Details

analyze3.0ms (0.1%)

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)

sample2.4s (63.3%)

Results

1.1s	2029×	body	1024	valid
475.0ms	4213×	body	64	valid
372.0ms	992×	body	512	valid
192.0ms	278×	body	2048	valid
158.0ms	498×	body	256	valid
44.0ms	246×	body	128	valid

preprocess19.0ms (0.5%)

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	164	8
9	200	8
10	226	8
11	228	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 8 to 6 computations (25% saved)

simplify10.0ms (0.3%)

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	164	8
9	200	8
10	226	8
11	228	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))

prune2.0ms (0.1%)

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

28.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	28.2b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 25 to 16 computations (36% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.8b	(-.f64 (log1p.f64 N) (log.f64 N))

series4.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	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))

rewrite64.0ms (1.7%)

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	1449	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 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)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (-.f64 (/.f64 (+.f64 N 1) N) 1))))))

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 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)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (-.f64 (/.f64 (+.f64 N 1) N) 1))))))

simplify28.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

746×	`fma-def_binary64`
701×	`associate-l_binary64`
458×	`fma-neg_binary64`
425×	`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	643	181
4	2042	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 N (.f64 N -1/2)) (log.f64 N)))
(-.f64 (fma.f64 N (*.f64 N -1/2) N) (log.f64 N))
(fma.f64 N (*.f64 N -1/2) (-.f64 N (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 N (*.f64 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 1 N) (-.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1/2 (*.f64 N N))))
(+.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 1 N) (-.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/3 (pow.f64 N 3))))
(+.f64 (/.f64 1/3 (pow.f64 N 3)) (-.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 (.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 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 1 N) (/.f64 -1/4 (pow.f64 N 4))) (-.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/3 (pow.f64 N 3))))
(+.f64 (/.f64 1/3 (pow.f64 N 3)) (+.f64 (/.f64 1 N) (-.f64 (/.f64 -1/4 (pow.f64 N 4)) (/.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 (/.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 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 1 N) (-.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/3 (pow.f64 N 3))))
(+.f64 (/.f64 1/3 (pow.f64 N 3)) (-.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 (.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 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 1 N) (/.f64 -1/4 (pow.f64 N 4))) (-.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/3 (pow.f64 N 3))))
(+.f64 (/.f64 1/3 (pow.f64 N 3)) (+.f64 (/.f64 1 N) (-.f64 (/.f64 -1/4 (pow.f64 N 4)) (/.f64 (/.f64 1/2 N) N))))

prune47.0ms (1.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	47	3	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	3	51

Error

0.0b

Counts

51 → 3

Alt Table

Status	Error	Program
	28.6b	(fma.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log1p.f64 N)) (neg.f64 (log.f64 N)))
	33.0b	(+.f64 (/.f64 1/3 (pow.f64 N 3)) (+.f64 (/.f64 1 N) (-.f64 (/.f64 -1/4 (pow.f64 N 4)) (/.f64 (/.f64 1/2 N) N))))
▶	28.0b	(log.f64 (/.f64 (+.f64 N 1) N))

Status

Error

Program

28.6b

(fma.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log1p.f64 N)) (neg.f64 (log.f64 N)))

33.0b

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

▶

28.0b

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

Compiler

Compiled 711 to 342 computations (51.9% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 N 1) N)
✓	2.8b	(log.f64 (/.f64 (+.f64 N 1) N))

series3.0ms (0.1%)

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

rewrite50.0ms (1.3%)

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	1703	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)))))))

simplify29.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

746×	`fma-def_binary64`
699×	`associate-l_binary64`
458×	`fma-neg_binary64`
425×	`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	647	250
4	2042	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 (-.f64 N (log.f64 N)) (.f64 -1/2 (.f64 N 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 (-.f64 N (log.f64 N)) (fma.f64 -1/2 (.f64 N N) (.f64 1/3 (pow.f64 N 3))))
(+.f64 N (-.f64 (.f64 (.f64 N N) (+.f64 -1/2 (*.f64 N 1/3))) (log.f64 N)))
(fma.f64 N (*.f64 N (fma.f64 N 1/3 -1/2)) (-.f64 N (log.f64 N)))
(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 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 1/3 (pow.f64 N 3)) (-.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 (.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 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 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 1 N) (+.f64 (/.f64 1/3 (pow.f64 N 3)) (-.f64 (/.f64 -1/4 (pow.f64 N 4)) (/.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 (/.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 1/3 (pow.f64 N 3)) (-.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 (.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 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 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 1 N) (+.f64 (/.f64 1/3 (pow.f64 N 3)) (-.f64 (/.f64 -1/4 (pow.f64 N 4)) (/.f64 (/.f64 1/2 N) 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))

prune94.0ms (2.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	77	3	80

Error

0.0b

Counts

80 → 3

Alt Table

Status

Error

Program

▶

28.6b

(fma.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log1p.f64 N)) (neg.f64 (log.f64 N)))

33.0b

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

✓

28.0b

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

Compiler

Compiled 908 to 554 computations (39% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (log1p.f64 N))
✓	28.5b	(fma.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log1p.f64 N)) (neg.f64 (log.f64 N)))

series10.0ms (0.3%)

Counts

2 → 17

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	N	@	-inf	(fma.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log1p.f64 N)) (neg.f64 (log.f64 N)))
2.0ms	N	@	0	(fma.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log1p.f64 N)) (neg.f64 (log.f64 N)))
1.0ms	N	@	inf	(fma.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log1p.f64 N)) (neg.f64 (log.f64 N)))
1.0ms	N	@	-inf	(sqrt.f64 (log1p.f64 N))
1.0ms	N	@	inf	(sqrt.f64 (log1p.f64 N))

rewrite43.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

527×	`pow1_binary64`
506×	`add-sqr-sqrt_binary64`
486×	`add-log-exp_binary64`
485×	`expm1-log1p-u_binary64`
484×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	139	13
2	1630	13

Stop Event

1×	node limit

Counts

2 → 42

Calls

Call 1

Inputs
(fma.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log1p.f64 N)) (neg.f64 (log.f64 N)))
(sqrt.f64 (log1p.f64 N))

Outputs

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

simplify57.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

565×	`fma-def_binary64`
451×	`fma-neg_binary64`
381×	`cancel-sign-sub-inv_binary64`
353×	`associate-+l+_binary64`
336×	`associate-/r*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	122	1437
1	387	1162
2	1333	902
3	5896	616

Stop Event

1×	node limit

Counts

59 → 74

Calls

Call 1

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

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

prune110.0ms (2.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	109	3	112

Error

0.0b

Counts

112 → 3

Alt Table

Status

Error

Program

✓

28.6b

(fma.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log1p.f64 N)) (neg.f64 (log.f64 N)))

▶

33.0b

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

✓

28.0b

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

Compiler

Compiled 2995 to 1880 computations (37.2% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 -1/4 (pow.f64 N 4))
✓	0.1b	(/.f64 (/.f64 1/2 N) N)
✓	0.4b	(/.f64 1/3 (pow.f64 N 3))
✓	22.0b	(+.f64 (/.f64 1/3 (pow.f64 N 3)) (-.f64 (/.f64 -1/4 (pow.f64 N 4)) (/.f64 (/.f64 1/2 N) N)))

series6.0ms (0.2%)

Counts

4 → 24

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	N	@	0	(/.f64 (/.f64 1/2 N) N)
1.0ms	N	@	0	(+.f64 (/.f64 1/3 (pow.f64 N 3)) (-.f64 (/.f64 -1/4 (pow.f64 N 4)) (/.f64 (/.f64 1/2 N) N)))
1.0ms	N	@	0	(/.f64 1/3 (pow.f64 N 3))
1.0ms	N	@	0	(/.f64 -1/4 (pow.f64 N 4))
0.0ms	N	@	inf	(+.f64 (/.f64 1/3 (pow.f64 N 3)) (-.f64 (/.f64 -1/4 (pow.f64 N 4)) (/.f64 (/.f64 1/2 N) N)))

rewrite104.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

634×	`fma-def_binary64`
389×	`log-div_binary64`
371×	`fma-neg_binary64`
306×	`expm1-udef_binary64`
306×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	46
1	369	42
2	5259	42

Stop Event

1×	node limit

Counts

4 → 181

Calls

Call 1

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

Outputs
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(pow.f64 N -4) (/.f64 1/2 (.f64 N N)))) (.f64 1/3 (pow.f64 N -3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (cbrt.f64 (fma.f64 -1/4 (pow.f64 N -4) (.f64 1/3 (pow.f64 N -3)))) (cbrt.f64 (fma.f64 -1/4 (pow.f64 N -4) (.f64 1/3 (pow.f64 N -3))))) (cbrt.f64 (fma.f64 -1/4 (pow.f64 N -4) (.f64 1/3 (pow.f64 N -3)))) (/.f64 (/.f64 -1/2 N) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 -1/4 (pow.f64 N -4) (.f64 1/3 (pow.f64 N -3)))) (sqrt.f64 (fma.f64 -1/4 (pow.f64 N -4) (.f64 1/3 (pow.f64 N -3)))) (/.f64 (/.f64 -1/2 N) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (/.f64 (sqrt.f64 -1/4) (.f64 N N)) (/.f64 (sqrt.f64 1/2) N)) (-.f64 (/.f64 (sqrt.f64 -1/4) (.f64 N N)) (/.f64 (sqrt.f64 1/2) N)) (*.f64 1/3 (pow.f64 N -3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 1/3 (pow.f64 N -3) (fma.f64 -1/4 (pow.f64 N -4) (/.f64 (/.f64 -1/2 N) N)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 1/3 (pow.f64 N -3)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/3 (pow.f64 N -3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 1/3 (pow.f64 N -3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 1/3 (pow.f64 N -3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 1/3) N) (pow.f64 (/.f64 (cbrt.f64 1/3) N) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (/.f64 (cbrt.f64 1/3) N) 2) (/.f64 (cbrt.f64 1/3) N))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 1/3) (pow.f64 N 3/2)) (/.f64 (sqrt.f64 1/3) (pow.f64 N 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1/3 (/.f64 1 (neg.f64 (pow.f64 N 3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 N -3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/3 (pow.f64 N -3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (cbrt.f64 1/3) N) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 1/3) (pow.f64 N 3/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/27 (.f64 (pow.f64 N 8) N)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 N 3) 3) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1/9 (pow.f64 N 6)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/3) (pow.f64 N -3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 1/3 (pow.f64 N -3)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 1/27 (.f64 (pow.f64 N 8) N)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 1/3 (pow.f64 N -3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 1/3 (pow.f64 N -3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 1/3 (pow.f64 N -3))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 1/3 (pow.f64 N -3))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1/2 (.f64 N N)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (.f64 (/.f64 1 N) (/.f64 1 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (/.f64 (/.f64 1 N) N))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (/.f64 1 (.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/2 N) (/.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/2 (.f64 N N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 1/2 (.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 1/4 (.f64 N N))) (.f64 (cbrt.f64 (/.f64 1/2 N)) (/.f64 1 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 1/2 (.f64 N N))) (cbrt.f64 (/.f64 1/4 (pow.f64 N 4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 1/4 (pow.f64 N 4))) (cbrt.f64 (/.f64 1/2 (.f64 N N))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 1/2 N)) (.f64 (sqrt.f64 (/.f64 1/2 N)) (/.f64 1 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 1/2) N) (/.f64 (sqrt.f64 1/2) N))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 -1/2 N) (/.f64 1 (neg.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 N) (/.f64 1/2 N))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (/.f64 1/4 (.f64 N N))) 1) (/.f64 (cbrt.f64 (/.f64 1/2 N)) N))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (/.f64 1/2 N)) 1) (/.f64 (sqrt.f64 (/.f64 1/2 N)) N))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/2 (cbrt.f64 (.f64 N N))) (/.f64 (/.f64 1 N) (cbrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 (.f64 N N))) (/.f64 (/.f64 1/2 N) (cbrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (/.f64 1/4 (.f64 N N))) (cbrt.f64 (.f64 N N))) (cbrt.f64 (/.f64 1/2 (.f64 N N))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (/.f64 1/2 N)) (cbrt.f64 (.f64 N N))) (/.f64 (sqrt.f64 (/.f64 1/2 N)) (cbrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/2 (sqrt.f64 N)) (/.f64 (/.f64 1 N) (sqrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (sqrt.f64 N)) (/.f64 (/.f64 1/2 N) (sqrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (/.f64 1/4 (.f64 N N))) (sqrt.f64 N)) (/.f64 (cbrt.f64 (/.f64 1/2 N)) (sqrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/2 (.f64 N N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 1/2 (.f64 N N))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 1/2) N) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/8 (pow.f64 N 6)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 N (.f64 N 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (/.f64 1/2 N) (neg.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1/4 (pow.f64 N 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1/2 (.f64 N N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1/2 (.f64 N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 1/8 (pow.f64 N 6)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1/2 (.f64 N N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 1/2 (.f64 N N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 1/2 (.f64 N N))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1/2 (*.f64 N N))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 -1/4 (pow.f64 N -4)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1/4 (pow.f64 N -4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 -1/4 (pow.f64 N -4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 -1/4 (pow.f64 N -4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/4 (/.f64 1 (neg.f64 (pow.f64 N 4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 -1/4 (pow.f64 N -4))) (cbrt.f64 (/.f64 1/16 (pow.f64 N 8))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 1/16 (pow.f64 N 8))) (cbrt.f64 (.f64 -1/4 (pow.f64 N -4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 -1/4) (.f64 N N)) (/.f64 (sqrt.f64 -1/4) (.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 N -4) -1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 -1/4 (pow.f64 N -4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 -1/4 (pow.f64 N -4))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 -1/4) (.f64 N N)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 -1/64 (pow.f64 (pow.f64 N -4) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 N 4) -4) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1/16 (pow.f64 N 8)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 -1/4) (pow.f64 N -4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 -1/4 (pow.f64 N -4)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 -1/64 (pow.f64 (pow.f64 N -4) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 -1/4 (pow.f64 N -4))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 -1/4 (pow.f64 N -4))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 -1/4 (pow.f64 N -4))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 -1/4 (pow.f64 N -4))))))))

simplify64.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

457×	`times-frac_binary64`
442×	`distribute-rgt-neg-in_binary64`
402×	`distribute-lft-neg-in_binary64`
356×	`div-sub_binary64`
337×	`associate-/l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	303
1	68	303
2	145	303
3	334	303
4	1118	303
5	5064	303
6	7158	303

Stop Event

1×	node limit

Counts

205 → 192

Calls

Call 1

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

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

prune562.0ms (14.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	192	0	192
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	192	3	195

Error

0.0b

Counts

195 → 3

Alt Table

Status

Error

Program

✓

28.6b

(fma.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log1p.f64 N)) (neg.f64 (log.f64 N)))

✓

33.0b

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

✓

28.0b

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

Compiler

Compiled 5521 to 4244 computations (23.1% saved)

regimes17.0ms (0.5%)

Accuracy

Total -61.8b remaining (-395461.6%)

Threshold costs -61.8b (-395461.6%)

Counts

6 → 2

Calls

Call 1

Inputs
(+.f64 (/.f64 1 N) (+.f64 (/.f64 1/3 (pow.f64 N 3)) (-.f64 (/.f64 -1/4 (pow.f64 N 4)) (/.f64 (/.f64 1/2 N) N))))
(fma.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log1p.f64 N)) (neg.f64 (log.f64 N)))
(+.f64 (/.f64 1/3 (pow.f64 N 3)) (+.f64 (/.f64 1 N) (-.f64 (/.f64 -1/4 (pow.f64 N 4)) (/.f64 (/.f64 1/2 N) N))))
(log.f64 (/.f64 (+.f64 N 1) N))
(-.f64 (log1p.f64 N) (log.f64 N))
(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))

Outputs
(+.f64 (/.f64 1 N) (+.f64 (/.f64 1/3 (pow.f64 N 3)) (-.f64 (/.f64 -1/4 (pow.f64 N 4)) (/.f64 (/.f64 1/2 N) N))))
(fma.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log1p.f64 N)) (neg.f64 (log.f64 N)))

Results

9.0ms	0.0b	`N`
6.0ms	0.0b	`(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))`

Compiler

Compiled 81 to 54 computations (33.3% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Calls

1 calls:

0.0ms

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

Steps

Iters	Point		Range
0.0002	∈ [	0.00015871288649549342	,	0.03589865757789745	]

Compiler

Compiled 12 to 9 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	64
1	41	64
2	49	64
3	57	64
4	60	64
5	61	64

Stop Event

1×

saturated

Calls

Call 1

Inputs

(if (<=.f64 (-.f64 (log.f64 (+.f64 N 1)) (log.f64 N)) 7378697629483821/36893488147419103232) (+.f64 (/.f64 1 N) (+.f64 (/.f64 1/3 (pow.f64 N 3)) (-.f64 (/.f64 -1/4 (pow.f64 N 4)) (/.f64 (/.f64 1/2 N) N)))) (fma.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log1p.f64 N)) (neg.f64 (log.f64 N))))

Outputs

(if (<=.f64 (-.f64 (log.f64 (+.f64 N 1)) (log.f64 N)) 7378697629483821/36893488147419103232) (+.f64 (/.f64 1 N) (+.f64 (/.f64 1/3 (pow.f64 N 3)) (-.f64 (/.f64 -1/4 (pow.f64 N 4)) (/.f64 (/.f64 1/2 N) N)))) (fma.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log1p.f64 N)) (neg.f64 (log.f64 N))))

(if (<=.f64 (-.f64 (log.f64 (+.f64 N 1)) (log.f64 N)) 7378697629483821/36893488147419103232) (+.f64 (/.f64 1 N) (+.f64 (/.f64 1/3 (pow.f64 N 3)) (+.f64 (/.f64 -1/4 (pow.f64 N 4)) (/.f64 (/.f64 -1/2 N) N)))) (fma.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log1p.f64 N)) (neg.f64 (log.f64 N))))

end29.0ms (0.8%)

Stop Event

1×

done

Compiler

Compiled 84 to 58 computations (31% saved)

Details

analyze3.0ms (0.1%)

sample2.4s (63.3%)

preprocess19.0ms (0.5%)

simplify10.0ms (0.3%)

prune2.0ms (0.1%)

localize5.0ms (0.1%)

series4.0ms (0.1%)

rewrite64.0ms (1.7%)

simplify28.0ms (0.8%)

prune47.0ms (1.2%)

localize4.0ms (0.1%)

series3.0ms (0.1%)

rewrite50.0ms (1.3%)

simplify29.0ms (0.8%)

prune94.0ms (2.5%)

localize8.0ms (0.2%)

series10.0ms (0.3%)

rewrite43.0ms (1.1%)

simplify57.0ms (1.5%)

prune110.0ms (2.9%)

localize12.0ms (0.3%)

series6.0ms (0.2%)

rewrite104.0ms (2.7%)

simplify64.0ms (1.7%)

prune562.0ms (14.9%)

regimes17.0ms (0.5%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end29.0ms (0.8%)

Profiling