Details

analyze3.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	50%	25%	3
37.5%	12.5%	50%	4
43.7%	6.2%	50%	5
46.9%	3.1%	50%	6
48.4%	1.6%	50%	7
49.2%	0.8%	50%	8
49.6%	0.4%	50%	9
49.8%	0.2%	50%	10
49.9%	0.1%	50%	11
49.9%	0%	50%	12

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample2.5s (38.7%)

Results

1.1s	4914×	body	256	valid
872.0ms	2030×	body	1024	valid
279.0ms	277×	body	2048	valid
244.0ms	1035×	body	512	valid

preprocess22.0ms (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	8
2	17	8
3	24	8
4	33	8
5	50	8
6	87	8
7	123	8
8	170	8
9	206	8
10	232	8
11	234	8
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

Outputs
(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify11.0ms (0.2%)

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: 1 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	8
2	17	8
3	24	8
4	33	8
5	50	8
6	87	8
7	123	8
8	170	8
9	206	8
10	232	8
11	234	8

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

Outputs
(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
(-.f64 (log1p.f64 N) (log.f64 N))

eval1.0ms (0%)

Compiler: Compiled 13 to 8 computations (38.5% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

28.6b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	28.6b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.6b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 11 to 4 computations (63.6% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	N	@	inf	(-.f64 (log1p.f64 N) (log.f64 N))
1.0ms	N	@	-inf	(-.f64 (log1p.f64 N) (log.f64 N))
1.0ms	N	@	0	(-.f64 (log1p.f64 N) (log.f64 N))

rewrite54.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

581×	`pow1_binary64`
541×	`add-log-exp_binary64`
541×	`expm1-log1p-u_binary64`
540×	`log1p-expm1-u_binary64`
529×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	106	8
2	1453	8

Stop Event

1×	node limit

Counts

1 → 35

Calls

Call 1

Inputs
(-.f64 (log1p.f64 N) (log.f64 N))

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

Outputs

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

simplify54.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

746×	`fma-def_binary64`
701×	`associate-l_binary64`
458×	`fma-neg_binary64`
427×	`cancel-sign-sub-inv_binary64`
415×	`times-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	36	192
1	95	188
2	237	185
3	646	181
4	2109	181

Stop Event

1×	node limit

Counts

47 → 50

Calls

Call 1

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

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

eval22.0ms (0.3%)

Compiler: Compiled 630 to 282 computations (55.2% saved)

prune11.0ms (0.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	43	7	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	7	51

Error

0.0b

Counts

51 → 7

Alt Table

Click to see full alt table

Status	Error	Program
▶	31.8b	(/.f64 1 N)
	61.1b	(*.f64 (+.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))) (-.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))))
▶	32.8b	(-.f64 (/.f64 1 N) (/.f64 (/.f64 1/2 N) N))
▶	28.4b	(log.f64 (/.f64 (+.f64 N 1) N))
	30.4b	(-.f64 N (log.f64 N))
▶	31.1b	(neg.f64 (log.f64 N))
▶	32.3b	(+.f64 (/.f64 1 N) (.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2)))

Compiler

Compiled 124 to 82 computations (33.9% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 N 1) N)
✓	2.4b	(log.f64 (/.f64 (+.f64 N 1) N))

Compiler

Compiled 17 to 11 computations (35.3% saved)

series3.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite56.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

680×	`pow1_binary64`
635×	`log1p-expm1-u_binary64`
635×	`expm1-log1p-u_binary64`
634×	`add-log-exp_binary64`
622×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	127	15
2	1707	15

Stop Event

1×	node limit

Counts

2 → 60

Calls

Call 1

Inputs
(log.f64 (/.f64 (+.f64 N 1) N))
(/.f64 (+.f64 N 1) N)

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

Outputs

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

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

simplify39.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

746×	`fma-def_binary64`
701×	`associate-l_binary64`
458×	`fma-neg_binary64`
427×	`cancel-sign-sub-inv_binary64`
415×	`times-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	37	261
1	97	257
2	239	254
3	645	250
4	2107	250

Stop Event

1×	node limit

Counts

84 → 77

Calls

Call 1

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

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

localize3.0ms (0%)

Compiler: Compiled 6 to 4 computations (33.3% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 1 N) (/.f64 (/.f64 1/2 N) N))
✓	0.1b	(/.f64 (/.f64 1/2 N) N)

Compiler

Compiled 24 to 16 computations (33.3% saved)

series3.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite100.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

819×	`prod-diff_binary64`
434×	`log-prod_binary64`
301×	`fma-def_binary64`
285×	`pow-prod-down_binary64`
248×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	186	17
2	2794	17

Stop Event

1×	node limit

Counts

2 → 294

Calls

Call 1

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

Outputs

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simplify50.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

730×	`times-frac_binary64`
554×	`fma-neg_binary64`
534×	`associate-/r*_binary64`
494×	`associate-/l/_binary64`
434×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	216
1	26	216
2	46	216
3	100	216
4	267	216
5	955	216
6	5068	216

Stop Event

1×	node limit

Counts

318 → 300

Calls

Call 1

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

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

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1 N) (.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2)))
✓	0.1b	(.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2))
✓	0.3b	(/.f64 1 (*.f64 N N))
✓	0.3b	(/.f64 1/3 N)

Compiler

Compiled 50 to 32 computations (36% saved)

series30.0ms (0.5%)

Counts

4 → 36

Calls

12 calls:

Time	Variable		Point	Expression
26.0ms	N	@	0	(/.f64 1/3 N)
1.0ms	N	@	0	(.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2))
0.0ms	N	@	inf	(/.f64 1/3 N)
0.0ms	N	@	-inf	(/.f64 1/3 N)
0.0ms	N	@	inf	(.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2))

rewrite179.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

564×	`log-prod_binary64`
422×	`fma-def_binary64`
322×	`pow2_binary64`
278×	`fma-neg_binary64`
221×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	43
1	274	38
2	3773	38

Stop Event

1×	node limit

Counts

4 → 193

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1/3 N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 1/3 N))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1/3 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1/3 N)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1/3 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1/3 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/3 (pow.f64 N -1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/3 N) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 1/3 N))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 N -1) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 1/3 N)) (pow.f64 (cbrt.f64 (/.f64 1/3 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (/.f64 1/3 N)) 2) (cbrt.f64 (/.f64 1/3 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 1/3 N)) (sqrt.f64 (/.f64 1/3 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1/3 (/.f64 1 (neg.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 1/3 (cbrt.f64 (pow.f64 N -2))) (cbrt.f64 (pow.f64 N -1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 1/3 (pow.f64 N -1/2)) (pow.f64 N -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/3 N) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/9 (pow.f64 N -2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 1/3 N)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 1/3 N)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/27 (pow.f64 N -3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 N 3) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (.f64 N 3) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 1/9 (pow.f64 N -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1/3 N)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1/3 N))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 1/27 (pow.f64 N -3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1/3 N)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 1/3 N)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 1/3 N)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1/3 N)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 N -2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 N -2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 N -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 N -2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 N -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 N -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 N -2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 N -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 N -1) (pow.f64 N -1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 N -2)) (pow.f64 (cbrt.f64 (pow.f64 N -2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 N -2)) (/.f64 (pow.f64 N -1) (cbrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 N -2)) (.f64 (cbrt.f64 (pow.f64 N -1)) (pow.f64 N -1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (pow.f64 N -2)) 2) (cbrt.f64 (pow.f64 N -2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 N -1/2) (/.f64 (pow.f64 N -1) (sqrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 N -1/2) (.f64 (pow.f64 N -1/2) (pow.f64 N -1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (/.f64 1 (.f64 N (neg.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 N -1/2) 3) (pow.f64 N -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 (pow.f64 N 4))) (cbrt.f64 (pow.f64 N -2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (pow.f64 N -2)) 1) (/.f64 (cbrt.f64 (pow.f64 N -1)) N))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 N -1/2) 1) (/.f64 (pow.f64 N -1/2) N))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (pow.f64 N -2)) (pow.f64 (cbrt.f64 N) 2)) (cbrt.f64 (pow.f64 N -2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 N -1/2) (pow.f64 (cbrt.f64 N) 2)) (/.f64 (pow.f64 N -1/2) (cbrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (pow.f64 N -2)) (sqrt.f64 N)) (/.f64 (cbrt.f64 (pow.f64 N -1)) (sqrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (pow.f64 N -1) (cbrt.f64 (pow.f64 N -2))) (cbrt.f64 (pow.f64 N -1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 N -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 N N) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 N -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 N -1) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (pow.f64 N 4)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 N -2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 N -2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (neg.f64 N) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 N -3) (pow.f64 N 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (.f64 N (neg.f64 N))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1 (pow.f64 N 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 N -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 N -2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 N -2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 N -3) (pow.f64 N 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 N -2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 -2 (log.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 2 (log.f64 N)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (*.f64 -2 (log.f64 N)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 N -2)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (pow.f64 N -2) (+.f64 (/.f64 1/3 N) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (/.f64 1/3 N) (pow.f64 N -2)) (.f64 -1/2 (pow.f64 N -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (pow.f64 N -2) (/.f64 1/3 N)) (.f64 (pow.f64 N -2) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (+.f64 (/.f64 1/3 N) -1/2)) (pow.f64 N -2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (+.f64 (/.f64 1/3 N) -1/2)) (pow.f64 N -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (+.f64 (/.f64 1/3 N) -1/2)) (pow.f64 N -2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (+.f64 (/.f64 1/3 N) -1/2)) (pow.f64 N -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (pow.f64 N -2) (+.f64 (/.f64 1/3 N) -1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (/.f64 1/3 N) (.f64 N N)) (/.f64 1/2 (.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (.f64 N N) (+.f64 (/.f64 1/3 N) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (/.f64 1/3 N) -1/2) (.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (pow.f64 (+.f64 (/.f64 1/3 N) -1/2) 2)) (/.f64 (.f64 N N) (cbrt.f64 (+.f64 (/.f64 1/3 N) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 (/.f64 1/3 N) -1/2)) (/.f64 (.f64 N N) (sqrt.f64 (+.f64 (/.f64 1/3 N) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 1/27 (pow.f64 N -3) -1/8) (.f64 (.f64 N N) (+.f64 (fma.f64 1/9 (pow.f64 N -2) 1/4) (/.f64 1/6 N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 1/9 (pow.f64 N -2) -1/4) (.f64 (.f64 N N) (+.f64 (/.f64 1/3 N) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (/.f64 1/3 N) -1/2)) (.f64 N (neg.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 -1 (+.f64 (/.f64 1/3 N) -1/2)) (.f64 N (neg.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 N -1) (fma.f64 1/27 (pow.f64 N -3) -1/8)) (.f64 N (+.f64 (fma.f64 1/9 (pow.f64 N -2) 1/4) (/.f64 1/6 N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 -1 (fma.f64 1/27 (pow.f64 N -3) -1/8)) (.f64 (.f64 N (neg.f64 N)) (+.f64 (fma.f64 1/9 (pow.f64 N -2) 1/4) (/.f64 1/6 N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 N -1) (fma.f64 1/9 (pow.f64 N -2) -1/4)) (.f64 N (+.f64 (/.f64 1/3 N) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 -1 (fma.f64 1/9 (pow.f64 N -2) -1/4)) (.f64 (.f64 N (neg.f64 N)) (+.f64 (/.f64 1/3 N) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (fma.f64 1/27 (pow.f64 N -3) -1/8) 1) (.f64 (+.f64 (fma.f64 1/9 (pow.f64 N -2) 1/4) (/.f64 1/6 N)) (.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (fma.f64 1/9 (pow.f64 N -2) -1/4) 1) (.f64 (+.f64 (/.f64 1/3 N) 1/2) (.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 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egg-rr> (2) ((x fma.f64 (/.f64 (cbrt.f64 (pow.f64 (+.f64 (/.f64 1/3 N) -1/2) 2)) (cbrt.f64 (pow.f64 N 4))) (cbrt.f64 (.f64 (pow.f64 N -2) (+.f64 (/.f64 1/3 N) -1/2))) (pow.f64 N -1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (+.f64 (/.f64 1/3 N) -1/2)) (cbrt.f64 (pow.f64 N 4))) (/.f64 (sqrt.f64 (+.f64 (/.f64 1/3 N) -1/2)) (pow.f64 (cbrt.f64 N) 2)) (pow.f64 N -1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (+.f64 (/.f64 1/3 N) -1/2) (pow.f64 N -1)) (pow.f64 N -1) (pow.f64 N -1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (pow.f64 N -2) (cbrt.f64 (pow.f64 (+.f64 (/.f64 1/3 N) -1/2) 2))) (cbrt.f64 (+.f64 (/.f64 1/3 N) -1/2)) (pow.f64 N -1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (pow.f64 N -2) (sqrt.f64 (+.f64 (/.f64 1/3 N) -1/2))) (sqrt.f64 (+.f64 (/.f64 1/3 N) -1/2)) (pow.f64 N -1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (+.f64 (/.f64 1/3 N) -1/2) (pow.f64 (cbrt.f64 (pow.f64 N -2)) 2)) (cbrt.f64 (pow.f64 N -2)) (pow.f64 N -1))))))

simplify62.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

770×	`fma-neg_binary64`
688×	`distribute-neg-frac_binary64`
536×	`unswap-sqr_binary64`
478×	`associate-/r/_binary64`
332×	`associate-/r*_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	23	438
1	56	438
2	105	438
3	223	438
4	610	438
5	2588	426
6	6165	426

Stop Event

1×	node limit

Counts

229 → 206

Calls

Call 1

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

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

localize5.0ms (0.1%)

Compiler: Compiled 7 to 3 computations (57.1% saved)

eval383.0ms (5.8%)

Compiler: Compiled 13267 to 9734 computations (26.6% saved)

prune84.0ms (1.3%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	577	6	583
Fresh	1	1	2
Picked	0	1	1
Done	1	3	4
Total	579	11	590

Error

0.0b

Counts

590 → 11

Alt Table

Click to see full alt table

Status	Error	Program
	53.1b	(/.f64 (fma.f64 (+.f64 (/.f64 1/3 N) -1/2) N (*.f64 N N)) (pow.f64 N 3))
✓	31.8b	(/.f64 1 N)
▶	61.4b	(log.f64 1)
	61.1b	(*.f64 (+.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))) (-.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))))
▶	47.3b	(/.f64 (-.f64 N (/.f64 (.f64 N 1/2) N)) (.f64 N N))
▶	32.3b	(+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N))
✓	32.8b	(-.f64 (/.f64 1 N) (/.f64 (/.f64 1/2 N) N))
✓	28.4b	(log.f64 (/.f64 (+.f64 N 1) N))
✓	31.1b	(neg.f64 (log.f64 N))
▶	32.8b	(/.f64 (+.f64 1 (/.f64 -1/2 N)) N)
▶	30.4b	(-.f64 N (log.f64 N))

Compiler

Compiled 171 to 112 computations (34.5% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 N (log.f64 N))

Compiler

Compiled 8 to 3 computations (62.5% saved)

series9.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
6.0ms	N	@	0	(-.f64 N (log.f64 N))
2.0ms	N	@	-inf	(-.f64 N (log.f64 N))
1.0ms	N	@	inf	(-.f64 N (log.f64 N))

rewrite47.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

508×	`pow1_binary64`
491×	`add-sqr-sqrt_binary64`
475×	`add-log-exp_binary64`
475×	`log1p-expm1-u_binary64`
475×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	88	6
2	1262	6

Stop Event

1×	node limit

Counts

1 → 35

Calls

Call 1

Inputs
(-.f64 N (log.f64 N))

Outputs

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

simplify161.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

1741×	`fma-neg_binary64`
851×	`distribute-rgt-in_binary64`
627×	`fma-def_binary64`
525×	`distribute-lft-in_binary64`
297×	`unsub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	79
1	37	61
2	72	61
3	141	61
4	331	61
5	941	61
6	3007	61
7	4269	61
8	4843	61
9	5305	61
10	5863	61
11	5960	61
12	7638	61
13	7666	61
14	7682	61
15	7718	61
16	7998	61

Stop Event

1×	node limit

Counts

47 → 42

Calls

Call 1

Inputs
(*.f64 -1 (log.f64 N))
(+.f64 N (*.f64 -1 (log.f64 N)))
(+.f64 N (*.f64 -1 (log.f64 N)))
(+.f64 N (*.f64 -1 (log.f64 N)))
N
(+.f64 N (log.f64 (/.f64 1 N)))
(+.f64 N (log.f64 (/.f64 1 N)))
(+.f64 N (log.f64 (/.f64 1 N)))
N
(+.f64 N (.f64 -1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))
(+.f64 N (.f64 -1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))
(+.f64 N (.f64 -1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))

Outputs
(*.f64 -1 (log.f64 N))
(neg.f64 (log.f64 N))
(+.f64 N (*.f64 -1 (log.f64 N)))
(+.f64 N (neg.f64 (log.f64 N)))
(-.f64 N (log.f64 N))
(+.f64 N (*.f64 -1 (log.f64 N)))
(+.f64 N (neg.f64 (log.f64 N)))
(-.f64 N (log.f64 N))
(+.f64 N (*.f64 -1 (log.f64 N)))
(+.f64 N (neg.f64 (log.f64 N)))
(-.f64 N (log.f64 N))
N
(+.f64 N (log.f64 (/.f64 1 N)))
(+.f64 N (neg.f64 (log.f64 N)))
(-.f64 N (log.f64 N))
(+.f64 N (log.f64 (/.f64 1 N)))
(+.f64 N (neg.f64 (log.f64 N)))
(-.f64 N (log.f64 N))
(+.f64 N (log.f64 (/.f64 1 N)))
(+.f64 N (neg.f64 (log.f64 N)))
(-.f64 N (log.f64 N))
N
(+.f64 N (.f64 -1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))
(+.f64 N (neg.f64 (log.f64 N)))
(-.f64 N (log.f64 N))
(+.f64 N (.f64 -1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))
(+.f64 N (neg.f64 (log.f64 N)))
(-.f64 N (log.f64 N))
(+.f64 N (.f64 -1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))
(+.f64 N (neg.f64 (log.f64 N)))
(-.f64 N (log.f64 N))

localize2.0ms (0%)

Compiler: Compiled 4 to 4 computations (0% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 1 (/.f64 -1/2 N)) N)

Compiler

Compiled 19 to 14 computations (26.3% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite53.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

809×	`pow1_binary64`
760×	`add-log-exp_binary64`
759×	`log1p-expm1-u_binary64`
759×	`expm1-log1p-u_binary64`
747×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	154	10
2	2042	10

Stop Event

1×	node limit

Counts

1 → 31

Calls

Call 1

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

Outputs

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

simplify44.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

732×	`times-frac_binary64`
554×	`fma-neg_binary64`
536×	`associate-/r*_binary64`
494×	`associate-/l/_binary64`
434×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	132
1	26	132
2	46	132
3	100	132
4	263	132
5	947	132
6	5090	132

Stop Event

1×	node limit

Counts

43 → 36

Calls

Call 1

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

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

localize13.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	14.6b	(/.f64 (-.f64 N (/.f64 (.f64 N 1/2) N)) (.f64 N N))

Compiler

Compiled 32 to 17 computations (46.9% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite177.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

884×	`prod-diff_binary64`
544×	`log-prod_binary64`
280×	`fma-def_binary64`
259×	`pow2_binary64`
218×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	191	16
2	3060	16

Stop Event

1×	node limit

Counts

1 → 199

Calls

Call 1

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

Outputs

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

simplify68.0ms (1%)

Algorithm

1×	egg-herbie

Rules

732×	`times-frac_binary64`
554×	`fma-neg_binary64`
536×	`associate-/r*_binary64`
494×	`associate-/l/_binary64`
434×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	132
1	26	132
2	46	132
3	100	132
4	263	132
5	947	132
6	5090	132

Stop Event

1×	node limit

Counts

211 → 204

Calls

Call 1

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

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

localize52.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N))
✓	0.1b	(/.f64 (+.f64 (/.f64 1/3 N) -1/2) N)
✓	0.1b	(/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N)
	0.3b	(/.f64 1/3 N)

Compiler

Compiled 45 to 32 computations (28.9% saved)

series6.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	N	@	-inf	(/.f64 (+.f64 (/.f64 1/3 N) -1/2) N)
1.0ms	N	@	0	(/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N)
1.0ms	N	@	inf	(/.f64 (+.f64 (/.f64 1/3 N) -1/2) N)
1.0ms	N	@	0	(/.f64 (+.f64 (/.f64 1/3 N) -1/2) N)
1.0ms	N	@	-inf	(/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N)

rewrite129.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

601×	`log-prod_binary64`
407×	`fma-def_binary64`
326×	`pow2_binary64`
315×	`log-div_binary64`
262×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	42
1	258	42
2	3889	40

Stop Event

1×	node limit

Counts

3 → 180

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (+.f64 (/.f64 1/3 N) -1/2) (pow.f64 N -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (*.f64 (+.f64 (/.f64 1/3 N) -1/2) (pow.f64 N -2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (*.f64 (+.f64 (/.f64 1/3 N) -1/2) (pow.f64 N -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (*.f64 (+.f64 (/.f64 1/3 N) -1/2) (pow.f64 N -2))))) (log.f64 (sqrt.f64 (exp.f64 (*.f64 (+.f64 (/.f64 1/3 N) -1/2) (pow.f64 N -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (+.f64 (/.f64 1/3 N) -1/2) (pow.f64 N -2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (/.f64 1/3 N) -1/2) (pow.f64 N -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) (/.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (/.f64 1/3 N) -1/2) (pow.f64 N -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x 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simplify155.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

617×	`fma-def_binary64`
536×	`unswap-sqr_binary64`
482×	`distribute-neg-frac_binary64`
401×	`div-sub_binary64`
356×	`*-commutative_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	28	486
1	69	486
2	127	486
3	274	486
4	802	486
5	3478	474
6	7161	474

Stop Event

1×	node limit

Counts

216 → 196

Calls

Call 1

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

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

eval359.0ms (5.5%)

Compiler: Compiled 15423 to 10190 computations (33.9% saved)

prune188.0ms (2.9%)

Pruning

11 alts after pruning (4 fresh and 7 done)

	Pruned	Kept	Total
New	504	3	507
Fresh	1	1	2
Picked	1	0	1
Done	1	7	8
Total	507	11	518

Error

0.0b

Counts

518 → 11

Alt Table

Click to see full alt table

Status	Error	Program
✓	31.8b	(/.f64 1 N)
✓	61.4b	(log.f64 1)
▶	61.1b	(*.f64 (+.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))) (-.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))))
▶	61.1b	(-.f64 (+.f64 1 (/.f64 (+.f64 1 (/.f64 -1/2 N)) N)) 1)
✓	28.4b	(log.f64 (/.f64 (+.f64 N 1) N))
✓	31.1b	(neg.f64 (log.f64 N))
▶	32.3b	(*.f64 (/.f64 1 N) (+.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) 1))
✓	32.8b	(-.f64 (/.f64 1 N) (/.f64 (/.f64 1/2 N) N))
✓	32.8b	(/.f64 (+.f64 1 (/.f64 -1/2 N)) N)
	61.1b	N
✓	30.4b	(-.f64 N (log.f64 N))

Compiler

Compiled 85 to 60 computations (29.4% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))) (-.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))))
✓	0.1b	(sqrt.f64 (log.f64 N))
✓	0.1b	(sqrt.f64 (log1p.f64 N))
✓	2.6b	(-.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N)))

Compiler

Compiled 41 to 8 computations (80.5% saved)

series55.0ms (0.8%)

Counts

4 → 34

Calls

12 calls:

Time	Variable		Point	Expression
19.0ms	N	@	0	(sqrt.f64 (log.f64 N))
15.0ms	N	@	-inf	(sqrt.f64 (log.f64 N))
6.0ms	N	@	inf	(sqrt.f64 (log.f64 N))
5.0ms	N	@	-inf	(*.f64 (+.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))) (-.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))))
2.0ms	N	@	inf	(*.f64 (+.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))) (-.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))))

rewrite80.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

982×	`pow1_binary64`
912×	`add-log-exp_binary64`
912×	`expm1-log1p-u_binary64`
911×	`log1p-expm1-u_binary64`
95×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	48
1	189	30
2	2618	30

Stop Event

1×	node limit

Counts

4 → 132

Calls

Call 1

Inputs
(-.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N)))
(sqrt.f64 (log1p.f64 N))
(sqrt.f64 (log.f64 N))
(*.f64 (+.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))) (-.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))))

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

simplify67.0ms (1%)

Algorithm

1×	egg-herbie

Rules

873×	`fma-def_binary64`
843×	`times-frac_binary64`
811×	`associate-/r*_binary64`
606×	`associate-l_binary64`
427×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	160	2995
1	524	2461
2	1962	2078

Stop Event

1×	node limit

Counts

166 → 181

Calls

Call 1

Inputs
(*.f64 -1 (sqrt.f64 (log.f64 N)))
(.f64 1/2 (.f64 (/.f64 1 (*.f64 N (sqrt.f64 -1))) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N))))))
(+.f64 (.f64 -1/2 (.f64 (/.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) 2)) (.f64 (pow.f64 N 2) (sqrt.f64 -1))) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) (.f64 1/2 (.f64 (/.f64 1 (.f64 N (sqrt.f64 -1))) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))))
(+.f64 (.f64 1/2 (.f64 (/.f64 (-.f64 1/3 (.f64 -1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) 2)) (.f64 (pow.f64 (sqrt.f64 -1) 2) (log.f64 (/.f64 1 N)))))) (.f64 (pow.f64 N 3) (sqrt.f64 -1))) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) (+.f64 (.f64 -1/2 (.f64 (/.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) 2)) (.f64 (pow.f64 N 2) (sqrt.f64 -1))) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) (.f64 1/2 (.f64 (/.f64 1 (*.f64 N (sqrt.f64 -1))) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N))))))))
(+.f64 (.f64 -1/2 (.f64 (/.f64 (+.f64 1/4 (+.f64 (.f64 1/2 (/.f64 (-.f64 1/3 (.f64 -1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) 2)) (.f64 (pow.f64 (sqrt.f64 -1) 2) (log.f64 (/.f64 1 N)))))) (.f64 (pow.f64 (sqrt.f64 -1) 2) (log.f64 (/.f64 1 N))))) (pow.f64 (.f64 -1/2 (.f64 (/.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) 2)) (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) 2))) (.f64 (pow.f64 N 4) (sqrt.f64 -1))) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) (+.f64 (.f64 1/2 (.f64 (/.f64 (-.f64 1/3 (.f64 -1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) 2)) (.f64 (pow.f64 (sqrt.f64 -1) 2) (log.f64 (/.f64 1 N)))))) (.f64 (pow.f64 N 3) (sqrt.f64 -1))) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) (+.f64 (.f64 -1/2 (.f64 (/.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) 2)) (.f64 (pow.f64 N 2) (sqrt.f64 -1))) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) (.f64 1/2 (.f64 (/.f64 1 (.f64 N (sqrt.f64 -1))) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))))))
(.f64 1/2 (.f64 (/.f64 1 N) (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 N))))))))
(+.f64 (.f64 1/2 (.f64 (/.f64 1 N) (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))))) (.f64 -1/2 (.f64 (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))) 2)) (pow.f64 N 2)) (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))))))
(+.f64 (.f64 1/2 (.f64 (/.f64 (+.f64 (.f64 1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))) 2)) (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))) 1/3) (pow.f64 N 3)) (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))))) (+.f64 (.f64 1/2 (.f64 (/.f64 1 N) (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))))) (.f64 -1/2 (.f64 (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))) 2)) (pow.f64 N 2)) (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 N))))))))))
(+.f64 (.f64 1/2 (.f64 (/.f64 (+.f64 (.f64 1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))) 2)) (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))) 1/3) (pow.f64 N 3)) (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))))) (+.f64 (.f64 1/2 (.f64 (/.f64 1 N) (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))))) (+.f64 (.f64 -1/2 (.f64 (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))) 2)) (pow.f64 N 2)) (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))))) (.f64 -1/2 (.f64 (/.f64 (+.f64 1/4 (+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))) 2)) (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))) 1/3) (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))) (pow.f64 (.f64 -1/2 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))) (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))) 2)))) 2))) (pow.f64 N 4)) (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 N)))))))))))
(*.f64 (sqrt.f64 -1) (sqrt.f64 (log.f64 (/.f64 1 N))))
(+.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 (log.f64 (/.f64 1 N)))) (.f64 1/2 (.f64 (/.f64 1 (.f64 N (sqrt.f64 -1))) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))))
(+.f64 (.f64 -1/2 (.f64 (/.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) 2)) (.f64 (pow.f64 N 2) (sqrt.f64 -1))) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) (+.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 (log.f64 (/.f64 1 N)))) (.f64 1/2 (.f64 (/.f64 1 (*.f64 N (sqrt.f64 -1))) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N))))))))
(+.f64 (.f64 1/2 (.f64 (/.f64 (-.f64 1/3 (.f64 -1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) 2)) (.f64 (pow.f64 (sqrt.f64 -1) 2) (log.f64 (/.f64 1 N)))))) (.f64 (pow.f64 N 3) (sqrt.f64 -1))) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) (+.f64 (.f64 -1/2 (.f64 (/.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) 2)) (.f64 (pow.f64 N 2) (sqrt.f64 -1))) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) (+.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 (log.f64 (/.f64 1 N)))) (.f64 1/2 (.f64 (/.f64 1 (.f64 N (sqrt.f64 -1))) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))))))
(sqrt.f64 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 N)))))
(+.f64 (.f64 1/2 (.f64 (/.f64 1 N) (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))))) (sqrt.f64 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))
(+.f64 (.f64 1/2 (.f64 (/.f64 1 N) (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))))) (+.f64 (.f64 -1/2 (.f64 (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))) 2)) (pow.f64 N 2)) (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))))) (sqrt.f64 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 N)))))))
(+.f64 (.f64 1/2 (.f64 (/.f64 (+.f64 (.f64 1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))) 2)) (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))) 1/3) (pow.f64 N 3)) (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))))) (+.f64 (.f64 1/2 (.f64 (/.f64 1 N) (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))))) (+.f64 (.f64 -1/2 (.f64 (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))) 2)) (pow.f64 N 2)) (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))))) (sqrt.f64 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))))
(*.f64 (sqrt.f64 -1) (sqrt.f64 (log.f64 (/.f64 1 N))))
(*.f64 (sqrt.f64 -1) (sqrt.f64 (log.f64 (/.f64 1 N))))
(*.f64 (sqrt.f64 -1) (sqrt.f64 (log.f64 (/.f64 1 N))))
(*.f64 (sqrt.f64 -1) (sqrt.f64 (log.f64 (/.f64 1 N))))
(sqrt.f64 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 N)))))
(sqrt.f64 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 N)))))
(sqrt.f64 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 N)))))
(sqrt.f64 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 N)))))
(*.f64 -1 (log.f64 N))
(/.f64 1 N)
(+.f64 (.f64 -1 (/.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) 2)) (pow.f64 N 2))) (+.f64 (/.f64 1 N) (/.f64 1/4 (.f64 (pow.f64 N 2) (*.f64 (pow.f64 (sqrt.f64 -1) 2) (log.f64 (/.f64 1 N)))))))
(+.f64 (.f64 -1 (/.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) 2)) (pow.f64 N 2))) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (pow.f64 N 2) (.f64 (pow.f64 (sqrt.f64 -1) 2) (log.f64 (/.f64 1 N)))))) (+.f64 (/.f64 1 N) (*.f64 1/3 (/.f64 1 (pow.f64 N 3))))))
(+.f64 (.f64 -1 (/.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) 2)) (pow.f64 N 2))) (+.f64 (.f64 1/2 (/.f64 (-.f64 1/3 (.f64 -1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) 2)) (.f64 (pow.f64 (sqrt.f64 -1) 2) (log.f64 (/.f64 1 N)))))) (.f64 (pow.f64 N 4) (.f64 (pow.f64 (sqrt.f64 -1) 2) (log.f64 (/.f64 1 N)))))) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (pow.f64 N 2) (.f64 (pow.f64 (sqrt.f64 -1) 2) (log.f64 (/.f64 1 N)))))) (+.f64 (/.f64 1 N) (+.f64 (.f64 -1 (/.f64 (+.f64 1/4 (+.f64 (.f64 1/2 (/.f64 (-.f64 1/3 (.f64 -1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) 2)) (.f64 (pow.f64 (sqrt.f64 -1) 2) (log.f64 (/.f64 1 N)))))) (.f64 (pow.f64 (sqrt.f64 -1) 2) (log.f64 (/.f64 1 N))))) (pow.f64 (.f64 -1/2 (.f64 (/.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) 2)) (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) 2))) (pow.f64 N 4))) (+.f64 (.f64 1/3 (/.f64 1 (pow.f64 N 3))) (.f64 1/4 (/.f64 (pow.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) 2)) 2) (.f64 (pow.f64 N 4) (.f64 (pow.f64 (sqrt.f64 -1) 2) (log.f64 (/.f64 1 N))))))))))))
(/.f64 1 N)
(+.f64 (/.f64 1/4 (.f64 (pow.f64 N 2) (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))) (+.f64 (/.f64 1 N) (.f64 -1 (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 N))))))) 2)) (pow.f64 N 2)))))
(+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))) 2)) (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))) (.f64 -1 (+.f64 (.f64 1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))) 2)) (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))) 1/3))) (pow.f64 N 3))) (+.f64 (/.f64 1 N) (+.f64 (.f64 -1 (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))) 2)) (pow.f64 N 2))) (.f64 1/4 (/.f64 1 (.f64 (pow.f64 N 2) (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))))))
(+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))) 2)) (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))) (.f64 -1 (+.f64 (.f64 1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))) 2)) (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))) 1/3))) (pow.f64 N 3))) (+.f64 (.f64 -1 (/.f64 (+.f64 1/4 (+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))) 2)) (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))) 1/3) (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))) (pow.f64 (.f64 -1/2 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))) (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))) 2)))) 2))) (pow.f64 N 4))) (+.f64 (/.f64 1 N) (+.f64 (.f64 -1 (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))) 2)) (pow.f64 N 2))) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (pow.f64 N 2) (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))) (+.f64 (.f64 1/4 (/.f64 (pow.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))) 2)) 2) (.f64 (pow.f64 N 4) (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))) (.f64 1/2 (/.f64 (+.f64 (.f64 1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))) 2)) (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))) 1/3) (.f64 (pow.f64 N 4) (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))))))))))

Outputs
(*.f64 -1 (sqrt.f64 (log.f64 N)))
(neg.f64 (sqrt.f64 (log.f64 N)))
(.f64 1/2 (.f64 (/.f64 1 (*.f64 N (sqrt.f64 -1))) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N))))))
(.f64 1/2 (.f64 (/.f64 1 (*.f64 N (sqrt.f64 -1))) (sqrt.f64 (/.f64 1 (neg.f64 (log.f64 N))))))
(/.f64 (.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) 1/2) (.f64 N (sqrt.f64 -1)))
(.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (/.f64 1/2 (.f64 N (sqrt.f64 -1))))
(+.f64 (.f64 -1/2 (.f64 (/.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) 2)) (.f64 (pow.f64 N 2) (sqrt.f64 -1))) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) (.f64 1/2 (.f64 (/.f64 1 (.f64 N (sqrt.f64 -1))) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))))
(fma.f64 -1/2 (/.f64 (.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (neg.f64 (log.f64 N)))) (/.f64 1 (sqrt.f64 -1)))) 2)) (sqrt.f64 (/.f64 1 (neg.f64 (log.f64 N))))) (.f64 (sqrt.f64 -1) (.f64 N N))) (.f64 1/2 (.f64 (/.f64 1 (.f64 N (sqrt.f64 -1))) (sqrt.f64 (/.f64 1 (neg.f64 (log.f64 N)))))))
(.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (+.f64 (/.f64 1/2 (.f64 N (sqrt.f64 -1))) (/.f64 (+.f64 -1/4 (.f64 (pow.f64 (.f64 1/2 (/.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (sqrt.f64 -1))) 2) -1/2)) (.f64 N (.f64 N (sqrt.f64 -1))))))
(.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (+.f64 (/.f64 1/2 (.f64 N (sqrt.f64 -1))) (/.f64 (fma.f64 -1/2 (pow.f64 (.f64 1/2 (/.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (sqrt.f64 -1))) 2) -1/4) (.f64 (sqrt.f64 -1) (*.f64 N N)))))
(+.f64 (.f64 1/2 (.f64 (/.f64 (-.f64 1/3 (.f64 -1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) 2)) (.f64 (pow.f64 (sqrt.f64 -1) 2) (log.f64 (/.f64 1 N)))))) (.f64 (pow.f64 N 3) (sqrt.f64 -1))) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) (+.f64 (.f64 -1/2 (.f64 (/.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) 2)) (.f64 (pow.f64 N 2) (sqrt.f64 -1))) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) (.f64 1/2 (.f64 (/.f64 1 (*.f64 N (sqrt.f64 -1))) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N))))))))
(fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (neg.f64 (log.f64 N)))) (/.f64 (+.f64 1/3 (.f64 1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (neg.f64 (log.f64 N)))) (/.f64 1 (sqrt.f64 -1)))) 2)) (.f64 (neg.f64 (log.f64 N)) (pow.f64 (sqrt.f64 -1) 2))))) (.f64 (sqrt.f64 -1) (pow.f64 N 3)))) (fma.f64 -1/2 (/.f64 (.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (neg.f64 (log.f64 N)))) (/.f64 1 (sqrt.f64 -1)))) 2)) (sqrt.f64 (/.f64 1 (neg.f64 (log.f64 N))))) (.f64 (sqrt.f64 -1) (.f64 N N))) (.f64 1/2 (.f64 (/.f64 1 (.f64 N (sqrt.f64 -1))) (sqrt.f64 (/.f64 1 (neg.f64 (log.f64 N))))))))
(fma.f64 1/2 (.f64 (/.f64 (-.f64 1/3 (.f64 1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (/.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (sqrt.f64 -1))) 2)) (neg.f64 (log.f64 N))))) (sqrt.f64 -1)) (/.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (pow.f64 N 3))) (.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (+.f64 (/.f64 1/2 (.f64 N (sqrt.f64 -1))) (/.f64 (+.f64 -1/4 (.f64 (pow.f64 (.f64 1/2 (/.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (sqrt.f64 -1))) 2) -1/2)) (.f64 N (*.f64 N (sqrt.f64 -1)))))))
(.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (+.f64 (/.f64 1/2 (.f64 N (sqrt.f64 -1))) (fma.f64 1/2 (/.f64 (-.f64 1/3 (/.f64 (fma.f64 -1/2 (pow.f64 (.f64 1/2 (/.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (sqrt.f64 -1))) 2) -1/4) (log.f64 N))) (.f64 (sqrt.f64 -1) (pow.f64 N 3))) (/.f64 (fma.f64 -1/2 (pow.f64 (.f64 1/2 (/.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (sqrt.f64 -1))) 2) -1/4) (.f64 (sqrt.f64 -1) (*.f64 N N))))))
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(fma.f64 -1/2 (.f64 (sqrt.f64 (/.f64 1 (neg.f64 (log.f64 N)))) (/.f64 (+.f64 1/4 (fma.f64 1/2 (/.f64 (+.f64 1/3 (.f64 1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (neg.f64 (log.f64 N)))) (/.f64 1 (sqrt.f64 -1)))) 2)) (.f64 (neg.f64 (log.f64 N)) (pow.f64 (sqrt.f64 -1) 2))))) (.f64 (neg.f64 (log.f64 N)) (pow.f64 (sqrt.f64 -1) 2))) (pow.f64 (.f64 -1/2 (.f64 (sqrt.f64 (/.f64 1 (neg.f64 (log.f64 N)))) (/.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (neg.f64 (log.f64 N)))) (/.f64 1 (sqrt.f64 -1)))) 2)) (sqrt.f64 -1)))) 2))) (.f64 (sqrt.f64 -1) (pow.f64 N 4)))) (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (neg.f64 (log.f64 N)))) (/.f64 (+.f64 1/3 (.f64 1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (neg.f64 (log.f64 N)))) (/.f64 1 (sqrt.f64 -1)))) 2)) (.f64 (neg.f64 (log.f64 N)) (pow.f64 (sqrt.f64 -1) 2))))) (.f64 (sqrt.f64 -1) (pow.f64 N 3)))) (fma.f64 -1/2 (/.f64 (.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (neg.f64 (log.f64 N)))) (/.f64 1 (sqrt.f64 -1)))) 2)) (sqrt.f64 (/.f64 1 (neg.f64 (log.f64 N))))) (.f64 (sqrt.f64 -1) (.f64 N N))) (.f64 1/2 (.f64 (/.f64 1 (*.f64 N (sqrt.f64 -1))) (sqrt.f64 (/.f64 1 (neg.f64 (log.f64 N)))))))))
(+.f64 (.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (+.f64 (/.f64 1/2 (.f64 N (sqrt.f64 -1))) (/.f64 (+.f64 -1/4 (.f64 (pow.f64 (.f64 1/2 (/.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (sqrt.f64 -1))) 2) -1/2)) (.f64 N (.f64 N (sqrt.f64 -1)))))) (.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (+.f64 (/.f64 (.f64 -1/2 (+.f64 1/4 (fma.f64 1/2 (/.f64 (-.f64 1/3 (.f64 1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (/.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (sqrt.f64 -1))) 2)) (neg.f64 (log.f64 N))))) (.f64 (log.f64 N) 1)) (pow.f64 (.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (/.f64 (+.f64 -1/4 (.f64 (pow.f64 (.f64 1/2 (/.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (sqrt.f64 -1))) 2) -1/2)) (sqrt.f64 -1))) 2)))) (.f64 (sqrt.f64 -1) (pow.f64 N 4))) (.f64 1/2 (/.f64 (-.f64 1/3 (.f64 1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (/.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (sqrt.f64 -1))) 2)) (neg.f64 (log.f64 N))))) (*.f64 (sqrt.f64 -1) (pow.f64 N 3)))))))
(.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (+.f64 (+.f64 (/.f64 1/2 (.f64 N (sqrt.f64 -1))) (/.f64 (fma.f64 -1/2 (pow.f64 (.f64 1/2 (/.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (sqrt.f64 -1))) 2) -1/4) (.f64 (sqrt.f64 -1) (.f64 N N)))) (fma.f64 -1/2 (/.f64 (fma.f64 1/2 (/.f64 (-.f64 1/3 (/.f64 (fma.f64 -1/2 (pow.f64 (.f64 1/2 (/.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (sqrt.f64 -1))) 2) -1/4) (log.f64 N))) (log.f64 N)) (+.f64 1/4 (pow.f64 (.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (/.f64 (fma.f64 -1/2 (pow.f64 (.f64 1/2 (/.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (sqrt.f64 -1))) 2) -1/4) (sqrt.f64 -1))) 2))) (.f64 (sqrt.f64 -1) (pow.f64 N 4))) (/.f64 (+.f64 1/6 (.f64 (/.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (/.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (sqrt.f64 -1))) 2)) (log.f64 N)) 1/4)) (.f64 (sqrt.f64 -1) (pow.f64 N 3))))))
(.f64 1/2 (.f64 (/.f64 1 N) (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 N))))))))
(.f64 1/2 (.f64 (/.f64 1 N) (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 N))))))))
(*.f64 (sqrt.f64 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N))))) (/.f64 1/2 N))
(+.f64 (.f64 1/2 (.f64 (/.f64 1 N) (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))))) (.f64 -1/2 (.f64 (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))) 2)) (pow.f64 N 2)) (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))))))
(fma.f64 1/2 (.f64 (/.f64 1 N) (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 N))))))) (.f64 -1/2 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 N)))))) (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 N))))))) 2)) (*.f64 N N)))))
(.f64 (sqrt.f64 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N))))) (+.f64 (/.f64 1/2 N) (/.f64 (.f64 -1/2 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))))) 2))) (.f64 N N))))
(.f64 (sqrt.f64 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N))))) (fma.f64 -1/2 (/.f64 (fma.f64 1/4 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))) 1/2) (.f64 N N)) (/.f64 1/2 N)))
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(fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 N)))))) (/.f64 (fma.f64 1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 N))))))) 2)) (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 N))))) 1/3) (pow.f64 N 3))) (fma.f64 1/2 (.f64 (/.f64 1 N) (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 N))))))) (.f64 -1/2 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 N)))))) (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 N))))))) 2)) (*.f64 N N))))))
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(-.f64 (-.f64 (+.f64 (/.f64 1 N) (+.f64 (-.f64 (/.f64 1/4 (.f64 (.f64 N N) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N))))) (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))))) 2)) (.f64 N N))) (fma.f64 1/2 (/.f64 (fma.f64 1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))))) 2)) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))) 1/3) (.f64 (pow.f64 N 4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N))))) (.f64 1/4 (/.f64 (pow.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))))) 2)) 2) (.f64 (pow.f64 N 4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N))))))))) (/.f64 (+.f64 1/4 (fma.f64 1/2 (/.f64 (fma.f64 1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))))) 2)) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))) 1/3) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))) (pow.f64 (.f64 -1/2 (.f64 (sqrt.f64 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N))))) (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))))) 2)))) 2))) (pow.f64 N 4))) (/.f64 (-.f64 (.f64 1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))))) 2)) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N))))) (fma.f64 1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))))) 2)) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))) 1/3)) (pow.f64 N 3)))
(+.f64 (-.f64 (/.f64 1 N) (/.f64 (fma.f64 1/2 (/.f64 (fma.f64 1/2 (/.f64 (fma.f64 1/4 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))) 1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))) 1/3) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))) (fma.f64 1/4 (.f64 (pow.f64 (fma.f64 1/4 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))) 1/2) 2) (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N))))) 1/4)) (pow.f64 N 4))) (-.f64 (-.f64 (fma.f64 1/4 (/.f64 (pow.f64 (fma.f64 1/4 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))) 1/2) 2) (.f64 (pow.f64 N 4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N))))) (fma.f64 (/.f64 1/2 (pow.f64 N 4)) (/.f64 (fma.f64 1/2 (/.f64 (fma.f64 1/4 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))) 1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))) 1/3) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))) (/.f64 1/4 (.f64 (.f64 N N) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N))))))) (/.f64 (fma.f64 1/4 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))) 1/2) (.f64 N N))) (/.f64 (+.f64 (.f64 (/.f64 (fma.f64 1/4 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))) 1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))) 0) -1/3) (pow.f64 N 3))))

localize18.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (/.f64 1 N) (+.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) 1))
	0.1b	(/.f64 (+.f64 (/.f64 1/3 N) -1/2) N)
	0.3b	(/.f64 1/3 N)

Compiler

Compiled 45 to 34 computations (24.4% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

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

0.0ms

-inf

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

0.0ms

inf

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

rewrite64.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

564×	`prod-diff_binary64`
561×	`log-prod_binary64`
309×	`pow2_binary64`
247×	`fma-def_binary64`
236×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	256	16
2	3576	16

Stop Event

1×	node limit

Counts

1 → 79

Calls

Call 1

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

Outputs

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

simplify57.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

770×	`fma-neg_binary64`
705×	`distribute-neg-frac_binary64`
536×	`unswap-sqr_binary64`
454×	`associate-/r/_binary64`
328×	`associate-/r*_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	21	189
1	55	189
2	103	189
3	219	189
4	595	189
5	2544	177
6	6092	177

Stop Event

1×	node limit

Counts

91 → 88

Calls

Call 1

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

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

localize15.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.1b	(/.f64 (+.f64 1 (/.f64 -1/2 N)) N)
✓	2.4b	(-.f64 (+.f64 1 (/.f64 (+.f64 1 (/.f64 -1/2 N)) N)) 1)

Compiler

Compiled 39 to 30 computations (23.1% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite103.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

600×	`prod-diff_binary64`
523×	`fma-def_binary64`
422×	`log-prod_binary64`
248×	`pow2_binary64`
230×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	215	10
2	3184	10

Stop Event

1×	node limit

Counts

1 → 108

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 (/.f64 (+.f64 1 (/.f64 -1/2 N)) N) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (+.f64 (/.f64 (+.f64 1 (/.f64 -1/2 N)) N) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (+.f64 1 (/.f64 -1/2 N)) N) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (/.f64 (+.f64 1 (/.f64 -1/2 N)) N)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (+.f64 1 (/.f64 -1/2 N)) N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (+.f64 1 (/.f64 (+.f64 1 (/.f64 -1/2 N)) N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (/.f64 (+.f64 1 (/.f64 -1/2 N)) N) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (+.f64 1 (/.f64 -1/2 N)) N))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (+.f64 1 (/.f64 -1/2 N)) N)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (+.f64 1 (/.f64 -1/2 N)) N)))) (log.f64 (sqrt.f64 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simplify43.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

732×	`times-frac_binary64`
554×	`fma-neg_binary64`
536×	`associate-/r*_binary64`
494×	`associate-/l/_binary64`
434×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	132
1	26	132
2	46	132
3	100	132
4	263	132
5	947	132
6	5090	132

Stop Event

1×	node limit

Counts

120 → 113

Calls

Call 1

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

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

eval326.0ms (5%)

Compiler: Compiled 13406 to 8716 computations (35% saved)

prune109.0ms (1.7%)

Pruning

12 alts after pruning (4 fresh and 8 done)

	Pruned	Kept	Total
New	550	3	553
Fresh	0	1	1
Picked	1	0	1
Done	1	8	9
Total	552	12	564

Error

0.0b

Counts

564 → 12

Alt Table

Click to see full alt table

Status	Error	Program
✓	31.8b	(/.f64 1 N)
✓	61.4b	(log.f64 1)
✓	61.1b	(*.f64 (+.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))) (-.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))))
	32.3b	(/.f64 (+.f64 1 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N)) N)
✓	28.4b	(log.f64 (/.f64 (+.f64 N 1) N))
	61.1b	(*.f64 (+.f64 (cbrt.f64 (pow.f64 (log1p.f64 N) 3/2)) (sqrt.f64 (log.f64 N))) (-.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))))
	61.1b	(*.f64 (+.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))) (pow.f64 (pow.f64 (-.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))) 3) 1/3))
✓	32.8b	(-.f64 (/.f64 1 N) (/.f64 (/.f64 1/2 N) N))
✓	31.1b	(neg.f64 (log.f64 N))
✓	32.8b	(/.f64 (+.f64 1 (/.f64 -1/2 N)) N)
	61.1b	N
✓	30.4b	(-.f64 N (log.f64 N))

Compiler

Compiled 109 to 71 computations (34.9% saved)

regimes94.0ms (1.4%)

Counts

21 → 2

Calls

Call 1

Inputs
(*.f64 (+.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))) (pow.f64 (pow.f64 (-.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))) 3) 1/3))
(*.f64 (+.f64 (cbrt.f64 (pow.f64 (log1p.f64 N) 3/2)) (sqrt.f64 (log.f64 N))) (-.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))))
(*.f64 (+.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))) (-.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))))
(/.f64 (fma.f64 (+.f64 (/.f64 1/3 N) -1/2) N (*.f64 N N)) (pow.f64 N 3))
(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
(-.f64 (log1p.f64 N) (log.f64 N))
(log.f64 (/.f64 (+.f64 N 1) N))
(-.f64 N (log.f64 N))
(-.f64 N (log.f64 N))
(neg.f64 (log.f64 N))
(+.f64 (/.f64 1 N) (.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2)))
(*.f64 (/.f64 1 N) (+.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) 1))
(+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N))
(/.f64 (+.f64 1 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N)) N)
(-.f64 (+.f64 1 (/.f64 (+.f64 1 (/.f64 -1/2 N)) N)) 1)
(/.f64 (-.f64 N (/.f64 (.f64 N 1/2) N)) (.f64 N N))
(-.f64 (/.f64 1 N) (/.f64 (/.f64 1/2 N) N))
(/.f64 (+.f64 1 (/.f64 -1/2 N)) N)
(/.f64 1 N)
N
(log.f64 1)

Outputs
(*.f64 (/.f64 1 N) (+.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) 1))
(log.f64 (/.f64 (+.f64 N 1) N))

Calls

3 calls:

42.0ms	N
21.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
20.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))

Results

Error	Segments	Branch
0.0b	2	`N`
0.0b	2	`(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))`
0.0b	2	`(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))`

Compiler

Compiled 209 to 117 computations (44% saved)

bsearch1.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	2.1946426151941978e-6	0.017448894512423152

Compiler

Compiled 12 to 9 computations (25% saved)

regimes16.0ms (0.3%)

Counts

8 → 1

Calls

Call 1

Inputs
(/.f64 (+.f64 1 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N)) N)
(-.f64 (+.f64 1 (/.f64 (+.f64 1 (/.f64 -1/2 N)) N)) 1)
(/.f64 (-.f64 N (/.f64 (.f64 N 1/2) N)) (.f64 N N))
(-.f64 (/.f64 1 N) (/.f64 (/.f64 1/2 N) N))
(/.f64 (+.f64 1 (/.f64 -1/2 N)) N)
(/.f64 1 N)
N
(log.f64 1)

Outputs
(/.f64 1 N)

Calls

1 calls:

12.0ms

Results

Error	Segments	Branch
31.8b	1	`N`

Compiler

Compiled 58 to 40 computations (31% saved)

regimes8.0ms (0.1%)

Accuracy

Total -1.0b remaining (-1.6%)

Threshold costs -1.0b (-1.6%)

Counts

2 → 1

Calls

Call 1

Inputs
N
(log.f64 1)

Outputs
N

Calls

1 calls:

7.0ms

Results

Error	Segments	Branch
61.1b	1	`N`

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	50
1	30	50
2	34	50
3	36	50
4	37	50

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(if (<=.f64 (-.f64 (log.f64 (+.f64 N 1)) (log.f64 N)) 4722366482869645/1180591620717411303424) (*.f64 (/.f64 1 N) (+.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) 1)) (log.f64 (/.f64 (+.f64 N 1) N)))
(/.f64 1 N)
N
(log.f64 1)

Outputs
(if (<=.f64 (-.f64 (log.f64 (+.f64 N 1)) (log.f64 N)) 4722366482869645/1180591620717411303424) (*.f64 (/.f64 1 N) (+.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) 1)) (log.f64 (/.f64 (+.f64 N 1) N)))
(if (<=.f64 (-.f64 (log.f64 (+.f64 N 1)) (log.f64 N)) 4722366482869645/1180591620717411303424) (*.f64 (/.f64 1 N) (+.f64 1 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N))) (log.f64 (/.f64 (+.f64 N 1) N)))
(/.f64 1 N)
N
(log.f64 1)
0

Compiler

Compiled 38 to 29 computations (23.7% saved)

soundness167.0ms (2.6%)

Algorithm

3×	egg-herbie

Rules

746×	`fma-def_binary64`
701×	`associate-l_binary64`
458×	`fma-neg_binary64`
427×	`cancel-sign-sub-inv_binary64`
415×	`times-frac_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	8
2	17	8
3	24	8
4	33	8
5	50	8
6	87	8
7	123	8
8	170	8
9	206	8
10	232	8
11	234	8
0	36	192
1	95	188
2	237	185
3	646	181
4	2109	181
0	7	11
1	12	8
2	17	8
3	24	8
4	33	8
5	50	8
6	87	8
7	123	8
8	170	8
9	206	8
10	232	8
11	234	8

Stop Event

1×	saturated
1×	node limit
1×	saturated

Compiler

Compiled 226 to 180 computations (20.4% saved)

end65.0ms (1%)

Compiler: Compiled 35 to 26 computations (25.7% saved)

Details

analyze3.0ms (0%)

sample2.5s (38.7%)

preprocess22.0ms (0.3%)

simplify11.0ms (0.2%)

eval1.0ms (0%)

prune1.0ms (0%)

localize7.0ms (0.1%)

series2.0ms (0%)

rewrite54.0ms (0.8%)

simplify54.0ms (0.8%)

eval22.0ms (0.3%)

prune11.0ms (0.2%)

localize10.0ms (0.1%)

series3.0ms (0%)

rewrite56.0ms (0.9%)

simplify39.0ms (0.6%)

localize3.0ms (0%)

localize10.0ms (0.2%)

series3.0ms (0%)

rewrite100.0ms (1.5%)

simplify50.0ms (0.8%)

localize19.0ms (0.3%)

series30.0ms (0.5%)

rewrite179.0ms (2.7%)

simplify62.0ms (0.9%)

localize5.0ms (0.1%)

eval383.0ms (5.8%)

prune84.0ms (1.3%)

localize5.0ms (0.1%)

series9.0ms (0.1%)

rewrite47.0ms (0.7%)

simplify161.0ms (2.5%)

localize2.0ms (0%)

localize8.0ms (0.1%)

series2.0ms (0%)

rewrite53.0ms (0.8%)

simplify44.0ms (0.7%)

localize13.0ms (0.2%)

series1.0ms (0%)

rewrite177.0ms (2.7%)

simplify68.0ms (1%)

localize52.0ms (0.8%)

series6.0ms (0.1%)

rewrite129.0ms (2%)

simplify155.0ms (2.4%)

eval359.0ms (5.5%)

prune188.0ms (2.9%)

localize16.0ms (0.2%)

series55.0ms (0.8%)

rewrite80.0ms (1.2%)

simplify67.0ms (1%)

localize18.0ms (0.3%)

series1.0ms (0%)

rewrite64.0ms (1%)

simplify57.0ms (0.9%)

localize15.0ms (0.2%)

series1.0ms (0%)

rewrite103.0ms (1.6%)

simplify43.0ms (0.7%)

eval326.0ms (5%)

prune109.0ms (1.7%)

regimes94.0ms (1.4%)

bsearch1.0ms (0%)

regimes16.0ms (0.3%)

regimes8.0ms (0.1%)

simplify8.0ms (0.1%)

soundness167.0ms (2.6%)

end65.0ms (1%)

Profiling