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)

sample4.3s (67.7%)

Results

1.9s	4453×	body	256	valid
1.5s	2240×	body	2048	valid
809.0ms	1076×	body	1024	valid
76.0ms	487×	body	512	valid

Bogosity

preprocess3.0ms (0%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

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)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

14.6b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	14.6b	(-.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))
✓	1.1b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 19 to 12 computations (36.8% saved)

series1.0ms (0%)

Counts

2 → 8

Calls

6 calls:

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

rewrite104.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1540×	`rational.json-simplify-35`
1352×	`bool.json-1`
1352×	`bool.json-2`
1304×	`rational.json-1`
1304×	`rational.json-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	32
1	94	32
2	269	32
3	544	32
4	1097	32
5	2409	32
6	5096	32

Stop Event

1×	node limit

Counts

2 → 61

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(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 (neg.f64 (atan.f64 N)) (atan.f64 (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (-.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 -2 (-.f64 1 (+.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 -1 (/.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -2)) (-.f64 1 (/.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -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 2 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) 1/2) (.f64 (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 (.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 (-.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 1/2 (-.f64 (.f64 (atan.f64 (+.f64 N 1)) 2) (.f64 (atan.f64 N) 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 (/.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 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)) 8) 8)))) (#(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 N) (atan.f64 (+.f64 N 1))) 4) -4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 2 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 4)) -8)))) (#(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 (neg.f64 (.f64 2 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 4)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 2 (.f64 2 (.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 8))) (.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 (.f64 2 (neg.f64 (.f64 2 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (.f64 2 (neg.f64 (.f64 2 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (neg.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 4)) (neg.f64 (.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 4))) 8)))) (#(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 not (not (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x and (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x or (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 (+.f64 N 1)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (atan.f64 (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.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)) 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 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 (/.f64 (atan.f64 (+.f64 N 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 (.f64 2 (.f64 2 (.f64 (atan.f64 (+.f64 N 1)) 8))) (.f64 2 (.f64 2 (.f64 (atan.f64 (+.f64 N 1)) 8)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x not (not (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x and (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x or (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1)))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(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 (neg.f64 (atan.f64 N)) (atan.f64 (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (-.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 -2 (-.f64 1 (+.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 -1 (/.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -2)) (-.f64 1 (/.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -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 2 (-.f64 (*.f64 (atan.f64 (+.f64 N 1)) 1/2) (*.f64 (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 (*.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 (-.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 1/2 (-.f64 (*.f64 (atan.f64 (+.f64 N 1)) 2) (*.f64 (atan.f64 N) 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 (/.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 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)) 8) 8)))) (#(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 N) (atan.f64 (+.f64 N 1))) 4) -4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 2 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 4)) -8)))) (#(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 (neg.f64 (*.f64 2 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 4)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 2 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 8))) (*.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 (*.f64 2 (neg.f64 (*.f64 2 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (*.f64 2 (neg.f64 (*.f64 2 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))))))) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (neg.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 4)) (neg.f64 (*.f64 (-.f64 (atan.f64 N) (atan.f64 (+.f64 N 1))) 4))) 8)))) (#(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 not (not (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x and (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x or (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 (+.f64 N 1)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (atan.f64 (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.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)) 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 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 (/.f64 (atan.f64 (+.f64 N 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 (*.f64 2 (*.f64 2 (*.f64 (atan.f64 (+.f64 N 1)) 8))) (*.f64 2 (*.f64 2 (*.f64 (atan.f64 (+.f64 N 1)) 8)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x not (not (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x and (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x or (atan.f64 (+.f64 N 1)) (atan.f64 (+.f64 N 1)))))))

simplify292.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

2280×	`rational.json-simplify-1`
1714×	`rational.json-simplify-35`
1242×	`rational.json-simplify-2`
1026×	`rational.json-simplify-42`
986×	`rational.json-simplify-26`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	123	1613
1	250	1475
2	628	1475
3	1715	1199
4	3112	1199
5	4387	1199
6	6055	1199
7	6801	1199
8	7233	1199
9	7518	1199
10	7785	1199

Stop Event

1×	node limit

Counts

69 → 67

Calls

Call 1

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

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

eval16.0ms (0.3%)

Compiler: Compiled 794 to 575 computations (27.6% saved)

prune8.0ms (0.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	66	2	68

Error

14.6b

Counts

68 → 2

Alt Table

Click to see full alt table

Status	Error	Program
✓	14.6b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
▶	14.7b	(+.f64 (-.f64 -1 (/.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -2)) (-.f64 1 (/.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -2)))

Compiler

Compiled 32 to 25 computations (21.9% saved)

localize674.0ms (10.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(atan.f64 (+.f64 N 1))
✓	0.0b	(-.f64 -1 (/.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -2))
	1.1b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
✓	1.1b	(+.f64 (-.f64 -1 (/.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -2)) (-.f64 1 (/.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -2)))

Compiler

Compiled 75 to 53 computations (29.3% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite101.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1930×	`bool.json-1`
1930×	`bool.json-2`
1132×	`rational.json-1`
1132×	`rational.json-2`
1132×	`rational.json-4`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	104
1	154	104
2	409	104
3	826	104
4	1707	104
5	3872	104
6	7531	104

Stop Event

1×	node limit

Counts

2 → 46

Calls

Call 1

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

Inputs

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

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

Outputs
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Outputs

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((#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 -1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (+.f64 -1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (+.f64 -1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2)) 1/2) (*.f64 (+.f64 -1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (+.f64 1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 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 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 (+.f64 -1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (/.f64 (+.f64 -1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 -2 (+.f64 1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -1/2))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -1/2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 -1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2)) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 -2 (+.f64 1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (+.f64 -1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 -1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2)) 1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 -1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2)) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 -1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -2 (+.f64 1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -1/2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 -1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2)) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (+.f64 1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -1/2))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (+.f64 -1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2)) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (+.f64 1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -1/2)))) -4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (+.f64 -1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2)) 4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 2 (+.f64 1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -1/2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 2 (*.f64 (+.f64 -1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2)) 4))) (*.f64 2 (*.f64 2 (*.f64 (+.f64 -1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2)) 4)))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (neg.f64 (*.f64 2 (+.f64 1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -1/2)))) (neg.f64 (*.f64 2 (+.f64 1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -1/2))))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (+.f64 1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x not (not (+.f64 -1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x and (+.f64 -1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2)) (+.f64 -1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x or (+.f64 -1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2)) (+.f64 -1 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1/2)))))))

simplify486.0ms (7.6%)

Algorithm

1×	egg-herbie

Rules

3670×	`rational.json-simplify-52`
1824×	`rational.json-simplify-1`
1768×	`rational.json-simplify-35`
1468×	`rational.json-simplify-2`
710×	`rational.json-simplify-48`

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	101	2904
1	195	2904
2	488	2812
3	1159	2710
4	2366	2676
5	3083	2676
6	3403	2676
7	3920	2608
8	4604	2608
9	5117	2608
10	5779	2608
11	6339	2608
12	6538	2608
13	6679	2608
14	6818	2608
15	6818	2608

Stop Event

1×	node limit

Counts

70 → 59

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

eval250.0ms (3.9%)

Compiler: Compiled 5300 to 4094 computations (22.8% saved)

prune31.0ms (0.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	193	0	193
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	193	2	195

Error

14.6b

Counts

195 → 2

Alt Table

Click to see full alt table

Status	Error	Program
✓	14.6b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
✓	14.7b	(+.f64 (-.f64 -1 (/.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -2)) (-.f64 1 (/.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -2)))

Compiler

Compiled 32 to 25 computations (21.9% saved)

regimes8.0ms (0.1%)

Accuracy

Total -0.0b remaining (-0.1%)

Threshold costs -0.0b (-0.1%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

2 calls:

5.0ms	N
2.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Results

Error	Segments	Branch
14.6b	1	`N`
14.6b	1	`(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))`

Compiler

Compiled 41 to 30 computations (26.8% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21

Stop Event

1×	done
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 8 to 6 computations (25% saved)

soundness0.0ms (0%)

end72.0ms (1.1%)

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

Details

analyze0.0ms (0%)

sample4.3s (67.7%)

preprocess3.0ms (0%)

simplify9.0ms (0.1%)

eval0.0ms (0%)

prune1.0ms (0%)

localize9.0ms (0.1%)

series1.0ms (0%)

rewrite104.0ms (1.6%)

simplify292.0ms (4.6%)

eval16.0ms (0.3%)

prune8.0ms (0.1%)

localize674.0ms (10.5%)

series2.0ms (0%)

rewrite101.0ms (1.6%)

simplify486.0ms (7.6%)

eval250.0ms (3.9%)

prune31.0ms (0.5%)

regimes8.0ms (0.1%)

simplify1.0ms (0%)

soundness0.0ms (0%)

end72.0ms (1.1%)

Profiling