rational.json-simplify-2`
1976×	`rational.json-simplify-35`
1662×	`rational.json-simplify-52`
1254×	`rational.json-simplify-1`
1014×	`rational.json-simplify-51`

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	179	4624
1	365	4618
2	945	4618
3	2016	4618
4	3187	4618
5	4058	4604
6	4881	4604
7	5616	4598
8	5946	4598
9	6120	4598
10	6331	4598
11	6557	4598
12	6587	4598
13	7681	4598

Stop Event

1×	node limit

Counts

118 → 100

Calls

Call 1

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

Outputs
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(/.f64 (.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (.f64 2 (-.f64 -1 (atan.f64 N))))) 4) 4)
(+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N)))))
(/.f64 (.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (.f64 2 (-.f64 -1 (atan.f64 N))))) 8) 8)
(+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N)))))
(/.f64 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))) 8)) 16)
(+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N)))))
(/.f64 (.f64 2 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (.f64 2 (-.f64 -1 (atan.f64 N))))) 8))) 32)
(+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N)))))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))) 8)))) 64)
(+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N)))))
(pow.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))) 1)
(+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N)))))

eval110.0ms (0.6%)

Compiler: Compiled 3451 to 2702 computations (21.7% saved)

prune19.0ms (0.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	142	1	143
Fresh	0	0	0
Picked	1	0	1
Done	0	4	4
Total	143	5	148

Error

15.4b

Counts

148 → 5

Alt Table

Click to see full alt table

Status	Error	Program
	15.4b	(/.f64 (+.f64 (+.f64 (atan.f64 (+.f64 1 N)) (+.f64 (atan.f64 (+.f64 1 N)) (*.f64 2 (-.f64 -1 (atan.f64 N))))) 2) 2)
✓	15.4b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
✓	15.4b	(+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) -1)
✓	15.4b	(+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1)
✓	15.4b	(+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (+.f64 (+.f64 (.f64 (-.f64 -1 (atan.f64 N)) 1/2) -1) (+.f64 1 (.f64 (-.f64 -1 (atan.f64 N)) 1/2)))) 1)

Compiler

Compiled 78 to 65 computations (16.7% saved)

regimes60.0ms (0.3%)

Accuracy

Total -0.1b remaining (-0.3%)

Threshold costs -0.1b (-0.3%)

Counts

8 → 1

Calls

Call 1

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

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

Calls

2 calls:

52.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
5.0ms	N

Results

Error	Segments	Branch
15.4b	1	`N`
15.4b	1	`(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))`

Compiler

Compiled 151 to 113 computations (25.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	54

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 20 to 16 computations (20% saved)

soundness0.0ms (0%)

end19.0ms (0.1%)

Compiler: Compiled 19 to 14 computations (26.3% saved)

Details

analyze0.0ms (0%)

sample10.4s (59.9%)

preprocess3.0ms (0%)

simplify116.0ms (0.7%)

eval0.0ms (0%)

prune1.0ms (0%)

localize10.0ms (0.1%)

series1.0ms (0%)

rewrite185.0ms (1.1%)

simplify216.0ms (1.2%)

eval11.0ms (0.1%)

prune101.0ms (0.6%)

localize384.0ms (2.2%)

series1.0ms (0%)

rewrite120.0ms (0.7%)

simplify448.0ms (2.6%)

localize17.0ms (0.1%)

series1.0ms (0%)

rewrite123.0ms (0.7%)

simplify390.0ms (2.2%)

localize29.0ms (0.2%)

series5.0ms (0%)

rewrite100.0ms (0.6%)

simplify754.0ms (4.3%)

eval477.0ms (2.7%)

prune566.0ms (3.3%)

localize61.0ms (0.3%)

series3.0ms (0%)

rewrite137.0ms (0.8%)

simplify223.0ms (1.3%)

localize103.0ms (0.6%)

series2.0ms (0%)

rewrite143.0ms (0.8%)

simplify410.0ms (2.4%)

eval456.0ms (2.6%)

prune367.0ms (2.1%)

localize100.0ms (0.6%)

series4.0ms (0%)

rewrite159.0ms (0.9%)

simplify531.0ms (3.1%)

eval110.0ms (0.6%)

prune19.0ms (0.1%)

regimes60.0ms (0.3%)

simplify2.0ms (0%)

soundness0.0ms (0%)

end19.0ms (0.1%)

Profiling