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)

sample10.2s (78.7%)

Results

5.1s	2236×	body	2048	valid
4.5s	4496×	body	256	valid
429.0ms	1011×	body	1024	valid
78.0ms	513×	body	512	valid

Bogosity

preprocess10.0ms (0.1%)

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)

simplify9.0ms (0.1%)

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)

prune54.0ms (0.4%)

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

13.2b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	13.2b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 8 to 6 computations (25% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(atan.f64 (+.f64 N 1))
✓	1.4b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 19 to 12 computations (36.8% saved)

series1.0ms (0%)

Counts

2 → 8

Calls

6 calls:

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

rewrite105.0ms (0.8%)

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	32
1	66	32
2	145	32
3	282	32
4	526	32
5	1165	32
6	2731	32
7	4446	32
8	6304	32

Stop Event

1×	node limit

Counts

2 → 77

Calls

Call 1

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

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

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

simplify309.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

2150×	`rational.json-simplify-2`
2062×	`rational.json-simplify-35`
1606×	`rational.json-simplify-42`
1362×	`rational.json-simplify-51`
1090×	`rational.json-simplify-1`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	142	2005
1	298	1835
2	1121	1835
3	2356	1495
4	3777	1495
5	4736	1495
6	5663	1495
7	6785	1495
8	7048	1495
9	7196	1495
10	7335	1495
11	7754	1495

Stop Event

1×	node limit

Counts

85 → 83

Calls

Call 1

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

Outputs
(-.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))
(-.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))
(-.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))
(-.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))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(atan.f64 (-.f64 1 (neg.f64 N)))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(atan.f64 (-.f64 1 (neg.f64 N)))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(atan.f64 (-.f64 1 (neg.f64 N)))
(atan.f64 (+.f64 1 N))
(atan.f64 (-.f64 1 (*.f64 -1 N)))
(atan.f64 (-.f64 1 (neg.f64 N)))
(atan.f64 (+.f64 1 N))
(+.f64 1 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))))
(-.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))
(+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N)))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (neg.f64 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(+.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0)
(-.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))
(+.f64 0 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
(-.f64 (atan.f64 (-.f64 1 (neg.f64 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(+.f64 -1 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))))
(-.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))
(+.f64 (neg.f64 (atan.f64 N)) (atan.f64 (+.f64 N 1)))
(-.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))
(+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) -1)
(-.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))
(+.f64 (.f64 (atan.f64 (+.f64 N 1)) 1/2) (-.f64 (.f64 (atan.f64 (+.f64 N 1)) 1/2) (atan.f64 N)))
(-.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))
(+.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 (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))
(+.f64 (-.f64 1 (atan.f64 N)) (+.f64 (atan.f64 (+.f64 N 1)) -1))
(-.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))
(+.f64 -2 (+.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2))
(-.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))
(+.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) (-.f64 -1 (atan.f64 N)))
(-.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))
(+.f64 (+.f64 (atan.f64 (+.f64 N 1)) -1) (-.f64 1 (atan.f64 N)))
(-.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))
(+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1)
(-.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))
(+.f64 (+.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2) -2)
(-.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))
(+.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 (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))
(+.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 (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))
(+.f64 (-.f64 -1 (atan.f64 N)) (+.f64 1 (atan.f64 (+.f64 N 1))))
(-.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))
(+.f64 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) 1/2) (atan.f64 N)) (.f64 (atan.f64 (+.f64 N 1)) 1/2))
(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
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(atan.f64 (-.f64 1 (*.f64 -1 N)))
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(atan.f64 (-.f64 1 (*.f64 -1 N)))
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(pow.f64 (atan.f64 (+.f64 N 1)) 1)
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eval18.0ms (0.1%)

Compiler: Compiled 944 to 682 computations (27.8% saved)

prune11.0ms (0.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	81	3	84

Error

13.2b

Counts

84 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	13.2b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
▶	13.2b	(+.f64 (+.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2) -2)
▶	13.2b	(+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1)

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(atan.f64 (+.f64 N 1))
✓	0.3b	(-.f64 -1 (atan.f64 N))
✓	0.8b	(+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))
✓	14.7b	(+.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	@	-inf	(+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N)))
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 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1)

rewrite124.0ms (1%)

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))))))))

simplify283.0ms (2.2%)

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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(*.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))

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2)
	0.0b	(atan.f64 (+.f64 N 1))
	1.4b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
✓	1.4b	(+.f64 (+.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2) -2)

Compiler

Compiled 41 to 28 computations (31.7% saved)

series1.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite168.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

1844×	`rational.json-simplify-35`
1806×	`rational.json-1`
1806×	`rational.json-2`
1216×	`exponential.json-3`
1216×	`rational.json-4`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	60
1	91	48
2	178	48
3	344	48
4	688	48
5	1720	48
6	3794	48
7	5391	48
8	7442	48

Stop Event

1×	node limit

Counts

2 → 88

Calls

Call 1

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

Outputs

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

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

simplify365.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

1956×	`rational.json-simplify-2`
1788×	`rational.json-simplify-35`
1274×	`rational.json-simplify-1`
1228×	`rational.json-simplify-52`
1206×	`rational.json-simplify-51`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	185	2694
1	429	2694
2	1004	2694
3	2697	2694
4	4736	2694
5	5832	2694
6	6673	2694
7	6978	2694
8	7201	2694
9	7217	2694
10	7217	2694
11	7874	2694

Stop Event

1×	node limit

Counts

112 → 92

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

eval123.0ms (0.9%)

Compiler: Compiled 4441 to 3455 computations (22.2% saved)

prune80.0ms (0.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	300	1	301
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	300	4	304

Error

13.1b

Counts

304 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	13.2b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
▶	13.2b	(-.f64 -1 (+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1)))))
✓	13.2b	(+.f64 (+.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2) -2)
✓	13.2b	(+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1)

Compiler

Compiled 44 to 36 computations (18.2% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(atan.f64 (+.f64 N 1))
✓	0.3b	(+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1))))
✓	0.3b	(-.f64 -1 (atan.f64 (+.f64 N 1)))
✓	14.7b	(-.f64 -1 (+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1)))))

Compiler

Compiled 39 to 28 computations (28.2% saved)

series1.0ms (0%)

Counts

3 → 36

Calls

9 calls:

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

rewrite140.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1520×	`rational.json-1`
1520×	`rational.json-2`
1504×	`rational.json-simplify-35`
1228×	`exponential.json-3`
1228×	`rational.json-4`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	12	77
1	86	77
2	174	77
3	339	75
4	653	73
5	1464	73
6	3027	73
7	4601	73
8	6093	73
9	7767	73

Stop Event

1×	node limit

Counts

3 → 104

Calls

Call 1

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

Outputs

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

((#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (neg.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (-.f64 -2 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 -1 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 2 (-.f64 -3 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (atan.f64 (+.f64 N 1))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 1/2) (*.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -2 (-.f64 1 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 -2 (atan.f64 (+.f64 N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 1 (atan.f64 (+.f64 N 1))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (*.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 1/2) -1) (+.f64 1 (*.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (+.f64 1 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 -1 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (/.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) -4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 (atan.f64 (+.f64 N 1)) -2) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) -4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (-.f64 (*.f64 (atan.f64 (+.f64 N 1)) -2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) -4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) 2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) -4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (atan.f64 (+.f64 N 1)) -2) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1 (atan.f64 (+.f64 N 1))) -4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (atan.f64 (+.f64 N 1)) 2) -2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 4 (+.f64 1 (atan.f64 (+.f64 N 1)))) -4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 4 (+.f64 1 (atan.f64 (+.f64 N 1))))) -8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 4 (+.f64 1 (atan.f64 (+.f64 N 1))))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 8)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (neg.f64 (*.f64 4 (+.f64 1 (atan.f64 (+.f64 N 1)))))) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 4 (+.f64 1 (atan.f64 (+.f64 N 1)))))) -16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 8))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (neg.f64 (*.f64 4 (+.f64 1 (atan.f64 (+.f64 N 1))))))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))))))

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

simplify292.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

2464×	`rational.json-simplify-2`
1938×	`rational.json-simplify-35`
1166×	`rational.json-simplify-52`
1066×	`rational.json-simplify-49`
1000×	`rational.json-simplify-1`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	199	3232
1	446	3232
2	1057	3036
3	2850	3036
4	4141	3036
5	4715	3036
6	5512	3036
7	6765	3036
8	7602	3036
9	7867	3036

Stop Event

1×	node limit

Counts

140 → 113

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

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

eval43.0ms (0.3%)

Compiler: Compiled 2050 to 1619 computations (21% saved)

prune19.0ms (0.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	140	1	141
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	140	5	145

Error

13.1b

Counts

145 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	13.2b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
✓	13.2b	(-.f64 -1 (+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1)))))
▶	13.2b	(-.f64 -1 (+.f64 (atan.f64 N) (+.f64 2 (-.f64 -3 (atan.f64 (+.f64 N 1))))))
✓	13.2b	(+.f64 (+.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2) -2)
✓	13.2b	(+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1)

Compiler

Compiled 58 to 48 computations (17.2% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(atan.f64 (+.f64 N 1))
✓	0.3b	(+.f64 (atan.f64 N) (+.f64 2 (-.f64 -3 (atan.f64 (+.f64 N 1)))))
✓	0.3b	(+.f64 2 (-.f64 -3 (atan.f64 (+.f64 N 1))))
✓	14.9b	(-.f64 -1 (+.f64 (atan.f64 N) (+.f64 2 (-.f64 -3 (atan.f64 (+.f64 N 1))))))

Compiler

Compiled 53 to 41 computations (22.6% saved)

series1.0ms (0%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
0.0ms	N	@	0	(-.f64 -1 (+.f64 (atan.f64 N) (+.f64 2 (-.f64 -3 (atan.f64 (+.f64 N 1))))))
0.0ms	N	@	-inf	(-.f64 -1 (+.f64 (atan.f64 N) (+.f64 2 (-.f64 -3 (atan.f64 (+.f64 N 1))))))
0.0ms	N	@	inf	(-.f64 -1 (+.f64 (atan.f64 N) (+.f64 2 (-.f64 -3 (atan.f64 (+.f64 N 1))))))
0.0ms	N	@	-inf	(+.f64 2 (-.f64 -3 (atan.f64 (+.f64 N 1))))
0.0ms	N	@	-inf	(+.f64 (atan.f64 N) (+.f64 2 (-.f64 -3 (atan.f64 (+.f64 N 1)))))

rewrite146.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1644×	`rational.json-simplify-35`
1524×	`rational.json-1`
1524×	`rational.json-2`
1524×	`rational.json-3`
1258×	`exponential.json-3`

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	15	95
1	106	95
2	205	93
3	414	93
4	889	93
5	1765	93
6	3041	77
7	4721	75
8	6094	73
9	7641	73

Stop Event

1×	node limit

Counts

3 → 101

Calls

Call 1

Inputs
(-.f64 -1 (+.f64 (atan.f64 N) (+.f64 2 (-.f64 -3 (atan.f64 (+.f64 N 1))))))
(+.f64 2 (-.f64 -3 (atan.f64 (+.f64 N 1))))
(+.f64 (atan.f64 N) (+.f64 2 (-.f64 -3 (atan.f64 (+.f64 N 1)))))

Outputs

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

((#(struct:change #<rule egg-rr> (2) ((x -.f64 -1 (atan.f64 (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 2 (+.f64 (atan.f64 (+.f64 N 1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 -3 (-.f64 (atan.f64 (+.f64 N 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 -3 (+.f64 (+.f64 -1 (atan.f64 (+.f64 N 1))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 1 (+.f64 2 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 1 (-.f64 -1 (-.f64 -3 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (+.f64 1 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (-.f64 (+.f64 (atan.f64 (+.f64 N 1)) 3) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (+.f64 (+.f64 2 (atan.f64 (+.f64 N 1))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (-.f64 (+.f64 -1 (atan.f64 (+.f64 N 1))) -2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (-.f64 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) 3) 2) (+.f64 1 (+.f64 1 (*.f64 (-.f64 -3 (atan.f64 (+.f64 N 1))) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (-.f64 -2 (atan.f64 (+.f64 N 1))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (neg.f64 (atan.f64 (+.f64 N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 -2 (+.f64 -1 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 1 (*.f64 (-.f64 -3 (atan.f64 (+.f64 N 1))) 1/2))) (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) 3) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 -1 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (/.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (-.f64 -1 (atan.f64 (+.f64 N 1)))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 2 (-.f64 -1 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (-.f64 -1 (atan.f64 (+.f64 N 1)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 8)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 8))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (-.f64 (+.f64 (atan.f64 (+.f64 N 1)) 3) 2))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (+.f64 (+.f64 2 (atan.f64 (+.f64 N 1))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (-.f64 (+.f64 -1 (atan.f64 (+.f64 N 1))) -2))))))

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

simplify242.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

2476×	`rational.json-simplify-1`
1816×	`rational.json-simplify-35`
1636×	`rational.json-simplify-51`
1356×	`rational.json-simplify-41`
1320×	`rational.json-simplify-2`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	198	3823
1	439	3319
2	1047	3319
3	2259	3319
4	4992	3319
5	6425	3319
6	6868	3319
7	7252	3319
8	7489	3319
9	7548	3319

Stop Event

1×	node limit

Counts

137 → 113

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

Outputs
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(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
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(+.f64 -1 (-.f64 1 (+.f64 (atan.f64 N) (neg.f64 (atan.f64 (+.f64 N 1))))))
(neg.f64 (+.f64 (atan.f64 N) (neg.f64 (atan.f64 (+.f64 N 1)))))
(/.f64 (*.f64 2 (+.f64 (atan.f64 N) (neg.f64 (atan.f64 (+.f64 N 1))))) -2)
(+.f64 -1 (-.f64 1 (+.f64 (atan.f64 N) (neg.f64 (atan.f64 (+.f64 N 1))))))
(neg.f64 (+.f64 (atan.f64 N) (neg.f64 (atan.f64 (+.f64 N 1)))))
(/.f64 (*.f64 (neg.f64 (+.f64 (atan.f64 N) (neg.f64 (atan.f64 (+.f64 N 1))))) 8) 8)
(+.f64 -1 (-.f64 1 (+.f64 (atan.f64 N) (neg.f64 (atan.f64 (+.f64 N 1))))))
(neg.f64 (+.f64 (atan.f64 N) (neg.f64 (atan.f64 (+.f64 N 1)))))
(/.f64 (.f64 2 (.f64 (neg.f64 (+.f64 (atan.f64 N) (neg.f64 (atan.f64 (+.f64 N 1))))) 8)) 16)
(+.f64 -1 (-.f64 1 (+.f64 (atan.f64 N) (neg.f64 (atan.f64 (+.f64 N 1))))))
(neg.f64 (+.f64 (atan.f64 N) (neg.f64 (atan.f64 (+.f64 N 1)))))
(/.f64 (*.f64 4 (+.f64 (atan.f64 N) (neg.f64 (atan.f64 (+.f64 N 1))))) -4)
(+.f64 -1 (-.f64 1 (+.f64 (atan.f64 N) (neg.f64 (atan.f64 (+.f64 N 1))))))
(neg.f64 (+.f64 (atan.f64 N) (neg.f64 (atan.f64 (+.f64 N 1)))))
(/.f64 (.f64 2 (.f64 2 (*.f64 (neg.f64 (+.f64 (atan.f64 N) (neg.f64 (atan.f64 (+.f64 N 1))))) 8))) 32)
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(neg.f64 (+.f64 (atan.f64 N) (neg.f64 (atan.f64 (+.f64 N 1)))))
(/.f64 (.f64 2 (.f64 4 (+.f64 (atan.f64 N) (neg.f64 (atan.f64 (+.f64 N 1)))))) -8)
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(neg.f64 (+.f64 (atan.f64 N) (neg.f64 (atan.f64 (+.f64 N 1)))))
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(neg.f64 (+.f64 (atan.f64 N) (neg.f64 (atan.f64 (+.f64 N 1)))))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (neg.f64 (+.f64 (atan.f64 N) (neg.f64 (atan.f64 (+.f64 N 1))))) 8)))) 64)
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(neg.f64 (+.f64 (atan.f64 N) (neg.f64 (atan.f64 (+.f64 N 1)))))
(/.f64 (.f64 2 (neg.f64 (.f64 4 (+.f64 (atan.f64 N) (neg.f64 (atan.f64 (+.f64 N 1))))))) 8)
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(neg.f64 (+.f64 (atan.f64 N) (neg.f64 (atan.f64 (+.f64 N 1)))))
(/.f64 (.f64 2 (.f64 2 (*.f64 4 (+.f64 (atan.f64 N) (neg.f64 (atan.f64 (+.f64 N 1))))))) -16)
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(neg.f64 (+.f64 (atan.f64 N) (neg.f64 (atan.f64 (+.f64 N 1)))))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (*.f64 (neg.f64 (+.f64 (atan.f64 N) (neg.f64 (atan.f64 (+.f64 N 1))))) 8))))) 128)
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(/.f64 (.f64 2 (.f64 2 (neg.f64 (*.f64 4 (+.f64 (atan.f64 N) (neg.f64 (atan.f64 (+.f64 N 1)))))))) 16)
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(neg.f64 (+.f64 (atan.f64 N) (neg.f64 (atan.f64 (+.f64 N 1)))))
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(neg.f64 (+.f64 (atan.f64 N) (neg.f64 (atan.f64 (+.f64 N 1)))))
(neg.f64 (+.f64 (atan.f64 N) (neg.f64 (atan.f64 (+.f64 N 1)))))
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(-.f64 1 (+.f64 2 (atan.f64 (+.f64 N 1))))
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(-.f64 -1 (atan.f64 (+.f64 N 1)))
(-.f64 1 (-.f64 -1 (-.f64 -3 (atan.f64 (+.f64 N 1)))))
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(-.f64 -1 (atan.f64 (+.f64 N 1)))
(-.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 0)
(neg.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(-.f64 -1 (atan.f64 (+.f64 N 1)))
(-.f64 0 (+.f64 1 (atan.f64 (+.f64 N 1))))
(neg.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(-.f64 -1 (atan.f64 (+.f64 N 1)))
(-.f64 0 (-.f64 (+.f64 (atan.f64 (+.f64 N 1)) 3) 2))
(neg.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(-.f64 -1 (atan.f64 (+.f64 N 1)))
(-.f64 0 (+.f64 (+.f64 2 (atan.f64 (+.f64 N 1))) -1))
(neg.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(-.f64 -1 (atan.f64 (+.f64 N 1)))
(-.f64 0 (-.f64 (+.f64 -1 (atan.f64 (+.f64 N 1))) -2))
(neg.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(-.f64 -1 (atan.f64 (+.f64 N 1)))
(-.f64 0 (-.f64 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) 3) 2) (+.f64 1 (+.f64 1 (*.f64 (-.f64 -3 (atan.f64 (+.f64 N 1))) 1/2)))))
(neg.f64 (-.f64 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) 3) 2) (+.f64 1 (+.f64 1 (*.f64 1/2 (-.f64 -3 (atan.f64 (+.f64 N 1))))))))
(-.f64 (+.f64 (*.f64 1/2 (-.f64 -3 (atan.f64 (+.f64 N 1)))) 2) (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) 3) 2))
(+.f64 2 (-.f64 (*.f64 1/2 (-.f64 -3 (atan.f64 (+.f64 N 1)))) (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) 3) 2)))
(-.f64 (-.f64 -2 (atan.f64 (+.f64 N 1))) -1)
(neg.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(-.f64 -1 (atan.f64 (+.f64 N 1)))
(-.f64 (neg.f64 (atan.f64 (+.f64 N 1))) 1)
(neg.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(-.f64 -1 (atan.f64 (+.f64 N 1)))
(-.f64 -2 (+.f64 -1 (atan.f64 (+.f64 N 1))))
(neg.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(-.f64 -1 (atan.f64 (+.f64 N 1)))
(-.f64 (+.f64 1 (+.f64 1 (*.f64 (-.f64 -3 (atan.f64 (+.f64 N 1))) 1/2))) (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) 3) 2))
(neg.f64 (-.f64 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) 3) 2) (+.f64 1 (+.f64 1 (*.f64 1/2 (-.f64 -3 (atan.f64 (+.f64 N 1))))))))
(-.f64 (+.f64 (*.f64 1/2 (-.f64 -3 (atan.f64 (+.f64 N 1)))) 2) (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) 3) 2))
(+.f64 2 (-.f64 (*.f64 1/2 (-.f64 -3 (atan.f64 (+.f64 N 1)))) (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) 3) 2)))
(.f64 2 (.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 1/2))
(neg.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(-.f64 -1 (atan.f64 (+.f64 N 1)))
(*.f64 1 (-.f64 -1 (atan.f64 (+.f64 N 1))))
(neg.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(-.f64 -1 (atan.f64 (+.f64 N 1)))
(*.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 1)
(neg.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(-.f64 -1 (atan.f64 (+.f64 N 1)))
(*.f64 4 (/.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 4))
(neg.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(-.f64 -1 (atan.f64 (+.f64 N 1)))
(.f64 (.f64 2 (-.f64 -1 (atan.f64 (+.f64 N 1)))) 1/2)
(neg.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(-.f64 -1 (atan.f64 (+.f64 N 1)))
(.f64 (.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 4) 1/4)
(neg.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(-.f64 -1 (atan.f64 (+.f64 N 1)))
(.f64 1/2 (.f64 2 (-.f64 -1 (atan.f64 (+.f64 N 1)))))
(neg.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(-.f64 -1 (atan.f64 (+.f64 N 1)))
(.f64 1/4 (.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 4))
(neg.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(-.f64 -1 (atan.f64 (+.f64 N 1)))
(.f64 (.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 1/2) 2)
(neg.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(-.f64 -1 (atan.f64 (+.f64 N 1)))
(*.f64 (/.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 4) 4)
(neg.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(-.f64 -1 (atan.f64 (+.f64 N 1)))
(/.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 1)
(neg.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(-.f64 -1 (atan.f64 (+.f64 N 1)))
(/.f64 (*.f64 2 (-.f64 -1 (atan.f64 (+.f64 N 1)))) 2)
(neg.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(-.f64 -1 (atan.f64 (+.f64 N 1)))
(/.f64 (*.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 4) 4)
(neg.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(-.f64 -1 (atan.f64 (+.f64 N 1)))
(/.f64 (*.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 8) 8)
(neg.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(-.f64 -1 (atan.f64 (+.f64 N 1)))
(/.f64 (.f64 2 (.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 8)) 16)
(neg.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(-.f64 -1 (atan.f64 (+.f64 N 1)))
(/.f64 (.f64 2 (.f64 2 (*.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 8))) 32)
(neg.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(-.f64 -1 (atan.f64 (+.f64 N 1)))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 8)))) 64)
(neg.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(-.f64 -1 (atan.f64 (+.f64 N 1)))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (*.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 8))))) 128)
(neg.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(-.f64 -1 (atan.f64 (+.f64 N 1)))
(pow.f64 (-.f64 -1 (atan.f64 (+.f64 N 1))) 1)
(neg.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(-.f64 -1 (atan.f64 (+.f64 N 1)))
(neg.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(-.f64 -1 (atan.f64 (+.f64 N 1)))
(neg.f64 (-.f64 (+.f64 (atan.f64 (+.f64 N 1)) 3) 2))
(neg.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(-.f64 -1 (atan.f64 (+.f64 N 1)))
(neg.f64 (+.f64 (+.f64 2 (atan.f64 (+.f64 N 1))) -1))
(neg.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(-.f64 -1 (atan.f64 (+.f64 N 1)))
(neg.f64 (-.f64 (+.f64 -1 (atan.f64 (+.f64 N 1))) -2))
(neg.f64 (+.f64 1 (atan.f64 (+.f64 N 1))))
(-.f64 -1 (atan.f64 (+.f64 N 1)))
(-.f64 (+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1)))) 0)
(+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1))))
(-.f64 (+.f64 (atan.f64 N) (neg.f64 (atan.f64 (+.f64 N 1)))) 1)
(+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1))))
(-.f64 (+.f64 (atan.f64 N) (-.f64 -2 (atan.f64 (+.f64 N 1)))) -1)
(+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1))))
(.f64 2 (.f64 (+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1)))) 1/2))
(+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1))))
(*.f64 1 (+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1)))))
(+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1))))
(*.f64 (+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1)))) 1)
(+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1))))
(.f64 (.f64 2 (+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1))))) 1/2)
(+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1))))
(*.f64 4 (/.f64 (+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1)))) 4))
(+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1))))
(.f64 (.f64 (+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1)))) 4) 1/4)
(+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1))))
(.f64 1/2 (.f64 2 (+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1))))))
(+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1))))
(.f64 1/2 (+.f64 (.f64 (atan.f64 N) 2) (*.f64 2 (-.f64 -1 (atan.f64 (+.f64 N 1))))))
(+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1))))
(.f64 (.f64 (+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1)))) 1/2) 2)
(+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1))))
(.f64 1/4 (.f64 (+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1)))) 4))
(+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1))))
(*.f64 (/.f64 (+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1)))) 4) 4)
(+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1))))
(.f64 (+.f64 (.f64 (atan.f64 N) 2) (*.f64 2 (-.f64 -1 (atan.f64 (+.f64 N 1))))) 1/2)
(+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1))))
(/.f64 (+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1)))) 1)
(+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1))))
(/.f64 (*.f64 2 (+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1))))) 2)
(+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1))))
(/.f64 (*.f64 (+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1)))) 4) 4)
(+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1))))
(/.f64 (*.f64 (+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1)))) 8) 8)
(+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1))))
(/.f64 (.f64 2 (.f64 (+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1)))) 8)) 16)
(+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1))))
(/.f64 (.f64 2 (.f64 2 (*.f64 (+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1)))) 8))) 32)
(+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1))))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1)))) 8)))) 64)
(+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1))))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (*.f64 (+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1)))) 8))))) 128)
(+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1))))
(pow.f64 (+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1)))) 1)
(+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1))))

eval39.0ms (0.3%)

Compiler: Compiled 2121 to 1687 computations (20.5% saved)

prune20.0ms (0.2%)

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	141	0	141
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	141	5	146

Error

13.1b

Counts

146 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	13.2b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
✓	13.2b	(-.f64 -1 (+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1)))))
✓	13.2b	(-.f64 -1 (+.f64 (atan.f64 N) (+.f64 2 (-.f64 -3 (atan.f64 (+.f64 N 1))))))
✓	13.2b	(+.f64 (+.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2) -2)
✓	13.2b	(+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1)

Compiler

Compiled 58 to 48 computations (17.2% saved)

regimes7.0ms (0.1%)

Accuracy

Total -0.1b remaining (-0.6%)

Threshold costs -0.1b (-0.6%)

Counts

5 → 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 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2) -2)
(-.f64 -1 (+.f64 (atan.f64 N) (-.f64 -1 (atan.f64 (+.f64 N 1)))))
(-.f64 -1 (+.f64 (atan.f64 N) (+.f64 2 (-.f64 -3 (atan.f64 (+.f64 N 1))))))

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

Calls

2 calls:

4.0ms	N
2.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Results

Error	Segments	Branch
13.2b	1	`N`
13.2b	1	`(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))`

Compiler

Compiled 64 to 47 computations (26.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	54

Stop Event

1×	done
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%)

end73.0ms (0.6%)

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

Details

analyze0.0ms (0%)

sample10.2s (78.7%)

preprocess10.0ms (0.1%)

simplify9.0ms (0.1%)

eval0.0ms (0%)

prune54.0ms (0.4%)

localize9.0ms (0.1%)

series1.0ms (0%)

rewrite105.0ms (0.8%)

simplify309.0ms (2.4%)

eval18.0ms (0.1%)

prune11.0ms (0.1%)

localize15.0ms (0.1%)

series1.0ms (0%)

rewrite124.0ms (1%)

simplify283.0ms (2.2%)

localize16.0ms (0.1%)

series1.0ms (0%)

rewrite168.0ms (1.3%)

simplify365.0ms (2.8%)

eval123.0ms (0.9%)

prune80.0ms (0.6%)

localize17.0ms (0.1%)

series1.0ms (0%)

rewrite140.0ms (1.1%)

simplify292.0ms (2.2%)

eval43.0ms (0.3%)

prune19.0ms (0.1%)

localize22.0ms (0.2%)

series1.0ms (0%)

rewrite146.0ms (1.1%)

simplify242.0ms (1.9%)

eval39.0ms (0.3%)

prune20.0ms (0.2%)

regimes7.0ms (0.1%)

simplify2.0ms (0%)

soundness0.0ms (0%)

end73.0ms (0.6%)

Profiling