Details

analyze0.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample2.0s (25.1%)

Results

805.0ms	2141×	body	2048	valid
732.0ms	4552×	body	256	valid
355.0ms	1080×	body	1024	valid
106.0ms	483×	body	512	valid

preprocess21.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
15×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	122	11
8	168	11
9	204	11
10	230	11
11	232	11
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)

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
15×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	122	11
8	168	11
9	204	11
10	230	11
11	232	11

Stop Event

1×

saturated

Counts

1 → 1

Calls

Call 1

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

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

15.3b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	15.3b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 8 to 6 computations (25% saved)

localize12.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.2b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 19 to 12 computations (36.8% saved)

series1.0ms (0%)

Counts

1 → 4

Calls

3 calls:

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

rewrite53.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

890×	`pow1_binary64`
828×	`log1p-expm1-u_binary64`
828×	`expm1-log1p-u_binary64`
827×	`add-log-exp_binary64`
810×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	156	11
2	2213	11

Stop Event

1×	node limit

Counts

1 → 36

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 (+.f64 N 1)) (.f64 (neg.f64 (atan.f64 N)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (fma.f64 (neg.f64 (atan.f64 N)) 1 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (fma.f64 (neg.f64 (cbrt.f64 (atan.f64 N))) (pow.f64 (cbrt.f64 (atan.f64 N)) 2) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (fma.f64 (neg.f64 (sqrt.f64 (atan.f64 N))) (sqrt.f64 (atan.f64 N)) (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 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 (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (pow.f64 (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2) (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (sqrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (atan.f64 N) 3)) (/.f64 1 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (.f64 (atan.f64 N) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (/.f64 1 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 N))) (-.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (.f64 (atan.f64 N) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (atan.f64 N) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (atan.f64 N) 3)) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (.f64 (atan.f64 N) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (atan.f64 N) 3))) (neg.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (.f64 (atan.f64 N) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))) (neg.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (neg.f64 (atan.f64 N)) 3)) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (-.f64 (.f64 (neg.f64 (atan.f64 N)) (neg.f64 (atan.f64 N))) (.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (.f64 (neg.f64 (atan.f64 N)) (neg.f64 (atan.f64 N)))) (-.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))))))) (#(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 pow.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) (cbrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 (+.f64 N 1)) (*.f64 (neg.f64 (atan.f64 N)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (fma.f64 (neg.f64 (atan.f64 N)) 1 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (fma.f64 (neg.f64 (cbrt.f64 (atan.f64 N))) (pow.f64 (cbrt.f64 (atan.f64 N)) 2) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (fma.f64 (neg.f64 (sqrt.f64 (atan.f64 N))) (sqrt.f64 (atan.f64 N)) (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 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 (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (pow.f64 (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2) (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (sqrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (atan.f64 N) 3)) (/.f64 1 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (*.f64 (atan.f64 N) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (/.f64 1 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 N))) (-.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (*.f64 (atan.f64 N) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (atan.f64 N) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (atan.f64 N) 3)) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (*.f64 (atan.f64 N) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (atan.f64 N) 3))) (neg.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (*.f64 (atan.f64 N) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2))) (neg.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (neg.f64 (atan.f64 N)) 3)) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (-.f64 (*.f64 (neg.f64 (atan.f64 N)) (neg.f64 (atan.f64 N))) (*.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (*.f64 (neg.f64 (atan.f64 N)) (neg.f64 (atan.f64 N)))) (-.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N))))))) (#(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 pow.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) (cbrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))))))

simplify69.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

52×	`fma-def_binary64`
43×	`fma-neg_binary64`
23×	`cancel-sign-sub-inv_binary64`
18×	`sub-neg_binary64`
14×	`associate--r+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	52
1	20	44
2	31	44
3	61	44
4	88	44
5	134	44
6	182	44
7	215	44
8	258	44
9	294	44
10	320	44
11	322	44

Stop Event

1×

saturated

Counts

40 → 38

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))

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))

eval12.0ms (0.1%)

Compiler: Compiled 599 to 388 computations (35.2% saved)

prune8.0ms (0.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	34	4	38
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	34	5	39

Error

14.2b

Counts

39 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	30.7b	(fma.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))
▶	42.7b	(+.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (fma.f64 (neg.f64 (sqrt.f64 (atan.f64 N))) (sqrt.f64 (atan.f64 N)) (atan.f64 N)))
▶	30.5b	(fma.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) (cbrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))
✓	15.3b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
▶	14.4b	(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))

Compiler

Compiled 73 to 52 computations (28.8% saved)

localize19.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(sqrt.f64 (atan.f64 N))
	1.2b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
✓	33.6b	(fma.f64 (neg.f64 (sqrt.f64 (atan.f64 N))) (sqrt.f64 (atan.f64 N)) (atan.f64 N))

Compiler

Compiled 54 to 20 computations (63% saved)

series6.0ms (0.1%)

Counts

2 → 12

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	N	@	-inf	(fma.f64 (neg.f64 (sqrt.f64 (atan.f64 N))) (sqrt.f64 (atan.f64 N)) (atan.f64 N))
1.0ms	N	@	0	(fma.f64 (neg.f64 (sqrt.f64 (atan.f64 N))) (sqrt.f64 (atan.f64 N)) (atan.f64 N))
1.0ms	N	@	inf	(fma.f64 (neg.f64 (sqrt.f64 (atan.f64 N))) (sqrt.f64 (atan.f64 N)) (atan.f64 N))
0.0ms	N	@	0	(sqrt.f64 (atan.f64 N))
0.0ms	N	@	-inf	(sqrt.f64 (atan.f64 N))

rewrite71.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

463×	`pow1_binary64`
446×	`add-sqr-sqrt_binary64`
438×	`*-un-lft-identity_binary64`
427×	`add-log-exp_binary64`
426×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	22
1	122	13
2	1490	13

Stop Event

1×	node limit

Counts

2 → 53

Calls

Call 1

Inputs
(fma.f64 (neg.f64 (sqrt.f64 (atan.f64 N))) (sqrt.f64 (atan.f64 N)) (atan.f64 N))
(sqrt.f64 (atan.f64 N))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 N) (atan.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 (atan.f64 N) (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (atan.f64 N)) (+.f64 (sqrt.f64 (atan.f64 N)) (sqrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (atan.f64 N) (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (+.f64 (atan.f64 N) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (+.f64 (atan.f64 N) (atan.f64 N))) (pow.f64 (cbrt.f64 (+.f64 (atan.f64 N) (atan.f64 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (+.f64 (atan.f64 N) (atan.f64 N))) 2) (cbrt.f64 (+.f64 (atan.f64 N) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (+.f64 (atan.f64 N) (atan.f64 N))) (sqrt.f64 (+.f64 (atan.f64 N) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (atan.f64 N) 3) (pow.f64 (atan.f64 N) 3)) (+.f64 (pow.f64 (atan.f64 N) 2) (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 N) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 N) 2)) (-.f64 (atan.f64 N) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (atan.f64 N) (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (atan.f64 N) (atan.f64 N)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (atan.f64 N) (atan.f64 N))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (atan.f64 N) (atan.f64 N))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (atan.f64 N) (atan.f64 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (atan.f64 N) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (atan.f64 N) (atan.f64 N)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (atan.f64 N) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (atan.f64 N) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (atan.f64 N) (atan.f64 N))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (sqrt.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (atan.f64 N)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (atan.f64 N)) (cbrt.f64 (sqrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (atan.f64 N)) (neg.f64 (cbrt.f64 (sqrt.f64 (atan.f64 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (sqrt.f64 (atan.f64 N))) (cbrt.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (atan.f64 N) 1/4) (pow.f64 (atan.f64 N) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (atan.f64 N) 1/4) (neg.f64 (pow.f64 (atan.f64 N) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (sqrt.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (cbrt.f64 (atan.f64 N)) 2)) (sqrt.f64 (cbrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/2) (sqrt.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (atan.f64 N)) 2) 1/2) (pow.f64 (cbrt.f64 (atan.f64 N)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (cbrt.f64 (atan.f64 N))) (cbrt.f64 (sqrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (pow.f64 (atan.f64 N) 1/4)) (pow.f64 (atan.f64 N) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 -1 (cbrt.f64 (atan.f64 N))) (cbrt.f64 (sqrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 -1 (pow.f64 (atan.f64 N) 1/4)) (pow.f64 (atan.f64 N) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 0 (pow.f64 (atan.f64 N) 3/2)) (+.f64 0 (+.f64 (atan.f64 N) (*.f64 0 (sqrt.f64 (atan.f64 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 0 (atan.f64 N)) (sqrt.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan.f64 N) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan.f64 N) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (atan.f64 N))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan.f64 N) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (sqrt.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan.f64 N) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (atan.f64 N))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 N) (atan.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 (atan.f64 N) (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan.f64 N)) (+.f64 (sqrt.f64 (atan.f64 N)) (sqrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (atan.f64 N) (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (atan.f64 N) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (atan.f64 N) (atan.f64 N))) (pow.f64 (cbrt.f64 (+.f64 (atan.f64 N) (atan.f64 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (atan.f64 N) (atan.f64 N))) 2) (cbrt.f64 (+.f64 (atan.f64 N) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (atan.f64 N) (atan.f64 N))) (sqrt.f64 (+.f64 (atan.f64 N) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (atan.f64 N) 3) (pow.f64 (atan.f64 N) 3)) (+.f64 (pow.f64 (atan.f64 N) 2) (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 N) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (atan.f64 N) 2) (pow.f64 (atan.f64 N) 2)) (-.f64 (atan.f64 N) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (atan.f64 N) (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (atan.f64 N) (atan.f64 N)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (atan.f64 N) (atan.f64 N))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (atan.f64 N) (atan.f64 N))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (atan.f64 N) (atan.f64 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (atan.f64 N) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (atan.f64 N) (atan.f64 N)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (atan.f64 N) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (atan.f64 N) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (atan.f64 N) (atan.f64 N))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (sqrt.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan.f64 N)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan.f64 N)) (cbrt.f64 (sqrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan.f64 N)) (neg.f64 (cbrt.f64 (sqrt.f64 (atan.f64 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (atan.f64 N))) (cbrt.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan.f64 N) 1/4) (pow.f64 (atan.f64 N) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan.f64 N) 1/4) (neg.f64 (pow.f64 (atan.f64 N) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (sqrt.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (atan.f64 N)) 2)) (sqrt.f64 (cbrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (atan.f64 N)) 2) 1/2) (pow.f64 (cbrt.f64 (atan.f64 N)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (cbrt.f64 (atan.f64 N))) (cbrt.f64 (sqrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (atan.f64 N) 1/4)) (pow.f64 (atan.f64 N) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 -1 (cbrt.f64 (atan.f64 N))) (cbrt.f64 (sqrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 -1 (pow.f64 (atan.f64 N) 1/4)) (pow.f64 (atan.f64 N) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 0 (pow.f64 (atan.f64 N) 3/2)) (+.f64 0 (+.f64 (atan.f64 N) (*.f64 0 (sqrt.f64 (atan.f64 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 0 (atan.f64 N)) (sqrt.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan.f64 N) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan.f64 N) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (atan.f64 N))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan.f64 N) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (sqrt.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan.f64 N) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (atan.f64 N))))))))

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`*-commutative_binary64`
1×	`associate-+l-_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	72
1	13	12
2	19	12
3	20	12
4	22	12
5	26	12
6	30	12
7	35	12

Stop Event

1×

saturated

Counts

65 → 55

Calls

Call 1

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

Outputs
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(*.f64 0 (atan.f64 N))
0
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(*.f64 0 (atan.f64 N))
0
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(*.f64 0 (atan.f64 N))
0
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(*.f64 0 (atan.f64 N))
0
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(*.f64 0 (atan.f64 N))
0
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(*.f64 0 (atan.f64 N))
0
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(*.f64 0 (atan.f64 N))
0
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(*.f64 0 (atan.f64 N))
0
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(*.f64 0 (atan.f64 N))
0
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(*.f64 0 (atan.f64 N))
0
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(*.f64 0 (atan.f64 N))
0
(+.f64 (atan.f64 N) (*.f64 -1 (atan.f64 N)))
(*.f64 0 (atan.f64 N))
0

localize34.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 N (+.f64 N 1))
✓	0.0b	(+.f64 1 (*.f64 N (+.f64 N 1)))
✓	0.0b	(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
✓	2.9b	(+.f64 N (-.f64 1 N))

Compiler

Compiled 39 to 26 computations (33.3% saved)

series5.0ms (0.1%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	N	@	-inf	(*.f64 N (+.f64 N 1))
0.0ms	N	@	inf	(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
0.0ms	N	@	inf	(+.f64 1 (*.f64 N (+.f64 N 1)))
0.0ms	N	@	-inf	(+.f64 1 (*.f64 N (+.f64 N 1)))
0.0ms	N	@	inf	(*.f64 N (+.f64 N 1))

rewrite203.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

616×	`fma-def_binary64`
473×	`log-prod_binary64`
352×	`pow-prod-down_binary64`
297×	`fma-neg_binary64`
270×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	43
1	210	37
2	3076	37

Stop Event

1×	node limit

Counts

4 → 240

Calls

Call 1

Inputs
(+.f64 N (-.f64 1 N))
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
(+.f64 1 (*.f64 N (+.f64 N 1)))
(*.f64 N (+.f64 N 1))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 1 (-.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 N 1) N)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 N (-.f64 1 N)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (.f64 N N) (+.f64 (+.f64 N -1) N)) (/.f64 (pow.f64 (-.f64 1 N) 2) (+.f64 (+.f64 N -1) N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (+.f64 N (-.f64 1 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 N (-.f64 1 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (+.f64 N (-.f64 1 N))) (pow.f64 (cbrt.f64 (+.f64 N (-.f64 1 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (+.f64 N (-.f64 1 N))) 2) (cbrt.f64 (+.f64 N (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (+.f64 N (-.f64 1 N))) (sqrt.f64 (+.f64 N (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (pow.f64 N 3) (pow.f64 (-.f64 1 N) 3)) (/.f64 1 (fma.f64 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 N (.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (fma.f64 N N N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 N N) N)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 N N) 1) N)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 N N N))) 2)) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 N N N)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 N N N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 N 6) (pow.f64 N 3)) (+.f64 (pow.f64 N 4) (-.f64 (.f64 N N) (pow.f64 N 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 N 4) (.f64 N N)) (fma.f64 N N (neg.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) 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N)) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 N 3/2) (sqrt.f64 N) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 N) 5) (cbrt.f64 N) N)))))

simplify83.0ms (1%)

Algorithm

1×	egg-herbie

Rules

968×	`fma-neg_binary64`
532×	`unswap-sqr_binary64`
447×	`distribute-rgt-neg-in_binary64`
354×	`cancel-sign-sub-inv_binary64`
329×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	327
1	44	269
2	67	269
3	163	269
4	583	269
5	1634	269
6	3616	269
7	5643	269
8	7339	269

Stop Event

1×	node limit

Counts

288 → 253

Calls

Call 1

Inputs
1
1
1
1
1
1
1
1
1
1
1
1
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 1 (.f64 N (-.f64 1 (.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (.f64 N (-.f64 1 (.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (.f64 N (-.f64 1 (.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (.f64 N (-.f64 1 (.f64 -1 N)))))
1
(+.f64 N 1)
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
N
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))

Outputs
1
1
1
1
1
1
1
1
1
1
1
1
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (.f64 N (-.f64 1 (.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (.f64 N (-.f64 1 (.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (.f64 N (-.f64 1 (.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 1 (.f64 N (-.f64 1 (.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
1
(+.f64 N 1)
(+.f64 1 N)
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 (+.f64 1 N) (*.f64 N N))
(+.f64 N (fma.f64 N N 1))
(fma.f64 N N (+.f64 1 N))
(+.f64 1 (fma.f64 N N N))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 (+.f64 1 N) (*.f64 N N))
(+.f64 N (fma.f64 N N 1))
(fma.f64 N N (+.f64 1 N))
(+.f64 1 (fma.f64 N N N))
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 (+.f64 1 N) (*.f64 N N))
(+.f64 N (fma.f64 N N 1))
(fma.f64 N N (+.f64 1 N))
(+.f64 1 (fma.f64 N N N))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 (+.f64 1 N) (*.f64 N N))
(+.f64 N (fma.f64 N N 1))
(fma.f64 N N (+.f64 1 N))
(+.f64 1 (fma.f64 N N N))
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 (+.f64 1 N) (*.f64 N N))
(+.f64 N (fma.f64 N N 1))
(fma.f64 N N (+.f64 1 N))
(+.f64 1 (fma.f64 N N N))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 (+.f64 1 N) (*.f64 N N))
(+.f64 N (fma.f64 N N 1))
(fma.f64 N N (+.f64 1 N))
(+.f64 1 (fma.f64 N N N))
N
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)

localize17.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.7b	(sqrt.f64 (atan.f64 (+.f64 N 1)))
✓	15.1b	(fma.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))

Compiler

Compiled 34 to 22 computations (35.3% saved)

series3.0ms (0%)

Counts

2 → 16

Calls

6 calls:

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

rewrite102.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

773×	`pow1_binary64`
714×	`log1p-expm1-u_binary64`
714×	`expm1-log1p-u_binary64`
713×	`add-log-exp_binary64`
697×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	183	19
2	2240	19

Stop Event

1×	node limit

Counts

2 → 42

Calls

Call 1

Inputs
(fma.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))
(sqrt.f64 (atan.f64 (+.f64 N 1)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (atan.f64 (+.f64 N 1)) 0) (atan.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (pow.f64 (cbrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2) (cbrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (sqrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (atan.f64 N) 3)) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (-.f64 (pow.f64 (atan.f64 N) 2) (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(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 pow.f64 (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (atan.f64 (+.f64 N 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) (cbrt.f64 (sqrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (atan.f64 (+.f64 N 1)))) (cbrt.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 1/4) (pow.f64 (atan.f64 (+.f64 N 1)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2)) (sqrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) 1/2) (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan.f64 (+.f64 N 1)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (atan.f64 (+.f64 N 1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (atan.f64 (+.f64 N 1)))))))))

simplify153.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

52×	`fma-def_binary64`
43×	`fma-neg_binary64`
22×	`cancel-sign-sub-inv_binary64`
19×	`sub-neg_binary64`
14×	`associate--r+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	172
1	26	164
2	36	164
3	66	164
4	93	164
5	139	164
6	187	164
7	220	164
8	266	164
9	302	164
10	328	164
11	330	164

Stop Event

1×

saturated

Counts

58 → 45

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

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

localize23.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2)
✓	1.0b	(cbrt.f64 (atan.f64 (+.f64 N 1)))
✓	27.9b	(fma.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) (cbrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))

Compiler

Compiled 44 to 31 computations (29.5% saved)

series10.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
4.0ms	N	@	-inf	(fma.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) (cbrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))
2.0ms	N	@	0	(fma.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) (cbrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))
2.0ms	N	@	inf	(fma.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) (cbrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))
0.0ms	N	@	-inf	(pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2)
0.0ms	N	@	-inf	(cbrt.f64 (atan.f64 (+.f64 N 1)))

rewrite66.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

886×	`pow1_binary64`
821×	`add-log-exp_binary64`
821×	`log1p-expm1-u_binary64`
821×	`expm1-log1p-u_binary64`
803×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	32
1	226	30
2	2608	30

Stop Event

1×	node limit

Counts

3 → 58

Calls

Call 1

Inputs
(fma.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) (cbrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))
(cbrt.f64 (atan.f64 (+.f64 N 1)))
(pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (atan.f64 N) (atan.f64 (+.f64 N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (atan.f64 (+.f64 N 1)) 0) (atan.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (pow.f64 (cbrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2) (cbrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) (sqrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3) (pow.f64 (atan.f64 N) 3)) (+.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (-.f64 (pow.f64 (atan.f64 N) 2) (*.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) (pow.f64 (atan.f64 N) 2)) (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)))))) (#(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 pow.f64 (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cbrt.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 2) (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) (pow.f64 (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 1/6) (pow.f64 (atan.f64 (+.f64 N 1)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 4))) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (cbrt.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) 1/3) (pow.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan.f64 (+.f64 N 1)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) (cbrt.f64 (atan.f64 (+.f64 N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 2) (cbrt.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 2) (*.f64 (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) (cbrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 4)) (pow.f64 (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (pow.f64 (atan.f64 (+.f64 N 1)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 1/6) (*.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 1/6) (cbrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) (pow.f64 (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))) 2)) (cbrt.f64 (cbrt.f64 (atan.f64 (+.f64 N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 2 (log.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))))))))))

simplify84.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1003×	`fma-def_binary64`
772×	`fma-neg_binary64`
506×	`associate-l_binary64`
390×	`distribute-rgt-neg-in_binary64`
361×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	396
1	68	360
2	104	360
3	168	360
4	286	360
5	664	360
6	2252	360
7	3256	360
8	4885	360
9	6855	360

Stop Event

1×	node limit

Counts

94 → 66

Calls

Call 1

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

Outputs
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (*.f64 (pow.f64 1 1/3) (atan.f64 (+.f64 N 1))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (.f64 -1 N)))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (.f64 -1 N)))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (.f64 -1 N)))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(-.f64 (.f64 (pow.f64 1 1/3) (atan.f64 (-.f64 1 (.f64 -1 N)))) (atan.f64 N))
(-.f64 (*.f64 1 (atan.f64 (+.f64 1 N))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 1 N)) (atan.f64 N))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(pow.f64 (atan.f64 (+.f64 N 1)) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 1/3)
(cbrt.f64 (atan.f64 (+.f64 1 N)))
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2))
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2))
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2))
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2))
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2))
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2))
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2))
(pow.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 2) 1/3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2))
(pow.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) 1/3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2))
(pow.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) 1/3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2))
(pow.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) 1/3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2))
(pow.f64 (pow.f64 (atan.f64 (-.f64 1 (*.f64 -1 N))) 2) 1/3)
(cbrt.f64 (pow.f64 (atan.f64 (+.f64 1 N)) 2))

eval465.0ms (5.7%)

Compiler: Compiled 10330 to 6077 computations (41.2% saved)

prune147.0ms (1.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	529	5	534
Fresh	0	0	0
Picked	1	0	1
Done	3	1	4
Total	533	6	539

Error

0.5b

Counts

539 → 6

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.5b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
▶	14.4b	(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (cbrt.f64 (pow.f64 (fma.f64 N N N) 3))))
▶	28.7b	(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))))
✓	15.3b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
▶	14.3b	(log1p.f64 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))
▶	0.5b	(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))

Compiler

Compiled 154 to 108 computations (29.9% saved)

localize16.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 N (+.f64 N 1))
	0.0b	(+.f64 1 (*.f64 N (+.f64 N 1)))
✓	0.5b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

Compiler

Compiled 27 to 19 computations (29.6% saved)

series1.0ms (0%)

Counts

1 → 8

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	N	@	0	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
0.0ms	N	@	inf	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
0.0ms	N	@	-inf	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite86.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

798×	`pow1_binary64`
742×	`log1p-expm1-u_binary64`
742×	`expm1-log1p-u_binary64`
741×	`add-log-exp_binary64`
727×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	152	11
2	2057	11

Stop Event

1×	node limit

Counts

1 → 16

Calls

Call 1

Inputs
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))))

simplify76.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

968×	`fma-neg_binary64`
532×	`unswap-sqr_binary64`
451×	`distribute-rgt-neg-in_binary64`
353×	`cancel-sign-sub-inv_binary64`
312×	`neg-sub0_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	104
1	33	88
2	54	88
3	151	88
4	575	88
5	1638	88
6	3627	88
7	5662	88
8	7359	88

Stop Event

1×	node limit

Counts

24 → 19

Calls

Call 1

Inputs
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 1 (.f64 N (-.f64 1 (.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (.f64 N (-.f64 1 (.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (.f64 N (-.f64 1 (.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (.f64 N (-.f64 1 (.f64 -1 N)))))

Outputs
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (-.f64 N -1)))
(atan2.f64 1 (-.f64 N (fma.f64 N N -1)))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (-.f64 N -1)))
(atan2.f64 1 (-.f64 N (fma.f64 N N -1)))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (-.f64 N -1)))
(atan2.f64 1 (-.f64 N (fma.f64 N N -1)))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (-.f64 N -1)))
(atan2.f64 1 (-.f64 N (fma.f64 N N -1)))
(atan2.f64 1 (+.f64 1 (.f64 N (-.f64 1 (.f64 -1 N)))))
(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (-.f64 N -1)))
(atan2.f64 1 (-.f64 N (fma.f64 N N -1)))
(atan2.f64 1 (+.f64 1 (.f64 N (-.f64 1 (.f64 -1 N)))))
(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (-.f64 N -1)))
(atan2.f64 1 (-.f64 N (fma.f64 N N -1)))
(atan2.f64 1 (+.f64 1 (.f64 N (-.f64 1 (.f64 -1 N)))))
(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (-.f64 N -1)))
(atan2.f64 1 (-.f64 N (fma.f64 N N -1)))
(atan2.f64 1 (+.f64 1 (.f64 N (-.f64 1 (.f64 -1 N)))))
(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (-.f64 N -1)))
(atan2.f64 1 (-.f64 N (fma.f64 N N -1)))

localize12.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 N (+.f64 1 (pow.f64 N 2)))
✓	0.5b	(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))

Compiler

Compiled 28 to 21 computations (25% saved)

series2.0ms (0%)

Counts

2 → 10

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	N	@	-inf	(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
0.0ms	N	@	-inf	(+.f64 N (+.f64 1 (pow.f64 N 2)))
0.0ms	N	@	0	(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
0.0ms	N	@	inf	(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
0.0ms	N	@	inf	(+.f64 N (+.f64 1 (pow.f64 N 2)))

rewrite88.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

895×	`pow1_binary64`
838×	`add-log-exp_binary64`
836×	`log1p-expm1-u_binary64`
836×	`expm1-log1p-u_binary64`
821×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	177	19
2	2337	19

Stop Event

1×	node limit

Counts

2 → 51

Calls

Call 1

Inputs
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(+.f64 N (+.f64 1 (pow.f64 N 2)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 2) (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 N (fma.f64 N N 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 N N) (-.f64 N (fma.f64 N N 1))) (/.f64 (pow.f64 (fma.f64 N N 1) 2) (-.f64 N (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 N (fma.f64 N N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 N (fma.f64 N N 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) (pow.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) 2) (cbrt.f64 (+.f64 N (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 (hypot.f64 1 N) (sqrt.f64 N)) (hypot.f64 (hypot.f64 1 N) (sqrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 N 3) (pow.f64 (fma.f64 N N 1) 3)) (/.f64 1 (fma.f64 N N (*.f64 (fma.f64 N N 1) (-.f64 (fma.f64 N N 1) N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 N N) (pow.f64 (fma.f64 N N 1) 2)) (/.f64 1 (-.f64 N (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 N N (*.f64 (fma.f64 N N 1) (-.f64 (fma.f64 N N 1) N))) (+.f64 (pow.f64 N 3) (pow.f64 (fma.f64 N N 1) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 N (fma.f64 N N 1)) (-.f64 (*.f64 N N) (pow.f64 (fma.f64 N N 1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 N 3) (pow.f64 (fma.f64 N N 1) 3)) (fma.f64 N N (*.f64 (fma.f64 N N 1) (-.f64 (fma.f64 N N 1) N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 N 3) (pow.f64 (fma.f64 N N 1) 3)) (+.f64 (pow.f64 (fma.f64 N N 1) 2) (-.f64 (*.f64 N N) (+.f64 N (pow.f64 N 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 N N) (pow.f64 (fma.f64 N N 1) 2)) (-.f64 N (fma.f64 N N 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 N 3) (pow.f64 (fma.f64 N N 1) 3))) (neg.f64 (fma.f64 N N (*.f64 (fma.f64 N N 1) (-.f64 (fma.f64 N N 1) N)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 N N) (pow.f64 (fma.f64 N N 1) 2))) (neg.f64 (-.f64 N (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 1 N) 3) (pow.f64 N 6)) (+.f64 (*.f64 (+.f64 1 N) (+.f64 1 N)) (-.f64 (pow.f64 N 4) (*.f64 (+.f64 1 N) (*.f64 N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 N N 1) 2) (*.f64 N N)) (-.f64 (fma.f64 N N 1) N))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (+.f64 1 N) (+.f64 1 N)) (pow.f64 N 4)) (-.f64 (+.f64 1 N) (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 N (fma.f64 N N 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 N (fma.f64 N N 1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 N (fma.f64 N N 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 (hypot.f64 1 N) (sqrt.f64 N)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 N (fma.f64 N N 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 N (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 N (fma.f64 N N 1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 N (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 N (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 N (fma.f64 N N 1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 N (fma.f64 N N 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 N N 1) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 N N 1)) 2) (cbrt.f64 (fma.f64 N N 1)) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 N) 2) (cbrt.f64 N) (fma.f64 N N 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 N) (hypot.f64 1 N) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 N) (sqrt.f64 N) (fma.f64 N N 1))))))

simplify81.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1010×	`fma-neg_binary64`
532×	`unswap-sqr_binary64`
450×	`distribute-rgt-neg-in_binary64`
362×	`cancel-sign-sub-inv_binary64`
312×	`neg-sub0_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	87
1	30	67
2	58	67
3	164	67
4	587	67
5	1660	67
6	3620	67
7	5653	67
8	7340	67

Stop Event

1×	node limit

Counts

61 → 60

Calls

Call 1

Inputs
(atan2.f64 1 (-.f64 (+.f64 1 (pow.f64 N 2)) (*.f64 -1 N)))
(atan2.f64 1 (-.f64 (+.f64 1 (pow.f64 N 2)) (*.f64 -1 N)))
(atan2.f64 1 (-.f64 (+.f64 1 (pow.f64 N 2)) (*.f64 -1 N)))
(atan2.f64 1 (-.f64 (+.f64 1 (pow.f64 N 2)) (*.f64 -1 N)))
1
(+.f64 N 1)
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))

Outputs
(atan2.f64 1 (-.f64 (+.f64 1 (pow.f64 N 2)) (*.f64 -1 N)))
(atan2.f64 1 (+.f64 1 (-.f64 (*.f64 N N) (neg.f64 N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (-.f64 (+.f64 1 (pow.f64 N 2)) (*.f64 -1 N)))
(atan2.f64 1 (+.f64 1 (-.f64 (*.f64 N N) (neg.f64 N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (-.f64 (+.f64 1 (pow.f64 N 2)) (*.f64 -1 N)))
(atan2.f64 1 (+.f64 1 (-.f64 (*.f64 N N) (neg.f64 N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (-.f64 (+.f64 1 (pow.f64 N 2)) (*.f64 -1 N)))
(atan2.f64 1 (+.f64 1 (-.f64 (*.f64 N N) (neg.f64 N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
1
(+.f64 N 1)
(+.f64 1 N)
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)

localize35.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))))
	2.9b	(+.f64 N (-.f64 1 N))
✓	11.8b	(-.f64 (pow.f64 N 4) (*.f64 N N))
✓	33.2b	(/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))

Compiler

Compiled 81 to 36 computations (55.6% saved)

series5.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	N	@	0	(/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))
1.0ms	N	@	-inf	(/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))
1.0ms	N	@	inf	(/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))
1.0ms	N	@	-inf	(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))))
0.0ms	N	@	inf	(-.f64 (pow.f64 N 4) (*.f64 N N))

rewrite106.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

798×	`fma-def_binary64`
545×	`fma-neg_binary64`
218×	`expm1-udef_binary64`
218×	`log1p-udef_binary64`
181×	`log-div_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	60
1	330	30
2	5214	30

Stop Event

1×	node limit

Counts

3 → 286

Calls

Call 1

Inputs

(/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))

(-.f64 (pow.f64 N 4) (*.f64 N N))

(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))))

Outputs

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(pow.f64 (cbrt.f64 N) 2)) (cbrt.f64 (pow.f64 N 4)) (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 N 3) N (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (fma.f64 N N N) 3) (/.f64 1 (fma.f64 N N N)) (fma.f64 N N (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (fma.f64 N N N) 3) (/.f64 1 (fma.f64 N N N)) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 N) 2)) (cbrt.f64 (pow.f64 N 4)) (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (*.f64 N N) (pow.f64 N 4))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (pow.f64 (fma.f64 N N N) 2) (fma.f64 N N (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (pow.f64 (fma.f64 N N N) 2) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 N) 2)) (cbrt.f64 (pow.f64 N 4)) (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (fma.f64 N N N) (hypot.f64 N (sqrt.f64 N))) (hypot.f64 N (sqrt.f64 N)) (fma.f64 N N (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (fma.f64 N N N) (hypot.f64 N (sqrt.f64 N))) (hypot.f64 N (sqrt.f64 N)) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 N) 2)) (cbrt.f64 (pow.f64 N 4)) (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 N (sqrt.f64 N)) (sqrt.f64 N) (pow.f64 N 4))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 (+.f64 1 (pow.f64 (fma.f64 N N N) 2))) (cbrt.f64 (+.f64 1 (pow.f64 (fma.f64 N N N) 2)))) (cbrt.f64 (+.f64 1 (pow.f64 (fma.f64 N N N) 2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (fma.f64 N N N)) (hypot.f64 1 (fma.f64 N N N)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (cbrt.f64 (pow.f64 N 8))) (sqrt.f64 (cbrt.f64 (pow.f64 N 4))) (pow.f64 N 4))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (cbrt.f64 (pow.f64 N 4))) (pow.f64 (cbrt.f64 N) 2) (pow.f64 N 4))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (pow.f64 (cbrt.f64 N) 2) 4) (pow.f64 (cbrt.f64 N) 4) (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (sqrt.f64 N) 4) (pow.f64 (sqrt.f64 N) 4) (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (cbrt.f64 (+.f64 (pow.f64 N 8) (pow.f64 N 4)))) (cbrt.f64 (pow.f64 (fma.f64 N N N) 2)) (fma.f64 N N (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (cbrt.f64 (+.f64 (pow.f64 N 8) (pow.f64 N 4)))) (cbrt.f64 (pow.f64 (fma.f64 N N N) 2)) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 N) 2)) (cbrt.f64 (pow.f64 N 4)) (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 N N 1) (*.f64 N N) (fma.f64 N N (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 N N 1) (*.f64 N N) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 N) 2)) (cbrt.f64 (pow.f64 N 4)) (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 N (pow.f64 (cbrt.f64 N) 2)) (cbrt.f64 N) (pow.f64 N 4))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (fma.f64 N N N) (cbrt.f64 (pow.f64 (fma.f64 N N N) 2))) (cbrt.f64 (fma.f64 N N N)) (fma.f64 N N (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (fma.f64 N N N) (cbrt.f64 (pow.f64 (fma.f64 N N N) 2))) (cbrt.f64 (fma.f64 N N N)) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 N) 2)) (cbrt.f64 (pow.f64 N 4)) (*.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 N N) (cbrt.f64 (pow.f64 N 4))) (pow.f64 (cbrt.f64 N) 2) (*.f64 N N))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1))) (pow.f64 (cbrt.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1))) 2) (cbrt.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1))) (sqrt.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (atan2.f64 (+.f64 N (+.f64 N 1)) (+.f64 (fma.f64 N N N) 1))) 1))))))

simplify59.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

824×	`associate-/r*_binary64`
749×	`fma-def_binary64`
681×	`associate-l_binary64`
377×	`associate-*l/_binary64`
256×	`associate-/r/_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	25	593
1	57	566
2	101	566
3	280	434
4	1636	374

Stop Event

1×	node limit

Counts

322 → 298

Calls

Call 1

Inputs
N
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(*.f64 -1 (pow.f64 N 2))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(pow.f64 N 4)
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(pow.f64 N 4)
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (.f64 -1 N)))) (/.f64 (pow.f64 N 2) (fma.f64 N N (.f64 -1 N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (.f64 -1 N)))) (/.f64 (pow.f64 N 2) (fma.f64 N N (.f64 -1 N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (.f64 -1 N)))) (/.f64 (pow.f64 N 2) (fma.f64 N N (.f64 -1 N)))))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (.f64 -1 N)))) (/.f64 (pow.f64 N 2) (fma.f64 N N (.f64 -1 N)))))

Outputs
N
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(*.f64 -1 (pow.f64 N 2))
(neg.f64 (*.f64 N N))
(*.f64 N (neg.f64 N))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(fma.f64 -1 (*.f64 N N) (pow.f64 N 4))
(-.f64 (pow.f64 N 4) (*.f64 N N))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(fma.f64 -1 (*.f64 N N) (pow.f64 N 4))
(-.f64 (pow.f64 N 4) (*.f64 N N))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(fma.f64 -1 (*.f64 N N) (pow.f64 N 4))
(-.f64 (pow.f64 N 4) (*.f64 N N))
(pow.f64 N 4)
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(fma.f64 -1 (*.f64 N N) (pow.f64 N 4))
(-.f64 (pow.f64 N 4) (*.f64 N N))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(fma.f64 -1 (*.f64 N N) (pow.f64 N 4))
(-.f64 (pow.f64 N 4) (*.f64 N N))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(fma.f64 -1 (*.f64 N N) (pow.f64 N 4))
(-.f64 (pow.f64 N 4) (*.f64 N N))
(pow.f64 N 4)
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(fma.f64 -1 (*.f64 N N) (pow.f64 N 4))
(-.f64 (pow.f64 N 4) (*.f64 N N))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(fma.f64 -1 (*.f64 N N) (pow.f64 N 4))
(-.f64 (pow.f64 N 4) (*.f64 N N))
(+.f64 (*.f64 -1 (pow.f64 N 2)) (pow.f64 N 4))
(fma.f64 -1 (*.f64 N N) (pow.f64 N 4))
(-.f64 (pow.f64 N 4) (*.f64 N N))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N))))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 N (/.f64 (fma.f64 N N (neg.f64 N)) N)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (.f64 N N) N)) (-.f64 (/.f64 (.f64 N N) (-.f64 (*.f64 N N) N)) 1)))
(atan2.f64 1 (+.f64 1 (.f64 (.f64 N (/.f64 1 (+.f64 N -1))) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N))))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 N (/.f64 (fma.f64 N N (neg.f64 N)) N)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (.f64 N N) N)) (-.f64 (/.f64 (.f64 N N) (-.f64 (*.f64 N N) N)) 1)))
(atan2.f64 1 (+.f64 1 (.f64 (.f64 N (/.f64 1 (+.f64 N -1))) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N))))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 N (/.f64 (fma.f64 N N (neg.f64 N)) N)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (.f64 N N) N)) (-.f64 (/.f64 (.f64 N N) (-.f64 (*.f64 N N) N)) 1)))
(atan2.f64 1 (+.f64 1 (.f64 (.f64 N (/.f64 1 (+.f64 N -1))) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N))))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 N (/.f64 (fma.f64 N N (neg.f64 N)) N)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (.f64 N N) N)) (-.f64 (/.f64 (.f64 N N) (-.f64 (*.f64 N N) N)) 1)))
(atan2.f64 1 (+.f64 1 (.f64 (.f64 N (/.f64 1 (+.f64 N -1))) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N))))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 N (/.f64 (fma.f64 N N (neg.f64 N)) N)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (.f64 N N) N)) (-.f64 (/.f64 (.f64 N N) (-.f64 (*.f64 N N) N)) 1)))
(atan2.f64 1 (+.f64 1 (.f64 (.f64 N (/.f64 1 (+.f64 N -1))) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N))))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 N (/.f64 (fma.f64 N N (neg.f64 N)) N)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (.f64 N N) N)) (-.f64 (/.f64 (.f64 N N) (-.f64 (*.f64 N N) N)) 1)))
(atan2.f64 1 (+.f64 1 (.f64 (.f64 N (/.f64 1 (+.f64 N -1))) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N))))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 N (/.f64 (fma.f64 N N (neg.f64 N)) N)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (.f64 N N) N)) (-.f64 (/.f64 (.f64 N N) (-.f64 (*.f64 N N) N)) 1)))
(atan2.f64 1 (+.f64 1 (.f64 (.f64 N (/.f64 1 (+.f64 N -1))) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) 1) (/.f64 (pow.f64 N 2) (fma.f64 N N (neg.f64 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N))))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 N (/.f64 (fma.f64 N N (neg.f64 N)) N)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (.f64 N N) N)) (-.f64 (/.f64 (.f64 N N) (-.f64 (*.f64 N N) N)) 1)))
(atan2.f64 1 (+.f64 1 (.f64 (.f64 N (/.f64 1 (+.f64 N -1))) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (.f64 -1 N)))) (/.f64 (pow.f64 N 2) (fma.f64 N N (.f64 -1 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N))))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 N (/.f64 (fma.f64 N N (neg.f64 N)) N)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (.f64 N N) N)) (-.f64 (/.f64 (.f64 N N) (-.f64 (*.f64 N N) N)) 1)))
(atan2.f64 1 (+.f64 1 (.f64 (.f64 N (/.f64 1 (+.f64 N -1))) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (.f64 -1 N)))) (/.f64 (pow.f64 N 2) (fma.f64 N N (.f64 -1 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N))))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 N (/.f64 (fma.f64 N N (neg.f64 N)) N)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (.f64 N N) N)) (-.f64 (/.f64 (.f64 N N) (-.f64 (*.f64 N N) N)) 1)))
(atan2.f64 1 (+.f64 1 (.f64 (.f64 N (/.f64 1 (+.f64 N -1))) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (.f64 -1 N)))) (/.f64 (pow.f64 N 2) (fma.f64 N N (.f64 -1 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N))))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 N (/.f64 (fma.f64 N N (neg.f64 N)) N)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (.f64 N N) N)) (-.f64 (/.f64 (.f64 N N) (-.f64 (*.f64 N N) N)) 1)))
(atan2.f64 1 (+.f64 1 (.f64 (.f64 N (/.f64 1 (+.f64 N -1))) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))
(atan2.f64 1 (-.f64 (+.f64 1 (/.f64 (pow.f64 N 4) (fma.f64 N N (.f64 -1 N)))) (/.f64 (pow.f64 N 2) (fma.f64 N N (.f64 -1 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 (*.f64 N N) (fma.f64 N N (neg.f64 N))))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (fma.f64 N N (neg.f64 N))) (-.f64 1 (/.f64 N (/.f64 (fma.f64 N N (neg.f64 N)) N)))))
(atan2.f64 1 (-.f64 (/.f64 (pow.f64 N 4) (-.f64 (.f64 N N) N)) (-.f64 (/.f64 (.f64 N N) (-.f64 (*.f64 N N) N)) 1)))
(atan2.f64 1 (+.f64 1 (.f64 (.f64 N (/.f64 1 (+.f64 N -1))) (fma.f64 N N -1))))
(atan2.f64 1 (fma.f64 (/.f64 N (+.f64 N -1)) (fma.f64 N N -1) 1))

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))
✓	0.0b	(expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))
✓	0.0b	(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))
	2.9b	(+.f64 N (-.f64 1 N))

Compiler

Compiled 60 to 31 computations (48.3% saved)

series3.0ms (0%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
0.0ms	N	@	inf	(expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))
0.0ms	N	@	-inf	(expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))
0.0ms	N	@	0	(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))
0.0ms	N	@	0	(expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))
0.0ms	N	@	0	(log1p.f64 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))

rewrite130.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

868×	`prod-diff_binary64`
605×	`unpow-prod-down_binary64`
430×	`log-prod_binary64`
405×	`fma-def_binary64`
258×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	53
1	201	53
2	2770	53

Stop Event

1×	node limit

Counts

3 → 91

Calls

Call 1

Inputs

(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))

(expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))

(log1p.f64 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))

Outputs

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((#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))) (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 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(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) 2) (cbrt.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) -1)))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))) (log.f64 (sqrt.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log1p.f64 (pow.f64 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 3)) (log.f64 (+.f64 1 (-.f64 (pow.f64 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 2) (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (atan2.f64 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(fma.f64 N N N))))) 1/3) (cbrt.f64 (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) 2) 3) (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))) 1))))))

simplify55.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

25×	`fma-def_binary64`
7×	`+-commutative_binary64`
4×	`distribute-lft-in_binary64`
3×	`distribute-rgt1-in_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	420
1	17	420
2	24	420
3	33	420
4	41	420
5	45	420
6	57	420
7	70	420
8	75	420
9	76	420

Stop Event

1×

saturated

Counts

127 → 67

Calls

Call 1

Inputs
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))

Outputs
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(expm1.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(expm1.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(expm1.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(expm1.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(expm1.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(expm1.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(expm1.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(expm1.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(expm1.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(expm1.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(expm1.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(-.f64 (exp.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))) 1)
(expm1.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

localize42.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (cbrt.f64 (pow.f64 (fma.f64 N N N) 3))))
✓	0.1b	(pow.f64 (fma.f64 N N N) 3)
	2.9b	(+.f64 N (-.f64 1 N))
✓	29.3b	(cbrt.f64 (pow.f64 (fma.f64 N N N) 3))

Compiler

Compiled 53 to 28 computations (47.2% saved)

series6.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	N	@	-inf	(pow.f64 (fma.f64 N N N) 3)
1.0ms	N	@	inf	(pow.f64 (fma.f64 N N N) 3)
1.0ms	N	@	0	(pow.f64 (fma.f64 N N N) 3)
1.0ms	N	@	0	(cbrt.f64 (pow.f64 (fma.f64 N N N) 3))
1.0ms	N	@	-inf	(cbrt.f64 (pow.f64 (fma.f64 N N N) 3))

rewrite104.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

986×	`prod-diff_binary64`
458×	`log-prod_binary64`
412×	`fma-def_binary64`
278×	`pow2_binary64`
217×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	30
1	247	30
2	3013	30

Stop Event

1×	node limit

Counts

3 → 105

Calls

Call 1

Inputs
(cbrt.f64 (pow.f64 (fma.f64 N N N) 3))
(pow.f64 (fma.f64 N N N) 3)
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (cbrt.f64 (pow.f64 (fma.f64 N N N) 3))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 N (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (fma.f64 N N N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 N N) N)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 N N) 1) N)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 N N N))) 2)) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 N N N)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (fma.f64 N N N) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 N (+.f64 N 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 N N N) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 N N N))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 N N N)) (pow.f64 (cbrt.f64 (fma.f64 N N N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 N N N)) 2) (cbrt.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 N (sqrt.f64 N)) (hypot.f64 N (sqrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 N 1) N)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (fma.f64 N N N))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 N N) 3) (pow.f64 N 3)) (+.f64 (pow.f64 (*.f64 N N) 2) (-.f64 (*.f64 N N) (pow.f64 N 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 N N) 2) (*.f64 N N)) (-.f64 (*.f64 N N) N))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 N N N) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 N N N) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 N N N) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 N N N)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 N (sqrt.f64 N)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 N N N) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 N) (exp.f64 (*.f64 N N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 N)) (exp.f64 (*.f64 N N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (*.f64 N N)) (+.f64 1 (expm1.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (*.f64 (log1p.f64 (fma.f64 N N N)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 N N N)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (fma.f64 N N N))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 N N N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 N 1 (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 N (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 (fma.f64 N N N) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 N N) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (fma.f64 N N N) 1) 1 -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 N N) 1 N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 N) (pow.f64 (cbrt.f64 N) 2) (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 N) 2) (cbrt.f64 N) (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 N) 2) (*.f64 (cbrt.f64 N) N) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 (fma.f64 N N N) 1)) (cbrt.f64 (pow.f64 (+.f64 (fma.f64 N N N) 1) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (+.f64 (fma.f64 N N N) 1) 2)) (cbrt.f64 (+.f64 (fma.f64 N N N) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 N) (sqrt.f64 N) (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 N) (*.f64 (sqrt.f64 N) N) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 N (sqrt.f64 (+.f64 N 1))) (hypot.f64 N (sqrt.f64 (+.f64 N 1))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (pow.f64 (fma.f64 N N N) 3) 1) (/.f64 1 (fma.f64 (fma.f64 N N N) (-.f64 (fma.f64 N N N) 1) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1 (pow.f64 (fma.f64 N N N) 2)) (/.f64 1 (-.f64 1 (fma.f64 N N N))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 N (sqrt.f64 N)) (sqrt.f64 N) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (pow.f64 (cbrt.f64 N) 2) 2) (pow.f64 (cbrt.f64 N) 2) N)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 N (pow.f64 (cbrt.f64 N) 2)) (cbrt.f64 N) N)))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (fma.f64 N N N) 3))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 N N) (pow.f64 (fma.f64 N N N) 2)) (*.f64 N (pow.f64 (fma.f64 N N N) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 (fma.f64 N N N) 2) (*.f64 N N)) (*.f64 (pow.f64 (fma.f64 N N N) 2) N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (fma.f64 N N N) 3))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (fma.f64 N N N) 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (fma.f64 N N N) 3)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (fma.f64 N N N) 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (pow.f64 (fma.f64 N N N) 3) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 N N N) (pow.f64 (fma.f64 N N N) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 N N N) 3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (fma.f64 N N N) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 N N N) 2) (fma.f64 N N N))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 N N N)) 2) (*.f64 (cbrt.f64 (fma.f64 N N N)) (pow.f64 (fma.f64 N N N) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 N (sqrt.f64 N)) (*.f64 (hypot.f64 N (sqrt.f64 N)) (pow.f64 (fma.f64 N N N) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 N N N) 3/2) (pow.f64 (fma.f64 N N N) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (fma.f64 N N N) 2) 1) (fma.f64 N N N))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (fma.f64 N N N) 2) (pow.f64 (cbrt.f64 (fma.f64 N N N)) 2)) (cbrt.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (fma.f64 N N N) 2) (hypot.f64 N (sqrt.f64 N))) (hypot.f64 N (sqrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 N N N) 6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (fma.f64 N N N) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (fma.f64 N N N) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (fma.f64 N N N) 3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (fma.f64 N N N) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (fma.f64 N N N) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 3 (log.f64 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (fma.f64 N N N))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 (pow.f64 (fma.f64 N N N) 3) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 N N) (pow.f64 (fma.f64 N N N) 2) (*.f64 N (pow.f64 (fma.f64 N N N) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (fma.f64 N N N) 2) (*.f64 N N) (*.f64 (pow.f64 (fma.f64 N N N) 2) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 (pow.f64 (fma.f64 N N N) 3) 1)) 2) (cbrt.f64 (+.f64 (pow.f64 (fma.f64 N N N) 3) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (pow.f64 (fma.f64 N N N) 3/2)) (hypot.f64 1 (pow.f64 (fma.f64 N N N) 3/2)) -1)))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1))))) (log.f64 (sqrt.f64 (exp.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1))) (pow.f64 (cbrt.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1))) 2) (cbrt.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1))) (sqrt.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (atan2.f64 (-.f64 1 (-.f64 N N)) (+.f64 (fma.f64 N N N) 1))) 1))))))

simplify129.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

534×	`associate-+l+_binary64`
492×	`unswap-sqr_binary64`
466×	`associate-+r+_binary64`
424×	`distribute-rgt-in_binary64`
412×	`sqr-pow_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	26	365
1	69	357
2	163	351
3	453	348
4	1697	346
5	3431	346
6	4093	346
7	4662	346
8	5394	346
9	6570	346
10	7813	346

Stop Event

1×	node limit

Counts

141 → 123

Calls

Call 1

Inputs
N
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(pow.f64 N 3)
(+.f64 (*.f64 3 (pow.f64 N 4)) (pow.f64 N 3))
(+.f64 (.f64 3 (pow.f64 N 4)) (+.f64 (.f64 3 (pow.f64 N 5)) (pow.f64 N 3)))
(+.f64 (.f64 3 (pow.f64 N 4)) (+.f64 (pow.f64 N 6) (+.f64 (.f64 3 (pow.f64 N 5)) (pow.f64 N 3))))
(pow.f64 N 6)
(+.f64 (pow.f64 N 6) (*.f64 3 (pow.f64 N 5)))
(+.f64 (.f64 3 (pow.f64 N 4)) (+.f64 (pow.f64 N 6) (.f64 3 (pow.f64 N 5))))
(+.f64 (.f64 3 (pow.f64 N 4)) (+.f64 (pow.f64 N 6) (+.f64 (.f64 3 (pow.f64 N 5)) (pow.f64 N 3))))
(pow.f64 N 6)
(+.f64 (pow.f64 N 6) (*.f64 3 (pow.f64 N 5)))
(+.f64 (.f64 3 (pow.f64 N 4)) (+.f64 (pow.f64 N 6) (.f64 3 (pow.f64 N 5))))
(+.f64 (.f64 3 (pow.f64 N 4)) (+.f64 (pow.f64 N 6) (+.f64 (.f64 3 (pow.f64 N 5)) (pow.f64 N 3))))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))

Outputs
N
(+.f64 N (pow.f64 N 2))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(fma.f64 N N N)
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(fma.f64 N N N)
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(fma.f64 N N N)
(pow.f64 N 3)
(+.f64 (*.f64 3 (pow.f64 N 4)) (pow.f64 N 3))
(fma.f64 3 (pow.f64 N 4) (pow.f64 N 3))
(+.f64 (.f64 3 (pow.f64 N 4)) (+.f64 (.f64 3 (pow.f64 N 5)) (pow.f64 N 3)))
(fma.f64 3 (pow.f64 N 4) (fma.f64 3 (pow.f64 N 5) (pow.f64 N 3)))
(fma.f64 3 (+.f64 (pow.f64 N 4) (pow.f64 N 5)) (pow.f64 N 3))
(+.f64 (.f64 3 (pow.f64 N 4)) (+.f64 (pow.f64 N 6) (+.f64 (.f64 3 (pow.f64 N 5)) (pow.f64 N 3))))
(fma.f64 3 (pow.f64 N 4) (+.f64 (fma.f64 3 (pow.f64 N 5) (pow.f64 N 3)) (pow.f64 N 6)))
(+.f64 (fma.f64 3 (pow.f64 N 5) (pow.f64 N 3)) (fma.f64 3 (pow.f64 N 4) (pow.f64 N 6)))
(+.f64 (fma.f64 3 (+.f64 (pow.f64 N 4) (pow.f64 N 5)) (pow.f64 N 3)) (pow.f64 N 6))
(fma.f64 (pow.f64 N 4) (fma.f64 N N 3) (fma.f64 3 (pow.f64 N 5) (pow.f64 N 3)))
(fma.f64 3 (pow.f64 N 5) (fma.f64 (pow.f64 N 4) (fma.f64 N N 3) (pow.f64 N 3)))
(pow.f64 N 6)
(+.f64 (pow.f64 N 6) (*.f64 3 (pow.f64 N 5)))
(+.f64 (*.f64 3 (pow.f64 N 5)) (pow.f64 N 6))
(fma.f64 3 (pow.f64 N 5) (pow.f64 N 6))
(*.f64 (pow.f64 N 5) (+.f64 N 3))
(+.f64 (.f64 3 (pow.f64 N 4)) (+.f64 (pow.f64 N 6) (.f64 3 (pow.f64 N 5))))
(fma.f64 3 (pow.f64 N 4) (+.f64 (*.f64 3 (pow.f64 N 5)) (pow.f64 N 6)))
(fma.f64 3 (pow.f64 N 4) (fma.f64 3 (pow.f64 N 5) (pow.f64 N 6)))
(fma.f64 3 (+.f64 (pow.f64 N 4) (pow.f64 N 5)) (pow.f64 N 6))
(fma.f64 3 (pow.f64 N 4) (*.f64 (pow.f64 N 5) (+.f64 N 3)))
(+.f64 (.f64 3 (pow.f64 N 4)) (+.f64 (pow.f64 N 6) (+.f64 (.f64 3 (pow.f64 N 5)) (pow.f64 N 3))))
(fma.f64 3 (pow.f64 N 4) (+.f64 (fma.f64 3 (pow.f64 N 5) (pow.f64 N 3)) (pow.f64 N 6)))
(+.f64 (fma.f64 3 (pow.f64 N 5) (pow.f64 N 3)) (fma.f64 3 (pow.f64 N 4) (pow.f64 N 6)))
(+.f64 (fma.f64 3 (+.f64 (pow.f64 N 4) (pow.f64 N 5)) (pow.f64 N 3)) (pow.f64 N 6))
(fma.f64 (pow.f64 N 4) (fma.f64 N N 3) (fma.f64 3 (pow.f64 N 5) (pow.f64 N 3)))
(fma.f64 3 (pow.f64 N 5) (fma.f64 (pow.f64 N 4) (fma.f64 N N 3) (pow.f64 N 3)))
(pow.f64 N 6)
(+.f64 (pow.f64 N 6) (*.f64 3 (pow.f64 N 5)))
(+.f64 (*.f64 3 (pow.f64 N 5)) (pow.f64 N 6))
(fma.f64 3 (pow.f64 N 5) (pow.f64 N 6))
(*.f64 (pow.f64 N 5) (+.f64 N 3))
(+.f64 (.f64 3 (pow.f64 N 4)) (+.f64 (pow.f64 N 6) (.f64 3 (pow.f64 N 5))))
(fma.f64 3 (pow.f64 N 4) (+.f64 (*.f64 3 (pow.f64 N 5)) (pow.f64 N 6)))
(fma.f64 3 (pow.f64 N 4) (fma.f64 3 (pow.f64 N 5) (pow.f64 N 6)))
(fma.f64 3 (+.f64 (pow.f64 N 4) (pow.f64 N 5)) (pow.f64 N 6))
(fma.f64 3 (pow.f64 N 4) (*.f64 (pow.f64 N 5) (+.f64 N 3)))
(+.f64 (.f64 3 (pow.f64 N 4)) (+.f64 (pow.f64 N 6) (+.f64 (.f64 3 (pow.f64 N 5)) (pow.f64 N 3))))
(fma.f64 3 (pow.f64 N 4) (+.f64 (fma.f64 3 (pow.f64 N 5) (pow.f64 N 3)) (pow.f64 N 6)))
(+.f64 (fma.f64 3 (pow.f64 N 5) (pow.f64 N 3)) (fma.f64 3 (pow.f64 N 4) (pow.f64 N 6)))
(+.f64 (fma.f64 3 (+.f64 (pow.f64 N 4) (pow.f64 N 5)) (pow.f64 N 3)) (pow.f64 N 6))
(fma.f64 (pow.f64 N 4) (fma.f64 N N 3) (fma.f64 3 (pow.f64 N 5) (pow.f64 N 3)))
(fma.f64 3 (pow.f64 N 5) (fma.f64 (pow.f64 N 4) (fma.f64 N N 3) (pow.f64 N 3)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))

eval1.3s (15.4%)

Compiler: Compiled 21663 to 12093 computations (44.2% saved)

prune239.0ms (2.9%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	985	10	995
Fresh	0	0	0
Picked	1	0	1
Done	3	2	5
Total	989	12	1001

Error

0.5b

Counts

1001 → 12

Alt Table

Click to see full alt table

Status	Error	Program
▶	29.8b	(atan2.f64 1 (+.f64 N 1))
✓	0.5b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
▶	22.7b	(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N))))
	0.5b	(log1p.f64 (expm1.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))))
	1.1b	(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 2)
▶	30.4b	(atan2.f64 1 1)
▶	0.5b	(atan2.f64 1 (fma.f64 N N (+.f64 N 1)))
	22.7b	(atan2.f64 1 (/.f64 (-.f64 (.f64 (+.f64 1 N) (+.f64 1 N)) (pow.f64 N 4)) (-.f64 (+.f64 1 N) (.f64 N N))))
	27.9b	(atan2.f64 1 (*.f64 N N))
✓	15.3b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
	1.9b	(pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 3)
▶	10.8b	(atan2.f64 1 (+.f64 1 (cbrt.f64 (pow.f64 (fma.f64 N N N) 3))))

Compiler

Compiled 244 to 182 computations (25.4% saved)

localize46.0ms (0.6%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 N N (+.f64 N 1))
✓	0.5b	(atan2.f64 1 (fma.f64 N N (+.f64 N 1)))

Compiler

Compiled 20 to 12 computations (40% saved)

series3.0ms (0%)

Counts

2 → 16

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	N	@	0	(atan2.f64 1 (fma.f64 N N (+.f64 N 1)))
1.0ms	N	@	-inf	(atan2.f64 1 (fma.f64 N N (+.f64 N 1)))
1.0ms	N	@	inf	(atan2.f64 1 (fma.f64 N N (+.f64 N 1)))
0.0ms	N	@	inf	(fma.f64 N N (+.f64 N 1))
0.0ms	N	@	-inf	(fma.f64 N N (+.f64 N 1))

rewrite69.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

586×	`pow1_binary64`
543×	`log1p-expm1-u_binary64`
543×	`expm1-log1p-u_binary64`
542×	`add-log-exp_binary64`
531×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	19
1	122	19
2	1492	19

Stop Event

1×	node limit

Counts

2 → 39

Calls

Call 1

Inputs
(atan2.f64 1 (fma.f64 N N (+.f64 N 1)))
(fma.f64 N N (+.f64 N 1))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (atan2.f64 1 (fma.f64 N N (+.f64 1 N)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (atan2.f64 1 (fma.f64 N N (+.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N)))) (pow.f64 (cbrt.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N)))) 2) (cbrt.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N)))) (sqrt.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N)))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 N) (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 N N) (+.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 N N) 1) (+.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (*.f64 N N) 1) N)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (*.f64 N N) N) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 N N (+.f64 1 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 N N (+.f64 1 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 N N (+.f64 1 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 N N (+.f64 1 N))) (pow.f64 (cbrt.f64 (fma.f64 N N (+.f64 1 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 N N (+.f64 1 N))) 2) (cbrt.f64 (fma.f64 N N (+.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 N (sqrt.f64 (+.f64 1 N))) (hypot.f64 N (sqrt.f64 (+.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 N N) 3) (pow.f64 (+.f64 1 N) 3)) (+.f64 (*.f64 (*.f64 N N) (*.f64 N N)) (-.f64 (pow.f64 (+.f64 1 N) 2) (*.f64 (*.f64 N N) (+.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 N N) (*.f64 N N)) (pow.f64 (+.f64 1 N) 2)) (-.f64 (*.f64 N N) (+.f64 1 N)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 N N (+.f64 1 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 N N (+.f64 1 N)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 N N (+.f64 1 N))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 N (sqrt.f64 (+.f64 1 N))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 N N (+.f64 1 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 N N (+.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 N N (+.f64 1 N)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 N N (+.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 N N (+.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 N N (+.f64 1 N))))))))

simplify152.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

957×	`fma-neg_binary64`
532×	`unswap-sqr_binary64`
470×	`distribute-rgt-neg-in_binary64`
353×	`cancel-sign-sub-inv_binary64`
327×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	139
1	34	115
2	57	115
3	145	115
4	524	115
5	1579	115
6	3507	115
7	5703	115
8	7556	115

Stop Event

1×	node limit

Counts

55 → 50

Calls

Call 1

Inputs
(atan2.f64 1 (fma.f64 N N (-.f64 1 (*.f64 -1 N))))
(atan2.f64 1 (fma.f64 N N (-.f64 1 (*.f64 -1 N))))
(atan2.f64 1 (fma.f64 N N (-.f64 1 (*.f64 -1 N))))
(atan2.f64 1 (fma.f64 N N (-.f64 1 (*.f64 -1 N))))
1
(+.f64 N 1)
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (pow.f64 N 2)))

Outputs
(atan2.f64 1 (fma.f64 N N (-.f64 1 (*.f64 -1 N))))
(atan2.f64 1 (fma.f64 N N (-.f64 1 (neg.f64 N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (-.f64 1 (*.f64 -1 N))))
(atan2.f64 1 (fma.f64 N N (-.f64 1 (neg.f64 N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (-.f64 1 (*.f64 -1 N))))
(atan2.f64 1 (fma.f64 N N (-.f64 1 (neg.f64 N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (fma.f64 N N (-.f64 1 (*.f64 -1 N))))
(atan2.f64 1 (fma.f64 N N (-.f64 1 (neg.f64 N))))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
1
(+.f64 N 1)
(+.f64 1 N)
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (*.f64 N N)))
(+.f64 1 (fma.f64 N N N))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (*.f64 N N)))
(+.f64 1 (fma.f64 N N N))
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (*.f64 N N)))
(+.f64 1 (fma.f64 N N N))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (*.f64 N N)))
(+.f64 1 (fma.f64 N N N))
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (*.f64 N N)))
(+.f64 1 (fma.f64 N N N))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (*.f64 N N)))
(+.f64 1 (fma.f64 N N N))

localize6.0ms (0.1%)

Compiler: Compiled 5 to 5 computations (0% saved)

localize26.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(atan2.f64 1 (+.f64 N 1))

Compiler

Compiled 11 to 8 computations (27.3% saved)

series2.0ms (0%)

Counts

1 → 4

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	N	@	0	(atan2.f64 1 (+.f64 N 1))
0.0ms	N	@	inf	(atan2.f64 1 (+.f64 N 1))
0.0ms	N	@	-inf	(atan2.f64 1 (+.f64 N 1))

rewrite60.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

486×	`pow1_binary64`
473×	`add-sqr-sqrt_binary64`
465×	`*-un-lft-identity_binary64`
452×	`log1p-expm1-u_binary64`
452×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	102	7
2	1249	7

Stop Event

1×	node limit

Counts

1 → 16

Calls

Call 1

Inputs
(atan2.f64 1 (+.f64 N 1))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (atan2.f64 1 (+.f64 1 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (atan2.f64 1 (+.f64 1 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan2.f64 1 (+.f64 1 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 N))) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 N))) 2) (cbrt.f64 (atan2.f64 1 (+.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 N))) (sqrt.f64 (atan2.f64 1 (+.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan2.f64 1 (+.f64 1 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 1 (+.f64 1 N)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 N))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 N))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan2.f64 1 (+.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 N)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan2.f64 1 (+.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan2.f64 1 (+.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan2.f64 1 (+.f64 1 N))))))))

simplify33.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

13×	`fma-def_binary64`
11×	`fma-neg_binary64`
8×	`cancel-sign-sub-inv_binary64`
6×	`associate--r+_binary64`
6×	`sub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	36
1	16	28
2	24	28
3	47	28
4	66	28
5	96	28
6	111	28
7	115	28

Stop Event

1×

saturated

Counts

20 → 18

Calls

Call 1

Inputs
(atan2.f64 1 (-.f64 1 (*.f64 -1 N)))
(atan2.f64 1 (-.f64 1 (*.f64 -1 N)))
(atan2.f64 1 (-.f64 1 (*.f64 -1 N)))
(atan2.f64 1 (-.f64 1 (*.f64 -1 N)))

Outputs
(atan2.f64 1 (-.f64 1 (*.f64 -1 N)))
(atan2.f64 1 (-.f64 1 (neg.f64 N)))
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 (-.f64 1 (*.f64 -1 N)))
(atan2.f64 1 (-.f64 1 (neg.f64 N)))
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 (-.f64 1 (*.f64 -1 N)))
(atan2.f64 1 (-.f64 1 (neg.f64 N)))
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 (-.f64 1 (*.f64 -1 N)))
(atan2.f64 1 (-.f64 1 (neg.f64 N)))
(atan2.f64 1 (+.f64 1 N))

localize155.0ms (1.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 N N 1) N)
✓	0.0b	(*.f64 (+.f64 1 (pow.f64 N 3)) N)
✓	0.5b	(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N))))
✓	19.7b	(/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N))

Compiler

Compiled 77 to 52 computations (32.5% saved)

series15.0ms (0.2%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
4.0ms	N	@	0	(-.f64 (fma.f64 N N 1) N)
2.0ms	N	@	-inf	(/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N))
1.0ms	N	@	0	(/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N))
1.0ms	N	@	inf	(/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N))
1.0ms	N	@	-inf	(*.f64 (+.f64 1 (pow.f64 N 3)) N)

rewrite130.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

661×	`fma-def_binary64`
652×	`log-prod_binary64`
350×	`pow2_binary64`
264×	`fma-neg_binary64`
240×	`pow1/3_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	64
1	275	64
2	3904	58

Stop Event

1×	node limit

Counts

4 → 224

Calls

Call 1

Inputs
(/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N))))
(*.f64 (+.f64 1 (pow.f64 N 3)) N)
(-.f64 (fma.f64 N N 1) N)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (fma.f64 (/.f64 (+.f64 1 (pow.f64 N 3)) (fma.f64 N N (-.f64 1 N))) N 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 N (.f64 (+.f64 1 (pow.f64 N 3)) (/.f64 1 (fma.f64 N N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 1 (pow.f64 N 3)) (/.f64 1 (/.f64 (fma.f64 N N (-.f64 1 N)) N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 1 (pow.f64 N 3)) (.f64 N (/.f64 1 (fma.f64 N N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 N (pow.f64 N 3) N) (/.f64 1 (fma.f64 N N (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N)))) (pow.f64 (cbrt.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N)))) 2) (cbrt.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 N (pow.f64 N 3) N)) 2) (.f64 (cbrt.f64 (fma.f64 N (pow.f64 N 3) N)) (/.f64 1 (fma.f64 N N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N)))) (sqrt.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 N (pow.f64 N 3) N)) (.f64 (sqrt.f64 (fma.f64 N (pow.f64 N 3) N)) (/.f64 1 (fma.f64 N N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (fma.f64 N (pow.f64 N 3) N)) (/.f64 1 (neg.f64 (fma.f64 N N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (fma.f64 N N (-.f64 1 N))) (fma.f64 N (pow.f64 N 3) N))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 N 1) (/.f64 (+.f64 1 (pow.f64 N 3)) (fma.f64 N N (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (+.f64 1 (pow.f64 N 3)) (fma.f64 N N (-.f64 1 N))) N)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (+.f64 1 (pow.f64 N 3)) 1) (/.f64 N (fma.f64 N N (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 N (pow.f64 N 3) N)) 2) 1) (/.f64 (cbrt.f64 (fma.f64 N (pow.f64 N 3) N)) (fma.f64 N N (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (fma.f64 N (pow.f64 N 3) N)) 1) (/.f64 (sqrt.f64 (fma.f64 N (pow.f64 N 3) N)) (fma.f64 N N (-.f64 1 N))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (pow.f64 (cbrt.f64 (fma.f64 N N (-.f64 1 N))) 2)) (/.f64 (fma.f64 N (pow.f64 N 3) N) (cbrt.f64 (fma.f64 N N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 N (pow.f64 (cbrt.f64 (fma.f64 N N (-.f64 1 N))) 2)) (/.f64 (+.f64 1 (pow.f64 N 3)) (cbrt.f64 (fma.f64 N N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (+.f64 1 (pow.f64 N 3)) (pow.f64 (cbrt.f64 (fma.f64 N N (-.f64 1 N))) 2)) (/.f64 N (cbrt.f64 (fma.f64 N N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 N (pow.f64 N 3) N)) 2) (pow.f64 (cbrt.f64 (fma.f64 N N (-.f64 1 N))) 2)) (cbrt.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (fma.f64 N (pow.f64 N 3) N)) (pow.f64 (cbrt.f64 (fma.f64 N N (-.f64 1 N))) 2)) (/.f64 (sqrt.f64 (fma.f64 N (pow.f64 N 3) N)) (cbrt.f64 (fma.f64 N N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (sqrt.f64 (fma.f64 N N (-.f64 1 N)))) (/.f64 (fma.f64 N (pow.f64 N 3) N) (sqrt.f64 (fma.f64 N N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 N (sqrt.f64 (fma.f64 N N (-.f64 1 N)))) (/.f64 (+.f64 1 (pow.f64 N 3)) (sqrt.f64 (fma.f64 N N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (+.f64 1 (pow.f64 N 3)) (sqrt.f64 (fma.f64 N N (-.f64 1 N)))) (/.f64 N (sqrt.f64 (fma.f64 N N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 N (pow.f64 N 3) N)) 2) (sqrt.f64 (fma.f64 N N (-.f64 1 N)))) (/.f64 (cbrt.f64 (fma.f64 N (pow.f64 N 3) N)) (sqrt.f64 (fma.f64 N N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (-.f64 (pow.f64 (fma.f64 N N 1) 3) (pow.f64 N 3))) (fma.f64 N (fma.f64 N N (+.f64 1 N)) (pow.f64 (fma.f64 N N 1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (-.f64 (pow.f64 (fma.f64 N N 1) 2) (.f64 N N))) (fma.f64 N N (+.f64 1 N)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 N N (-.f64 1 N)) (fma.f64 N (pow.f64 N 3) N)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (fma.f64 N N (-.f64 1 N)) (fma.f64 N (pow.f64 N 3) N)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (neg.f64 (fma.f64 N N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (fma.f64 N (pow.f64 N 3) N) (fma.f64 N N (-.f64 1 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (.f64 (log1p.f64 (/.f64 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#<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 N N 1) (neg.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 N N 1) (.f64 (neg.f64 N) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 N N (-.f64 1 N)) (fma.f64 (neg.f64 N) 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 N N (-.f64 1 N)) (fma.f64 (neg.f64 (cbrt.f64 N)) (pow.f64 (cbrt.f64 N) 2) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 N N (-.f64 1 N)) (+.f64 (neg.f64 N) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 N N) (-.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 N N) (+.f64 1 (neg.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (neg.f64 N) (fma.f64 N N 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 N N (-.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 N N (+.f64 1 (neg.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 N N 1) 1 (neg.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 N N 1) 1 (.f64 (neg.f64 N) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 N N (-.f64 1 N)) 1 (fma.f64 (neg.f64 N) 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 N N (-.f64 1 N)) 1 (fma.f64 (neg.f64 (cbrt.f64 N)) (pow.f64 (cbrt.f64 N) 2) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 N N (-.f64 1 N)) 1 (+.f64 (neg.f64 N) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 N N 1)) (cbrt.f64 (pow.f64 (fma.f64 N N 1) 2)) (neg.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 N N 1)) (cbrt.f64 (pow.f64 (fma.f64 N N 1) 2)) (.f64 (neg.f64 N) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (fma.f64 N N 1) 2)) (cbrt.f64 (fma.f64 N N 1)) (neg.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (fma.f64 N N 1) 2)) (cbrt.f64 (fma.f64 N N 1)) (.f64 (neg.f64 N) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 N N (-.f64 1 N))) (pow.f64 (cbrt.f64 (fma.f64 N N (-.f64 1 N))) 2) (fma.f64 (neg.f64 N) 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 N N (-.f64 1 N))) (pow.f64 (cbrt.f64 (fma.f64 N N (-.f64 1 N))) 2) (fma.f64 (neg.f64 (cbrt.f64 N)) (pow.f64 (cbrt.f64 N) 2) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 N N (-.f64 1 N))) (pow.f64 (cbrt.f64 (fma.f64 N N (-.f64 1 N))) 2) (+.f64 (neg.f64 N) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 N N (-.f64 1 N))) 2) (cbrt.f64 (fma.f64 N N (-.f64 1 N))) (fma.f64 (neg.f64 N) 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 N N (-.f64 1 N))) 2) (cbrt.f64 (fma.f64 N N (-.f64 1 N))) (fma.f64 (neg.f64 (cbrt.f64 N)) (pow.f64 (cbrt.f64 N) 2) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 N N (-.f64 1 N))) 2) (cbrt.f64 (fma.f64 N N (-.f64 1 N))) (+.f64 (neg.f64 N) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 N) 2) (neg.f64 (cbrt.f64 N)) (fma.f64 N N 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 N) 2) (.f64 (cbrt.f64 N) N) (-.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 N) 2) (.f64 (cbrt.f64 N) N) (+.f64 1 (neg.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 N) (hypot.f64 1 N) (neg.f64 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 N) (hypot.f64 1 N) (.f64 (neg.f64 N) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 N N (-.f64 1 N))) (sqrt.f64 (fma.f64 N N (-.f64 1 N))) (fma.f64 (neg.f64 N) 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 N N (-.f64 1 N))) (sqrt.f64 (fma.f64 N N (-.f64 1 N))) (fma.f64 (neg.f64 (cbrt.f64 N)) (pow.f64 (cbrt.f64 N) 2) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 N N (-.f64 1 N))) (sqrt.f64 (fma.f64 N N (-.f64 1 N))) (+.f64 (neg.f64 N) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 N) (pow.f64 N 3/2) (-.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 N) (pow.f64 N 3/2) (+.f64 1 (neg.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 N) (neg.f64 (sqrt.f64 N)) (fma.f64 N N 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 (fma.f64 N N 1) 3) (pow.f64 N 3)) (/.f64 1 (fma.f64 N (fma.f64 N N (+.f64 1 N)) (pow.f64 (fma.f64 N N 1) 2))) (fma.f64 (neg.f64 N) 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 (fma.f64 N N 1) 3) (pow.f64 N 3)) (/.f64 1 (fma.f64 N (fma.f64 N N (+.f64 1 N)) (pow.f64 (fma.f64 N N 1) 2))) (fma.f64 (neg.f64 (cbrt.f64 N)) (pow.f64 (cbrt.f64 N) 2) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 (fma.f64 N N 1) 3) (pow.f64 N 3)) (/.f64 1 (fma.f64 N (fma.f64 N N (+.f64 1 N)) (pow.f64 (fma.f64 N N 1) 2))) (+.f64 (neg.f64 N) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 (fma.f64 N N 1) 2) (.f64 N N)) (/.f64 1 (fma.f64 N N (+.f64 1 N))) (fma.f64 (neg.f64 N) 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 (fma.f64 N N 1) 2) (.f64 N N)) (/.f64 1 (fma.f64 N N (+.f64 1 N))) (fma.f64 (neg.f64 (cbrt.f64 N)) (pow.f64 (cbrt.f64 N) 2) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 (fma.f64 N N 1) 2) (.f64 N N)) (/.f64 1 (fma.f64 N N (+.f64 1 N))) (+.f64 (neg.f64 N) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 N 3/2) (sqrt.f64 N) (-.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 N 3/2) (sqrt.f64 N) (+.f64 1 (neg.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (pow.f64 (cbrt.f64 N) 2) 2) (pow.f64 (cbrt.f64 N) 2) (-.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (pow.f64 (cbrt.f64 N) 2) 2) (pow.f64 (cbrt.f64 N) 2) (+.f64 1 (neg.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (neg.f64 N)) 2) (cbrt.f64 (neg.f64 N)) (fma.f64 N N 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (neg.f64 N)) (sqrt.f64 (neg.f64 N)) (fma.f64 N N 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (sqrt.f64 N)) (sqrt.f64 N) (fma.f64 N N 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 N (fma.f64 N N 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (hypot.f64 1 N) (sqrt.f64 N)) (-.f64 (hypot.f64 1 N) (sqrt.f64 N)) (fma.f64 (neg.f64 N) 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (hypot.f64 1 N) (sqrt.f64 N)) (-.f64 (hypot.f64 1 N) (sqrt.f64 N)) (fma.f64 (neg.f64 (cbrt.f64 N)) (pow.f64 (cbrt.f64 N) 2) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (hypot.f64 1 N) (sqrt.f64 N)) (-.f64 (hypot.f64 1 N) (sqrt.f64 N)) (+.f64 (neg.f64 N) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (pow.f64 (cbrt.f64 N) 2)) (cbrt.f64 N) (fma.f64 N N 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 N (pow.f64 (cbrt.f64 N) 2)) (cbrt.f64 N) (-.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 N (pow.f64 (cbrt.f64 N) 2)) (cbrt.f64 N) (+.f64 1 (neg.f64 N)))))))

simplify61.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

451×	`associate-/l*_binary64`
396×	`fma-neg_binary64`
382×	`fma-def_binary64`
350×	`div-sub_binary64`
301×	`sub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	32	561
1	78	477
2	143	477
3	360	477
4	1393	477
5	4958	477

Stop Event

1×	node limit

Counts

272 → 241

Calls

Call 1

Inputs
N
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(+.f64 N (pow.f64 N 2))
(atan2.f64 1 (+.f64 (/.f64 (*.f64 N (+.f64 1 (pow.f64 N 3))) (-.f64 (fma.f64 N N 1) N)) 1))
(atan2.f64 1 (+.f64 (/.f64 (*.f64 N (+.f64 1 (pow.f64 N 3))) (-.f64 (fma.f64 N N 1) N)) 1))
(atan2.f64 1 (+.f64 (/.f64 (*.f64 N (+.f64 1 (pow.f64 N 3))) (-.f64 (fma.f64 N N 1) N)) 1))
(atan2.f64 1 (+.f64 (/.f64 (*.f64 N (+.f64 1 (pow.f64 N 3))) (-.f64 (fma.f64 N N 1) N)) 1))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (-.f64 (fma.f64 N N 1) N)) (+.f64 1 (/.f64 N (-.f64 (fma.f64 N N 1) N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (-.f64 (fma.f64 N N 1) N)) (+.f64 1 (/.f64 N (-.f64 (fma.f64 N N 1) N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (-.f64 (fma.f64 N N 1) N)) (+.f64 1 (/.f64 N (-.f64 (fma.f64 N N 1) N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (-.f64 (fma.f64 N N 1) N)) (+.f64 1 (/.f64 N (-.f64 (fma.f64 N N 1) N)))))
(atan2.f64 1 (+.f64 1 (/.f64 (.f64 N (+.f64 1 (pow.f64 N 3))) (+.f64 (fma.f64 N N 1) (.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (/.f64 (.f64 N (+.f64 1 (pow.f64 N 3))) (+.f64 (fma.f64 N N 1) (.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (/.f64 (.f64 N (+.f64 1 (pow.f64 N 3))) (+.f64 (fma.f64 N N 1) (.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (/.f64 (.f64 N (+.f64 1 (pow.f64 N 3))) (+.f64 (fma.f64 N N 1) (.f64 -1 N)))))
N
(+.f64 N (pow.f64 N 4))
(+.f64 N (pow.f64 N 4))
(+.f64 N (pow.f64 N 4))
(pow.f64 N 4)
(+.f64 N (pow.f64 N 4))
(+.f64 N (pow.f64 N 4))
(+.f64 N (pow.f64 N 4))
(pow.f64 N 4)
(+.f64 N (pow.f64 N 4))
(+.f64 N (pow.f64 N 4))
(+.f64 N (pow.f64 N 4))
1
(+.f64 1 (*.f64 -1 N))
(+.f64 1 (+.f64 (pow.f64 N 2) (*.f64 -1 N)))
(+.f64 1 (+.f64 (pow.f64 N 2) (*.f64 -1 N)))
(pow.f64 N 2)
(+.f64 (pow.f64 N 2) (*.f64 -1 N))
(+.f64 1 (+.f64 (pow.f64 N 2) (*.f64 -1 N)))
(+.f64 1 (+.f64 (pow.f64 N 2) (*.f64 -1 N)))
(pow.f64 N 2)
(+.f64 (pow.f64 N 2) (*.f64 -1 N))
(+.f64 1 (+.f64 (pow.f64 N 2) (*.f64 -1 N)))
(+.f64 1 (+.f64 (pow.f64 N 2) (*.f64 -1 N)))

Outputs
N
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(+.f64 N (pow.f64 N 2))
(+.f64 N (*.f64 N N))
(fma.f64 N N N)
(atan2.f64 1 (+.f64 (/.f64 (*.f64 N (+.f64 1 (pow.f64 N 3))) (-.f64 (fma.f64 N N 1) N)) 1))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (-.f64 (fma.f64 N N 1) N) (+.f64 1 (pow.f64 N 3))))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (-.f64 (fma.f64 N N 1) N))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N (+.f64 N -1) 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N N (-.f64 1 N)))))
(atan2.f64 1 (+.f64 (/.f64 (*.f64 N (+.f64 1 (pow.f64 N 3))) (-.f64 (fma.f64 N N 1) N)) 1))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (-.f64 (fma.f64 N N 1) N) (+.f64 1 (pow.f64 N 3))))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (-.f64 (fma.f64 N N 1) N))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N (+.f64 N -1) 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N N (-.f64 1 N)))))
(atan2.f64 1 (+.f64 (/.f64 (*.f64 N (+.f64 1 (pow.f64 N 3))) (-.f64 (fma.f64 N N 1) N)) 1))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (-.f64 (fma.f64 N N 1) N) (+.f64 1 (pow.f64 N 3))))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (-.f64 (fma.f64 N N 1) N))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N (+.f64 N -1) 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N N (-.f64 1 N)))))
(atan2.f64 1 (+.f64 (/.f64 (*.f64 N (+.f64 1 (pow.f64 N 3))) (-.f64 (fma.f64 N N 1) N)) 1))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (-.f64 (fma.f64 N N 1) N) (+.f64 1 (pow.f64 N 3))))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (-.f64 (fma.f64 N N 1) N))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N (+.f64 N -1) 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N N (-.f64 1 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (-.f64 (fma.f64 N N 1) N)) (+.f64 1 (/.f64 N (-.f64 (fma.f64 N N 1) N)))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (-.f64 (fma.f64 N N 1) N) (+.f64 1 (pow.f64 N 3))))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (-.f64 (fma.f64 N N 1) N))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N (+.f64 N -1) 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N N (-.f64 1 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (-.f64 (fma.f64 N N 1) N)) (+.f64 1 (/.f64 N (-.f64 (fma.f64 N N 1) N)))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (-.f64 (fma.f64 N N 1) N) (+.f64 1 (pow.f64 N 3))))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (-.f64 (fma.f64 N N 1) N))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N (+.f64 N -1) 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N N (-.f64 1 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (-.f64 (fma.f64 N N 1) N)) (+.f64 1 (/.f64 N (-.f64 (fma.f64 N N 1) N)))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (-.f64 (fma.f64 N N 1) N) (+.f64 1 (pow.f64 N 3))))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (-.f64 (fma.f64 N N 1) N))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N (+.f64 N -1) 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N N (-.f64 1 N)))))
(atan2.f64 1 (+.f64 (/.f64 (pow.f64 N 4) (-.f64 (fma.f64 N N 1) N)) (+.f64 1 (/.f64 N (-.f64 (fma.f64 N N 1) N)))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (-.f64 (fma.f64 N N 1) N) (+.f64 1 (pow.f64 N 3))))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (-.f64 (fma.f64 N N 1) N))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N (+.f64 N -1) 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N N (-.f64 1 N)))))
(atan2.f64 1 (+.f64 1 (/.f64 (.f64 N (+.f64 1 (pow.f64 N 3))) (+.f64 (fma.f64 N N 1) (.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (-.f64 (fma.f64 N N 1) N) (+.f64 1 (pow.f64 N 3))))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (-.f64 (fma.f64 N N 1) N))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N (+.f64 N -1) 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N N (-.f64 1 N)))))
(atan2.f64 1 (+.f64 1 (/.f64 (.f64 N (+.f64 1 (pow.f64 N 3))) (+.f64 (fma.f64 N N 1) (.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (-.f64 (fma.f64 N N 1) N) (+.f64 1 (pow.f64 N 3))))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (-.f64 (fma.f64 N N 1) N))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N (+.f64 N -1) 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N N (-.f64 1 N)))))
(atan2.f64 1 (+.f64 1 (/.f64 (.f64 N (+.f64 1 (pow.f64 N 3))) (+.f64 (fma.f64 N N 1) (.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (-.f64 (fma.f64 N N 1) N) (+.f64 1 (pow.f64 N 3))))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (-.f64 (fma.f64 N N 1) N))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N (+.f64 N -1) 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N N (-.f64 1 N)))))
(atan2.f64 1 (+.f64 1 (/.f64 (.f64 N (+.f64 1 (pow.f64 N 3))) (+.f64 (fma.f64 N N 1) (.f64 -1 N)))))
(atan2.f64 1 (+.f64 1 (/.f64 N (/.f64 (-.f64 (fma.f64 N N 1) N) (+.f64 1 (pow.f64 N 3))))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (-.f64 (fma.f64 N N 1) N))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N (+.f64 N -1) 1))))
(atan2.f64 1 (+.f64 1 (/.f64 (+.f64 N (pow.f64 N 4)) (fma.f64 N N (-.f64 1 N)))))
N
(+.f64 N (pow.f64 N 4))
(+.f64 N (pow.f64 N 4))
(+.f64 N (pow.f64 N 4))
(pow.f64 N 4)
(+.f64 N (pow.f64 N 4))
(+.f64 N (pow.f64 N 4))
(+.f64 N (pow.f64 N 4))
(pow.f64 N 4)
(+.f64 N (pow.f64 N 4))
(+.f64 N (pow.f64 N 4))
(+.f64 N (pow.f64 N 4))
1
(+.f64 1 (*.f64 -1 N))
(+.f64 1 (neg.f64 N))
(-.f64 1 N)
(+.f64 1 (+.f64 (pow.f64 N 2) (*.f64 -1 N)))
(+.f64 1 (+.f64 (*.f64 N N) (neg.f64 N)))
(-.f64 (fma.f64 N N 1) N)
(fma.f64 N (+.f64 N -1) 1)
(fma.f64 N N (-.f64 1 N))
(+.f64 1 (+.f64 (pow.f64 N 2) (*.f64 -1 N)))
(+.f64 1 (+.f64 (*.f64 N N) (neg.f64 N)))
(-.f64 (fma.f64 N N 1) N)
(fma.f64 N (+.f64 N -1) 1)
(fma.f64 N N (-.f64 1 N))
(pow.f64 N 2)
(*.f64 N N)
(+.f64 (pow.f64 N 2) (*.f64 -1 N))
(+.f64 (*.f64 N N) (neg.f64 N))
(*.f64 N (+.f64 N -1))
(-.f64 (*.f64 N N) N)
(fma.f64 N N (neg.f64 N))
(+.f64 1 (+.f64 (pow.f64 N 2) (*.f64 -1 N)))
(+.f64 1 (+.f64 (*.f64 N N) (neg.f64 N)))
(-.f64 (fma.f64 N N 1) N)
(fma.f64 N (+.f64 N -1) 1)
(fma.f64 N N (-.f64 1 N))
(+.f64 1 (+.f64 (pow.f64 N 2) (*.f64 -1 N)))
(+.f64 1 (+.f64 (*.f64 N N) (neg.f64 N)))
(-.f64 (fma.f64 N N 1) N)
(fma.f64 N (+.f64 N -1) 1)
(fma.f64 N N (-.f64 1 N))
(pow.f64 N 2)
(*.f64 N N)
(+.f64 (pow.f64 N 2) (*.f64 -1 N))
(+.f64 (*.f64 N N) (neg.f64 N))
(*.f64 N (+.f64 N -1))
(-.f64 (*.f64 N N) N)
(fma.f64 N N (neg.f64 N))
(+.f64 1 (+.f64 (pow.f64 N 2) (*.f64 -1 N)))
(+.f64 1 (+.f64 (*.f64 N N) (neg.f64 N)))
(-.f64 (fma.f64 N N 1) N)
(fma.f64 N (+.f64 N -1) 1)
(fma.f64 N N (-.f64 1 N))
(+.f64 1 (+.f64 (pow.f64 N 2) (*.f64 -1 N)))
(+.f64 1 (+.f64 (*.f64 N N) (neg.f64 N)))
(-.f64 (fma.f64 N N 1) N)
(fma.f64 N (+.f64 N -1) 1)
(fma.f64 N N (-.f64 1 N))

localize45.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (cbrt.f64 (pow.f64 (fma.f64 N N N) 3)))
	0.1b	(pow.f64 (fma.f64 N N N) 3)
✓	0.5b	(atan2.f64 1 (+.f64 1 (cbrt.f64 (pow.f64 (fma.f64 N N N) 3))))
	29.3b	(cbrt.f64 (pow.f64 (fma.f64 N N N) 3))

Compiler

Compiled 41 to 21 computations (48.8% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	N	@	-inf	(+.f64 1 (cbrt.f64 (pow.f64 (fma.f64 N N N) 3)))
0.0ms	N	@	0	(atan2.f64 1 (+.f64 1 (cbrt.f64 (pow.f64 (fma.f64 N N N) 3))))
0.0ms	N	@	inf	(+.f64 1 (cbrt.f64 (pow.f64 (fma.f64 N N N) 3)))
0.0ms	N	@	-inf	(atan2.f64 1 (+.f64 1 (cbrt.f64 (pow.f64 (fma.f64 N N N) 3))))
0.0ms	N	@	inf	(atan2.f64 1 (+.f64 1 (cbrt.f64 (pow.f64 (fma.f64 N N N) 3))))

rewrite196.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

749×	`pow1_binary64`
703×	`add-log-exp_binary64`
701×	`log1p-expm1-u_binary64`
701×	`expm1-log1p-u_binary64`
688×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	188	19
2	1942	19

Stop Event

1×	node limit

Counts

2 → 46

Calls

Call 1

Inputs
(atan2.f64 1 (+.f64 1 (cbrt.f64 (pow.f64 (fma.f64 N N N) 3))))
(+.f64 1 (cbrt.f64 (pow.f64 (fma.f64 N N N) 3)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 1 (fma.f64 N N N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 1 (fma.f64 N N N))) (/.f64 (pow.f64 (fma.f64 N N N) 2) (-.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (fma.f64 N N N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) (pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) 2) (cbrt.f64 (+.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 1 (hypot.f64 N (sqrt.f64 N))) (hypot.f64 1 (hypot.f64 N (sqrt.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 (fma.f64 N N N) 3)) (/.f64 1 (+.f64 1 (-.f64 (pow.f64 (fma.f64 N N N) 2) (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 (fma.f64 N N N) 2)) (/.f64 1 (-.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (-.f64 (pow.f64 (fma.f64 N N N) 2) (fma.f64 N N N))) (+.f64 1 (pow.f64 (fma.f64 N N N) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1 (fma.f64 N N N)) (-.f64 1 (pow.f64 (fma.f64 N N N) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (fma.f64 N N N) 3)) (+.f64 1 (-.f64 (pow.f64 (fma.f64 N N N) 2) (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (fma.f64 N N N) 3)) (+.f64 (pow.f64 (fma.f64 N N N) 2) (-.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (fma.f64 N N N) 2)) (-.f64 1 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 (fma.f64 N N N) 3))) (neg.f64 (+.f64 1 (-.f64 (pow.f64 (fma.f64 N N N) 2) (fma.f64 N N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (fma.f64 N N N) 2))) (neg.f64 (-.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 N N N) 2) 1) (-.f64 (fma.f64 N N N) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (fma.f64 N N N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (fma.f64 N N N)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 1 (hypot.f64 N (sqrt.f64 N))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 (fma.f64 N N N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (fma.f64 N N N)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (fma.f64 N N N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (fma.f64 N N N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 N N N) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 N N N)) 2) (cbrt.f64 (fma.f64 N N N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 N (sqrt.f64 N)) (hypot.f64 N (sqrt.f64 N)) 1)))))

simplify179.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

1082×	`sqr-pow_binary64`
902×	`fma-def_binary64`
572×	`cube-prod_binary64`
555×	`fabs-mul_binary64`
523×	`pow-sqr_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	215
1	25	203
2	35	203
3	54	203
4	112	203
5	308	203
6	993	203
7	2246	203
8	2714	203
9	2930	203
10	3168	203
11	3531	203
12	3968	203
13	4474	203
14	5060	203
15	5785	203
16	6626	203
17	7018	203
18	7306	203
19	7585	203
20	7657	203
21	7691	203

Stop Event

1×	node limit

Counts

70 → 57

Calls

Call 1

Inputs
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
1
(+.f64 N 1)
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(pow.f64 N 2)
(+.f64 N (pow.f64 N 2))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 N (+.f64 1 (pow.f64 N 2)))

Outputs
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
(atan2.f64 1 (+.f64 (fma.f64 N N N) 1))
(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
1
(+.f64 N 1)
(+.f64 1 N)
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 (+.f64 1 N) (*.f64 N N))
(+.f64 1 (fma.f64 N N N))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 (+.f64 1 N) (*.f64 N N))
(+.f64 1 (fma.f64 N N N))
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(fma.f64 N N N)
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 (+.f64 1 N) (*.f64 N N))
(+.f64 1 (fma.f64 N N N))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 (+.f64 1 N) (*.f64 N N))
(+.f64 1 (fma.f64 N N N))
(pow.f64 N 2)
(*.f64 N N)
(+.f64 N (pow.f64 N 2))
(fma.f64 N N N)
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 (+.f64 1 N) (*.f64 N N))
(+.f64 1 (fma.f64 N N N))
(+.f64 N (+.f64 1 (pow.f64 N 2)))
(+.f64 (+.f64 1 N) (*.f64 N N))
(+.f64 1 (fma.f64 N N N))

eval311.0ms (3.8%)

Compiler: Compiled 8863 to 5999 computations (32.3% saved)

prune75.0ms (0.9%)

Pruning

14 alts after pruning (9 fresh and 5 done)

	Pruned	Kept	Total
New	459	6	465
Fresh	2	3	5
Picked	0	1	1
Done	2	4	6
Total	463	14	477

Error

0.5b

Counts

477 → 14

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.5b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
	1.1b	(pow.f64 (sqrt.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N)))) 2)
✓	29.8b	(atan2.f64 1 (+.f64 N 1))
	1.9b	(atan2.f64 1 (+.f64 1 (*.f64 N N)))
	1.9b	(pow.f64 (cbrt.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N)))) 3)
	22.7b	(atan2.f64 1 (+.f64 1 (/.f64 (.f64 (+.f64 1 (pow.f64 N 3)) N) (+.f64 (.f64 N N) (-.f64 1 N)))))
	0.5b	(log1p.f64 (expm1.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))))
	27.9b	(atan2.f64 1 (*.f64 N N))
✓	15.3b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
✓	30.4b	(atan2.f64 1 1)
	19.4b	(atan2.f64 1 (+.f64 1 (.f64 (+.f64 1 (pow.f64 N 3)) (.f64 N (/.f64 1 (fma.f64 N N (-.f64 1 N)))))))
	0.5b	(atan2.f64 1 (+.f64 (+.f64 1 N) (*.f64 N N)))
✓	10.8b	(atan2.f64 1 (+.f64 1 (cbrt.f64 (pow.f64 (fma.f64 N N N) 3))))
	22.7b	(atan2.f64 1 (/.f64 (-.f64 (.f64 (+.f64 1 N) (+.f64 1 N)) (pow.f64 N 4)) (-.f64 (+.f64 1 N) (.f64 N N))))

Compiler

Compiled 162 to 122 computations (24.7% saved)

regimes30.0ms (0.4%)

Counts

26 → 1

Calls

Call 1

Inputs
(atan2.f64 1 1)
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (*.f64 N N))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(atan2.f64 1 (+.f64 (+.f64 1 N) (*.f64 N N)))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
(atan2.f64 1 (fma.f64 N N (+.f64 N 1)))
(atan2.f64 1 (+.f64 N (+.f64 1 (pow.f64 N 2))))
(atan2.f64 1 (+.f64 1 (/.f64 (.f64 (+.f64 1 (pow.f64 N 3)) N) (+.f64 (.f64 N N) (-.f64 1 N)))))
(atan2.f64 1 (/.f64 (-.f64 (.f64 (+.f64 1 N) (+.f64 1 N)) (pow.f64 N 4)) (-.f64 (+.f64 1 N) (.f64 N N))))
(atan2.f64 1 (+.f64 1 (/.f64 (*.f64 (+.f64 1 (pow.f64 N 3)) N) (-.f64 (fma.f64 N N 1) N))))
(atan2.f64 1 (+.f64 1 (.f64 (+.f64 1 (pow.f64 N 3)) (.f64 N (/.f64 1 (fma.f64 N N (-.f64 1 N)))))))
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (/.f64 (-.f64 (pow.f64 N 4) (*.f64 N N)) (fma.f64 N N (neg.f64 N)))))
(log1p.f64 (expm1.f64 (atan2.f64 1 (+.f64 (fma.f64 N N N) 1))))
(pow.f64 (sqrt.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N)))) 2)
(pow.f64 (cbrt.f64 (atan2.f64 1 (fma.f64 N N (+.f64 1 N)))) 3)
(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 2)
(pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 3)
(atan2.f64 1 (+.f64 1 (cbrt.f64 (pow.f64 (fma.f64 N N N) 3))))
(log1p.f64 (expm1.f64 (atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (fma.f64 N N N)))))
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (cbrt.f64 (pow.f64 (fma.f64 N N N) 3))))
(fma.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))
(fma.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) (cbrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))
(+.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (fma.f64 (neg.f64 (sqrt.f64 (atan.f64 N))) (sqrt.f64 (atan.f64 N)) (atan.f64 N)))

Outputs
(atan2.f64 1 (fma.f64 N N (+.f64 N 1)))

Calls

3 calls:

14.0ms	N
4.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
3.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Results

Error	Segments	Branch
0.5b	1	`N`
0.5b	1	`(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))`
0.5b	1	`(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))`

Compiler

Compiled 335 to 225 computations (32.8% saved)

regimes24.0ms (0.3%)

Counts

8 → 1

Calls

Call 1

Inputs
(atan2.f64 1 1)
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (*.f64 N N))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(atan2.f64 1 (+.f64 (+.f64 1 N) (*.f64 N N)))
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
(atan2.f64 (+.f64 N (-.f64 1 N)) (+.f64 1 (*.f64 N (+.f64 N 1))))
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Outputs
(atan2.f64 1 (+.f64 (+.f64 1 N) (*.f64 N N)))

Calls

3 calls:

11.0ms	N
5.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
4.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Results

Error	Segments	Branch
0.5b	1	`N`
0.5b	1	`(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))`
0.5b	1	`(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))`

Compiler

Compiled 77 to 54 computations (29.9% saved)

regimes9.0ms (0.1%)

Counts

4 → 1

Calls

Call 1

Inputs
(atan2.f64 1 1)
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (*.f64 N N))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))

Outputs
(atan2.f64 1 (+.f64 1 (*.f64 N N)))

Calls

1 calls:

7.0ms

Results

Error	Segments	Branch
1.9b	1	`N`

Compiler

Compiled 23 to 16 computations (30.4% saved)

regimes23.0ms (0.3%)

Counts

3 → 3

Calls

Call 1

Inputs
(atan2.f64 1 1)
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (*.f64 N N))

Outputs
(atan2.f64 1 (*.f64 N N))
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (*.f64 N N))

Calls

1 calls:

22.0ms

Results

Error	Segments	Branch
1.7b	3	`N`

Compiler

Compiled 16 to 12 computations (25% saved)

bsearch83.0ms (1%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
39.0ms	1.5419197210007654	422.6936260233725
44.0ms	-2825946.7282828824	-0.0013079059934821581

Compiler

Compiled 12 to 9 computations (25% saved)

regimes7.0ms (0.1%)

Accuracy

Total -0.6b remaining (-2.1%)

Threshold costs -0.6b (-2.1%)

Counts

2 → 1

Calls

Call 1

Inputs
(atan2.f64 1 1)
(atan2.f64 1 (+.f64 N 1))

Outputs
(atan2.f64 1 (+.f64 N 1))

Calls

1 calls:

6.0ms

Results

Error	Segments	Branch
29.8b	1	`N`

Compiler

Compiled 11 to 9 computations (18.2% saved)

simplify16.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	78
1	28	78

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(atan2.f64 1 (fma.f64 N N (+.f64 N 1)))
(atan2.f64 1 (+.f64 (+.f64 1 N) (*.f64 N N)))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(if (<=.f64 N -6068674389106589/2147483648) (atan2.f64 1 (.f64 N N)) (if (<=.f64 N 3472094540467133/2251799813685248) (atan2.f64 1 (+.f64 N 1)) (atan2.f64 1 (.f64 N N))))
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 1)

Outputs
(atan2.f64 1 (fma.f64 N N (+.f64 N 1)))
(atan2.f64 1 (fma.f64 N N (+.f64 1 N)))
(atan2.f64 1 (+.f64 (+.f64 1 N) (*.f64 N N)))
(atan2.f64 1 (+.f64 1 (*.f64 N N)))
(if (<=.f64 N -6068674389106589/2147483648) (atan2.f64 1 (.f64 N N)) (if (<=.f64 N 3472094540467133/2251799813685248) (atan2.f64 1 (+.f64 N 1)) (atan2.f64 1 (.f64 N N))))
(if (<=.f64 N -6068674389106589/2147483648) (atan2.f64 1 (.f64 N N)) (if (<=.f64 N 3472094540467133/2251799813685248) (atan2.f64 1 (+.f64 1 N)) (atan2.f64 1 (.f64 N N))))
(atan2.f64 1 (+.f64 N 1))
(atan2.f64 1 (+.f64 1 N))
(atan2.f64 1 1)

Compiler

Compiled 61 to 44 computations (27.9% saved)

soundness0.0ms (0%)

end95.0ms (1.2%)

Compiler: Compiled 56 to 37 computations (33.9% saved)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	122	11
8	168	11
9	204	11
10	230	11
11	232	11
0	1	1

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	122	11
8	168	11
9	204	11
10	230	11
11	232	11

Iter	Nodes	Cost
0	9	52
1	20	44
2	31	44
3	61	44
4	88	44
5	134	44
6	182	44
7	215	44
8	258	44
9	294	44
10	320	44
11	322	44

Iter	Nodes	Cost
0	13	172
1	26	164
2	36	164
3	66	164
4	93	164
5	139	164
6	187	164
7	220	164
8	266	164
9	302	164
10	328	164
11	330	164

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	122	11
8	168	11
9	204	11
10	230	11
11	232	11
0	1	1

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	122	11
8	168	11
9	204	11
10	230	11
11	232	11

Iter	Nodes	Cost
0	9	52
1	20	44
2	31	44
3	61	44
4	88	44
5	134	44
6	182	44
7	215	44
8	258	44
9	294	44
10	320	44
11	322	44

Iter	Nodes	Cost
0	13	172
1	26	164
2	36	164
3	66	164
4	93	164
5	139	164
6	187	164
7	220	164
8	266	164
9	302	164
10	328	164
11	330	164

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	122	11
8	168	11
9	204	11
10	230	11
11	232	11
0	1	1

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	122	11
8	168	11
9	204	11
10	230	11
11	232	11

Iter	Nodes	Cost
0	9	52
1	20	44
2	31	44
3	61	44
4	88	44
5	134	44
6	182	44
7	215	44
8	258	44
9	294	44
10	320	44
11	322	44

Iter	Nodes	Cost
0	13	172
1	26	164
2	36	164
3	66	164
4	93	164
5	139	164
6	187	164
7	220	164
8	266	164
9	302	164
10	328	164
11	330	164