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)

sample11.1s (79.2%)

Results

5.4s	4503×	body	256	valid
4.5s	1050×	body	1024	valid
1.2s	2189×	body	2048	valid
79.0ms	514×	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)

simplify36.0ms (0.3%)

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

17.3b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	17.3b	(-.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))
✓	1.5b	(-.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))

rewrite110.0ms (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)))))

simplify315.0ms (2.2%)

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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(-.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) (atan.f64 N))
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(/.f64 (*.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) -4) -4)
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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)

prune10.0ms (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

17.3b

Counts

84 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	17.3b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
▶	17.3b	(+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) -1)
▶	17.3b	(+.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)))
✓	14.0b	(+.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)

rewrite206.0ms (1.5%)

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))))))))

simplify477.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Counts

125 → 98

Calls

Call 1

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

localize79.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(atan.f64 (+.f64 N 1))
✓	0.2b	(-.f64 1 (atan.f64 N))
✓	0.2b	(+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N)))
✓	19.4b	(+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) -1)

Compiler

Compiled 37 to 25 computations (32.4% saved)

series1.0ms (0%)

Counts

3 → 24

Calls

9 calls:

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

rewrite130.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 86

Calls

Call 1

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

Outputs

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

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

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

simplify245.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

110 → 93

Calls

Call 1

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

eval79.0ms (0.6%)

Compiler: Compiled 3709 to 2894 computations (22% saved)

prune30.0ms (0.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	246	1	247
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	246	4	250

Error

17.2b

Counts

250 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	17.3b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
✓	17.3b	(+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) -1)
✓	17.3b	(+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1)
▶	17.3b	(+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (+.f64 (+.f64 (.f64 (-.f64 -1 (atan.f64 N)) 1/2) -1) (+.f64 1 (.f64 (-.f64 -1 (atan.f64 N)) 1/2)))) 1)

Compiler

Compiled 57 to 47 computations (17.5% saved)

localize40.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 103 to 77 computations (25.2% saved)

series3.0ms (0%)

Counts

3 → 36

Calls

9 calls:

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

rewrite137.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 4 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 91

Calls

Call 1

Inputs

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

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

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

Outputs

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

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

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

simplify341.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Counts

127 → 102

Calls

Call 1

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

eval336.0ms (2.4%)

Compiler: Compiled 4062 to 3258 computations (19.8% saved)

prune26.0ms (0.2%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	192	0	192
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	192	4	196

Error

17.2b

Counts

196 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	17.3b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
✓	17.3b	(+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 1 (atan.f64 N))) -1)
✓	17.3b	(+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (-.f64 -1 (atan.f64 N))) 1)
✓	17.3b	(+.f64 (+.f64 (atan.f64 (+.f64 N 1)) (+.f64 (+.f64 (.f64 (-.f64 -1 (atan.f64 N)) 1/2) -1) (+.f64 1 (.f64 (-.f64 -1 (atan.f64 N)) 1/2)))) 1)

Compiler

Compiled 57 to 47 computations (17.5% saved)

regimes60.0ms (0.4%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

2 calls:

56.0ms	N
2.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Results

Error	Segments	Branch
17.3b	1	`N`
17.3b	1	`(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))`

Compiler

Compiled 64 to 48 computations (25% saved)

regimes6.0ms (0%)

Accuracy

Total -0.1b remaining (-0.4%)

Threshold costs -0.1b (-0.4%)

Counts

3 → 1

Calls

Call 1

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

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

Calls

2 calls:

3.0ms	N
2.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Results

Error	Segments	Branch
17.3b	1	`N`
17.3b	1	`(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))`

Compiler

Compiled 40 to 29 computations (27.5% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	127

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs

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

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

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

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

Compiler

Compiled 45 to 37 computations (17.8% saved)

soundness0.0ms (0%)

end183.0ms (1.3%)

Compiler: Compiled 43 to 33 computations (23.3% saved)

Details

analyze0.0ms (0%)

sample11.1s (79.2%)

preprocess10.0ms (0.1%)

simplify36.0ms (0.3%)

eval0.0ms (0%)

prune1.0ms (0%)

localize9.0ms (0.1%)

series1.0ms (0%)

rewrite110.0ms (0.8%)

simplify315.0ms (2.2%)

eval18.0ms (0.1%)

prune10.0ms (0.1%)

localize15.0ms (0.1%)

series1.0ms (0%)

rewrite206.0ms (1.5%)

simplify477.0ms (3.4%)

localize79.0ms (0.6%)

series1.0ms (0%)

rewrite130.0ms (0.9%)

simplify245.0ms (1.7%)

eval79.0ms (0.6%)

prune30.0ms (0.2%)

localize40.0ms (0.3%)

series3.0ms (0%)

rewrite137.0ms (1%)

simplify341.0ms (2.4%)

eval336.0ms (2.4%)

prune26.0ms (0.2%)

regimes60.0ms (0.4%)

regimes6.0ms (0%)

simplify4.0ms (0%)

soundness0.0ms (0%)

end183.0ms (1.3%)

Profiling