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
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample2.1s (61.1%)

Results

893.0ms	2062×	body	1024	valid
544.0ms	4413×	body	128	valid
333.0ms	1013×	body	512	valid
191.0ms	223×	body	2048	valid
107.0ms	545×	body	256	valid

preprocess19.0ms (0.6%)

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

28.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	28.5b	(-.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
✓	3.9b	(-.f64 (log1p.f64 N) (log.f64 N))

series2.0ms (0.1%)

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))

rewrite36.0ms (1.1%)

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 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 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 expm1.f64 (log1p.f64 (-.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 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 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 expm1.f64 (log1p.f64 (-.f64 (log1p.f64 N) (log.f64 N))))))))

simplify24.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

746×	`fma-def_binary64`
458×	`fma-neg_binary64`
425×	`cancel-sign-sub-inv_binary64`
415×	`times-frac_binary64`
169×	`unswap-sqr_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))))

prune86.0ms (2.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	46	4	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	4	51

Error

0.0b

Counts

51 → 4

Alt Table

Status	Error	Program
	29.2b	(pow.f64 (cbrt.f64 (-.f64 (log1p.f64 N) (log.f64 N))) 3)
	29.6b	(+.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)))
	32.9b	(+.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))))
▶	28.4b	(log.f64 (/.f64 (+.f64 N 1) N))

Compiler

Compiled 745 to 364 computations (51.1% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 N 1) N)
✓	4.0b	(log.f64 (/.f64 (+.f64 N 1) N))

series3.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite42.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

680×	`pow1_binary64`
635×	`log1p-expm1-u_binary64`
635×	`expm1-log1p-u_binary64`
634×	`add-log-exp_binary64`
64×	`add-sqr-sqrt_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 (exp.f64 (log1p.f64 (-.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 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 expm1.f64 (log1p.f64 (-.f64 (log1p.f64 N) (log.f64 N))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.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 log.f64 (+.f64 1 (expm1.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 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)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.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 (exp.f64 (log1p.f64 (-.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 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 expm1.f64 (log1p.f64 (-.f64 (log1p.f64 N) (log.f64 N))))))))

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

simplify27.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

746×	`fma-def_binary64`
458×	`fma-neg_binary64`
425×	`cancel-sign-sub-inv_binary64`
415×	`times-frac_binary64`
169×	`unswap-sqr_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))

prune143.0ms (4.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	76	5	81

Error

0.0b

Counts

81 → 5

Alt Table

Status	Error	Program
	32.9b	(+.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))))
	29.2b	(pow.f64 (cbrt.f64 (-.f64 (log1p.f64 N) (log.f64 N))) 3)
	29.6b	(+.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)))
▶	28.5b	(+.f64 (log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N))) (log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N))))
✓	28.4b	(log.f64 (/.f64 (+.f64 N 1) N))

Compiler

Compiled 974 to 599 computations (38.5% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (+.f64 N 1) N)
✓	0.1b	(sqrt.f64 (/.f64 (+.f64 N 1) N))
✓	4.1b	(log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N)))

series4.0ms (0.1%)

Counts

2 → 16

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	N	@	0	(log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N)))
1.0ms	N	@	inf	(log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N)))
0.0ms	N	@	0	(sqrt.f64 (/.f64 (+.f64 N 1) N))
0.0ms	N	@	-inf	(log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N)))
0.0ms	N	@	inf	(sqrt.f64 (/.f64 (+.f64 N 1) N))

rewrite43.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

755×	`pow1_binary64`
705×	`log1p-expm1-u_binary64`
705×	`expm1-log1p-u_binary64`
73×	`add-sqr-sqrt_binary64`
70×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
1	147	20
2	1935	20

Stop Event

1×	node limit

Counts

2 → 54

Calls

Call 1

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

Outputs

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

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

simplify25.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

844×	`times-frac_binary64`
599×	`fma-def_binary64`
488×	`associate-/l/_binary64`
359×	`fma-neg_binary64`
317×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	34	238
1	101	238
2	244	238
3	604	238
4	1824	234

Stop Event

1×	node limit

Counts

70 → 68

Calls

Call 1

Inputs
(/.f64 1/2 N)
(-.f64 (.f64 1/2 (/.f64 1 N)) (.f64 1/4 (/.f64 1 (pow.f64 N 2))))
(-.f64 (+.f64 (.f64 1/6 (/.f64 1 (pow.f64 N 3))) (.f64 1/2 (/.f64 1 N))) (*.f64 1/4 (/.f64 1 (pow.f64 N 2))))
(-.f64 (+.f64 (.f64 1/6 (/.f64 1 (pow.f64 N 3))) (.f64 1/2 (/.f64 1 N))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 N 4))) (.f64 1/4 (/.f64 1 (pow.f64 N 2)))))
(/.f64 1/2 N)
(-.f64 (.f64 1/2 (/.f64 1 N)) (.f64 1/4 (/.f64 1 (pow.f64 N 2))))
(-.f64 (+.f64 (.f64 1/6 (/.f64 1 (pow.f64 N 3))) (.f64 1/2 (/.f64 1 N))) (*.f64 1/4 (/.f64 1 (pow.f64 N 2))))
(-.f64 (+.f64 (.f64 1/6 (/.f64 1 (pow.f64 N 3))) (.f64 1/2 (/.f64 1 N))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 N 4))) (.f64 1/4 (/.f64 1 (pow.f64 N 2)))))
1
(+.f64 1 (*.f64 1/2 (/.f64 1 N)))
(-.f64 (+.f64 1 (.f64 1/2 (/.f64 1 N))) (.f64 1/8 (/.f64 1 (pow.f64 N 2))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 N 3))) (+.f64 1 (.f64 1/2 (/.f64 1 N)))) (*.f64 1/8 (/.f64 1 (pow.f64 N 2))))
1
(+.f64 1 (*.f64 1/2 (/.f64 1 N)))
(-.f64 (+.f64 1 (.f64 1/2 (/.f64 1 N))) (.f64 1/8 (/.f64 1 (pow.f64 N 2))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 N 3))) (+.f64 1 (.f64 1/2 (/.f64 1 N)))) (*.f64 1/8 (/.f64 1 (pow.f64 N 2))))

Outputs
(/.f64 1/2 N)
(-.f64 (.f64 1/2 (/.f64 1 N)) (.f64 1/4 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1/2 N) (/.f64 1/4 (*.f64 N N)))
(+.f64 (/.f64 1/2 N) (/.f64 -1/4 (*.f64 N N)))
(-.f64 (/.f64 1/2 N) (/.f64 (/.f64 1/4 N) N))
(-.f64 (+.f64 (.f64 1/6 (/.f64 1 (pow.f64 N 3))) (.f64 1/2 (/.f64 1 N))) (*.f64 1/4 (/.f64 1 (pow.f64 N 2))))
(-.f64 (+.f64 (/.f64 1/2 N) (/.f64 1/6 (pow.f64 N 3))) (/.f64 1/4 (*.f64 N N)))
(+.f64 (/.f64 1/2 N) (-.f64 (/.f64 1/6 (pow.f64 N 3)) (/.f64 1/4 (*.f64 N N))))
(+.f64 (/.f64 1/2 N) (+.f64 (/.f64 1/6 (pow.f64 N 3)) (/.f64 -1/4 (*.f64 N N))))
(+.f64 (+.f64 (/.f64 1/2 N) (/.f64 1/6 (pow.f64 N 3))) (/.f64 -1/4 (*.f64 N N)))
(+.f64 (/.f64 1/2 N) (-.f64 (/.f64 1/6 (pow.f64 N 3)) (/.f64 (/.f64 1/4 N) N)))
(-.f64 (+.f64 (.f64 1/6 (/.f64 1 (pow.f64 N 3))) (.f64 1/2 (/.f64 1 N))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 N 4))) (.f64 1/4 (/.f64 1 (pow.f64 N 2)))))
(-.f64 (+.f64 (/.f64 1/2 N) (/.f64 1/6 (pow.f64 N 3))) (+.f64 (/.f64 1/4 (*.f64 N N)) (/.f64 1/8 (pow.f64 N 4))))
(+.f64 (/.f64 1/2 N) (-.f64 (/.f64 1/6 (pow.f64 N 3)) (+.f64 (/.f64 1/4 (*.f64 N N)) (/.f64 1/8 (pow.f64 N 4)))))
(+.f64 (/.f64 1/2 N) (+.f64 (/.f64 1/6 (pow.f64 N 3)) (+.f64 (/.f64 -1/4 (*.f64 N N)) (/.f64 -1/8 (pow.f64 N 4)))))
(+.f64 (/.f64 1/2 N) (+.f64 (/.f64 -1/4 (*.f64 N N)) (-.f64 (/.f64 1/6 (pow.f64 N 3)) (/.f64 1/8 (pow.f64 N 4)))))
(+.f64 (/.f64 1/2 N) (fma.f64 (/.f64 1 (pow.f64 N 3)) (+.f64 1/6 (/.f64 -1/8 N)) (/.f64 -1/4 (*.f64 N N))))
(/.f64 1/2 N)
(-.f64 (.f64 1/2 (/.f64 1 N)) (.f64 1/4 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1/2 N) (/.f64 1/4 (*.f64 N N)))
(+.f64 (/.f64 1/2 N) (/.f64 -1/4 (*.f64 N N)))
(-.f64 (/.f64 1/2 N) (/.f64 (/.f64 1/4 N) N))
(-.f64 (+.f64 (.f64 1/6 (/.f64 1 (pow.f64 N 3))) (.f64 1/2 (/.f64 1 N))) (*.f64 1/4 (/.f64 1 (pow.f64 N 2))))
(-.f64 (+.f64 (/.f64 1/2 N) (/.f64 1/6 (pow.f64 N 3))) (/.f64 1/4 (*.f64 N N)))
(+.f64 (/.f64 1/2 N) (-.f64 (/.f64 1/6 (pow.f64 N 3)) (/.f64 1/4 (*.f64 N N))))
(+.f64 (/.f64 1/2 N) (+.f64 (/.f64 1/6 (pow.f64 N 3)) (/.f64 -1/4 (*.f64 N N))))
(+.f64 (+.f64 (/.f64 1/2 N) (/.f64 1/6 (pow.f64 N 3))) (/.f64 -1/4 (*.f64 N N)))
(+.f64 (/.f64 1/2 N) (-.f64 (/.f64 1/6 (pow.f64 N 3)) (/.f64 (/.f64 1/4 N) N)))
(-.f64 (+.f64 (.f64 1/6 (/.f64 1 (pow.f64 N 3))) (.f64 1/2 (/.f64 1 N))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 N 4))) (.f64 1/4 (/.f64 1 (pow.f64 N 2)))))
(-.f64 (+.f64 (/.f64 1/2 N) (/.f64 1/6 (pow.f64 N 3))) (+.f64 (/.f64 1/4 (*.f64 N N)) (/.f64 1/8 (pow.f64 N 4))))
(+.f64 (/.f64 1/2 N) (-.f64 (/.f64 1/6 (pow.f64 N 3)) (+.f64 (/.f64 1/4 (*.f64 N N)) (/.f64 1/8 (pow.f64 N 4)))))
(+.f64 (/.f64 1/2 N) (+.f64 (/.f64 1/6 (pow.f64 N 3)) (+.f64 (/.f64 -1/4 (*.f64 N N)) (/.f64 -1/8 (pow.f64 N 4)))))
(+.f64 (/.f64 1/2 N) (+.f64 (/.f64 -1/4 (*.f64 N N)) (-.f64 (/.f64 1/6 (pow.f64 N 3)) (/.f64 1/8 (pow.f64 N 4)))))
(+.f64 (/.f64 1/2 N) (fma.f64 (/.f64 1 (pow.f64 N 3)) (+.f64 1/6 (/.f64 -1/8 N)) (/.f64 -1/4 (*.f64 N N))))
1
(+.f64 1 (*.f64 1/2 (/.f64 1 N)))
(+.f64 1 (/.f64 1/2 N))
(-.f64 (+.f64 1 (.f64 1/2 (/.f64 1 N))) (.f64 1/8 (/.f64 1 (pow.f64 N 2))))
(+.f64 1 (-.f64 (/.f64 1/2 N) (/.f64 1/8 (*.f64 N N))))
(+.f64 (/.f64 1/2 N) (-.f64 1 (/.f64 (/.f64 1/8 N) N)))
(-.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 N 3))) (+.f64 1 (.f64 1/2 (/.f64 1 N)))) (*.f64 1/8 (/.f64 1 (pow.f64 N 2))))
(+.f64 (/.f64 1/16 (pow.f64 N 3)) (+.f64 1 (-.f64 (/.f64 1/2 N) (/.f64 1/8 (*.f64 N N)))))
(+.f64 (+.f64 1 (/.f64 1/2 N)) (-.f64 (/.f64 1/16 (pow.f64 N 3)) (/.f64 1/8 (*.f64 N N))))
(+.f64 1 (+.f64 (/.f64 1/2 N) (-.f64 (/.f64 1/16 (pow.f64 N 3)) (/.f64 1/8 (*.f64 N N)))))
(+.f64 (+.f64 1 (/.f64 1/2 N)) (-.f64 (/.f64 1/16 (pow.f64 N 3)) (/.f64 (/.f64 1/8 N) N)))
(+.f64 (/.f64 1/2 N) (+.f64 1 (-.f64 (/.f64 1/16 (pow.f64 N 3)) (/.f64 (/.f64 1/8 N) N))))
1
(+.f64 1 (*.f64 1/2 (/.f64 1 N)))
(+.f64 1 (/.f64 1/2 N))
(-.f64 (+.f64 1 (.f64 1/2 (/.f64 1 N))) (.f64 1/8 (/.f64 1 (pow.f64 N 2))))
(+.f64 1 (-.f64 (/.f64 1/2 N) (/.f64 1/8 (*.f64 N N))))
(+.f64 (/.f64 1/2 N) (-.f64 1 (/.f64 (/.f64 1/8 N) N)))
(-.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 N 3))) (+.f64 1 (.f64 1/2 (/.f64 1 N)))) (*.f64 1/8 (/.f64 1 (pow.f64 N 2))))
(+.f64 (/.f64 1/16 (pow.f64 N 3)) (+.f64 1 (-.f64 (/.f64 1/2 N) (/.f64 1/8 (*.f64 N N)))))
(+.f64 (+.f64 1 (/.f64 1/2 N)) (-.f64 (/.f64 1/16 (pow.f64 N 3)) (/.f64 1/8 (*.f64 N N))))
(+.f64 1 (+.f64 (/.f64 1/2 N) (-.f64 (/.f64 1/16 (pow.f64 N 3)) (/.f64 1/8 (*.f64 N N)))))
(+.f64 (+.f64 1 (/.f64 1/2 N)) (-.f64 (/.f64 1/16 (pow.f64 N 3)) (/.f64 (/.f64 1/8 N) N)))
(+.f64 (/.f64 1/2 N) (+.f64 1 (-.f64 (/.f64 1/16 (pow.f64 N 3)) (/.f64 (/.f64 1/8 N) N))))

prune534.0ms (15.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	210	0	210
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	210	5	215

Error

0.0b

Counts

215 → 5

Alt Table

Status	Error	Program
	32.9b	(+.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))))
▶	29.2b	(pow.f64 (cbrt.f64 (-.f64 (log1p.f64 N) (log.f64 N))) 3)
	29.6b	(+.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)))
✓	28.5b	(+.f64 (log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N))) (log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N))))
✓	28.4b	(log.f64 (/.f64 (+.f64 N 1) N))

Compiler

Compiled 4312 to 3081 computations (28.5% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(cbrt.f64 (-.f64 (log1p.f64 N) (log.f64 N)))
✓	0.4b	(pow.f64 (cbrt.f64 (-.f64 (log1p.f64 N) (log.f64 N))) 3)
	3.9b	(-.f64 (log1p.f64 N) (log.f64 N))

series17.0ms (0.5%)

Counts

2 → 8

Calls

6 calls:

Time	Variable		Point	Expression
8.0ms	N	@	0	(pow.f64 (cbrt.f64 (-.f64 (log1p.f64 N) (log.f64 N))) 3)
5.0ms	N	@	inf	(pow.f64 (cbrt.f64 (-.f64 (log1p.f64 N) (log.f64 N))) 3)
2.0ms	N	@	-inf	(pow.f64 (cbrt.f64 (-.f64 (log1p.f64 N) (log.f64 N))) 3)
1.0ms	N	@	0	(cbrt.f64 (-.f64 (log1p.f64 N) (log.f64 N)))
1.0ms	N	@	inf	(cbrt.f64 (-.f64 (log1p.f64 N) (log.f64 N)))

rewrite41.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

744×	`pow1_binary64`
700×	`expm1-log1p-u_binary64`
699×	`log1p-expm1-u_binary64`
76×	`add-sqr-sqrt_binary64`
74×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	173	18
2	1933	18

Stop Event

1×	node limit

Counts

2 → 68

Calls

Call 1

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

simplify38.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

775×	`fma-def_binary64`
387×	`distribute-rgt-in_binary64`
385×	`distribute-lft-in_binary64`
170×	`associate-r_binary64`
147×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	130	1479
1	438	1447
2	1763	1361

Stop Event

1×	node limit

Counts

76 → 84

Calls

Call 1

Inputs
(*.f64 -1 (log.f64 N))
(+.f64 (.f64 -1 (log.f64 N)) (.f64 N (+.f64 (.f64 2/3 (.f64 (pow.f64 (pow.f64 (log.f64 N) 4) 1/9) (pow.f64 (pow.f64 (cbrt.f64 -1) 4) 1/3))) (.f64 1/3 (.f64 (pow.f64 (pow.f64 (log.f64 N) 4) 1/9) (pow.f64 (pow.f64 (cbrt.f64 -1) 4) 1/3))))))
(+.f64 (.f64 -1 (log.f64 N)) (+.f64 (.f64 N (+.f64 (.f64 2/3 (.f64 (pow.f64 (pow.f64 (log.f64 N) 4) 1/9) (pow.f64 (pow.f64 (cbrt.f64 -1) 4) 1/3))) (.f64 1/3 (.f64 (pow.f64 (pow.f64 (log.f64 N) 4) 1/9) (pow.f64 (pow.f64 (cbrt.f64 -1) 4) 1/3))))) (.f64 (pow.f64 N 2) (+.f64 (.f64 -1/3 (+.f64 1/2 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3))))) (+.f64 (.f64 2/9 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3))) (.f64 (pow.f64 (log.f64 N) 1/3) (.f64 (cbrt.f64 -1) (+.f64 (.f64 -2/3 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/3) (/.f64 (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3))) 1/2) (cbrt.f64 -1)))) (.f64 1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 4)) 1/9) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 4)) 1/3)))))))))))
(+.f64 (.f64 (pow.f64 N 3) (+.f64 (.f64 -2/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 5)) 1/9) (.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 1/3) (+.f64 1/2 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3))))))) (+.f64 (.f64 1/3 (-.f64 1/3 (+.f64 (.f64 1/27 (.f64 (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 2)) 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)))) (.f64 -2/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 5)) 1/9) (.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 1/3) (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3))) 1/2))))))) (+.f64 (.f64 (pow.f64 (log.f64 N) 1/3) (.f64 (+.f64 (.f64 -2/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 8)) 1/9) (.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 8)) 1/3) (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3))) 1/2)))) (.f64 2/3 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/3) (/.f64 (-.f64 1/3 (+.f64 (.f64 1/27 (.f64 (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 2)) 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)))) (.f64 -2/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 5)) 1/9) (.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 1/3) (+.f64 1/2 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3))))))))) (cbrt.f64 -1))))) (cbrt.f64 -1))) (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 2)) 1/9) (.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)) 1/3) (+.f64 (.f64 -2/3 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/3) (/.f64 (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3))) 1/2) (cbrt.f64 -1)))) (.f64 1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 4)) 1/9) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 4)) 1/3))))))))))) (+.f64 (.f64 -1 (log.f64 N)) (+.f64 (.f64 N (+.f64 (.f64 2/3 (.f64 (pow.f64 (pow.f64 (log.f64 N) 4) 1/9) (pow.f64 (pow.f64 (cbrt.f64 -1) 4) 1/3))) (.f64 1/3 (.f64 (pow.f64 (pow.f64 (log.f64 N) 4) 1/9) (pow.f64 (pow.f64 (cbrt.f64 -1) 4) 1/3))))) (.f64 (pow.f64 N 2) (+.f64 (.f64 -1/3 (+.f64 1/2 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3))))) (+.f64 (.f64 2/9 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3))) (.f64 (pow.f64 (log.f64 N) 1/3) (.f64 (cbrt.f64 -1) (+.f64 (.f64 -2/3 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/3) (/.f64 (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3))) 1/2) (cbrt.f64 -1)))) (.f64 1/9 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 4)) 1/9) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 4)) 1/3))))))))))))
(*.f64 (pow.f64 (log.f64 N) 1/3) (cbrt.f64 -1))
(+.f64 (.f64 1/3 (.f64 N (.f64 (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 2)) 1/9) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)) 1/3)))) (.f64 (pow.f64 (log.f64 N) 1/3) (cbrt.f64 -1)))
(+.f64 (.f64 1/3 (.f64 N (.f64 (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 2)) 1/9) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)) 1/3)))) (+.f64 (.f64 -1/3 (.f64 (/.f64 (.f64 (pow.f64 N 2) (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3))) 1/2)) (pow.f64 (cbrt.f64 -1) 2)) (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 2)) 1/3))) (*.f64 (pow.f64 (log.f64 N) 1/3) (cbrt.f64 -1))))
(+.f64 (.f64 1/3 (.f64 N (.f64 (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 2)) 1/9) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)) 1/3)))) (+.f64 (.f64 -1/3 (.f64 (/.f64 (.f64 (pow.f64 N 2) (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3))) 1/2)) (pow.f64 (cbrt.f64 -1) 2)) (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 2)) 1/3))) (+.f64 (.f64 1/3 (.f64 (/.f64 (.f64 (pow.f64 N 3) (-.f64 1/3 (+.f64 (.f64 1/27 (.f64 (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 2)) 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)))) (.f64 -2/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 5)) 1/9) (.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 1/3) (+.f64 1/2 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3)))))))))) (pow.f64 (cbrt.f64 -1) 2)) (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 2)) 1/3))) (*.f64 (pow.f64 (log.f64 N) 1/3) (cbrt.f64 -1)))))

Outputs
(*.f64 -1 (log.f64 N))
(neg.f64 (log.f64 N))
(+.f64 (.f64 -1 (log.f64 N)) (.f64 N (+.f64 (.f64 2/3 (.f64 (pow.f64 (pow.f64 (log.f64 N) 4) 1/9) (pow.f64 (pow.f64 (cbrt.f64 -1) 4) 1/3))) (.f64 1/3 (.f64 (pow.f64 (pow.f64 (log.f64 N) 4) 1/9) (pow.f64 (pow.f64 (cbrt.f64 -1) 4) 1/3))))))
(fma.f64 -1 (log.f64 N) (.f64 N (.f64 (.f64 (.f64 (pow.f64 (pow.f64 (log.f64 N) 4) 1/18) (pow.f64 (pow.f64 (log.f64 N) 4) 1/18)) (cbrt.f64 (pow.f64 (cbrt.f64 -1) 4))) 1)))
(fma.f64 N (.f64 (.f64 (pow.f64 (pow.f64 (log.f64 N) 4) 1/18) (pow.f64 (pow.f64 (log.f64 N) 4) 1/18)) (cbrt.f64 (pow.f64 (cbrt.f64 -1) 4))) (neg.f64 (log.f64 N)))
(fma.f64 N (.f64 (.f64 (pow.f64 (pow.f64 (log.f64 N) 4) 1/18) (pow.f64 (pow.f64 (log.f64 N) 4) 1/18)) (cbrt.f64 (*.f64 -1 (cbrt.f64 -1)))) (neg.f64 (log.f64 N)))
(+.f64 (.f64 -1 (log.f64 N)) (+.f64 (.f64 N (+.f64 (.f64 2/3 (.f64 (pow.f64 (pow.f64 (log.f64 N) 4) 1/9) (pow.f64 (pow.f64 (cbrt.f64 -1) 4) 1/3))) (.f64 1/3 (.f64 (pow.f64 (pow.f64 (log.f64 N) 4) 1/9) (pow.f64 (pow.f64 (cbrt.f64 -1) 4) 1/3))))) (.f64 (pow.f64 N 2) (+.f64 (.f64 -1/3 (+.f64 1/2 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3))))) (+.f64 (.f64 2/9 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3))) (.f64 (pow.f64 (log.f64 N) 1/3) (.f64 (cbrt.f64 -1) (+.f64 (.f64 -2/3 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/3) (/.f64 (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3))) 1/2) (cbrt.f64 -1)))) (.f64 1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 4)) 1/9) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 4)) 1/3)))))))))))
(fma.f64 -1 (log.f64 N) (fma.f64 N (.f64 (.f64 (.f64 (pow.f64 (pow.f64 (log.f64 N) 4) 1/18) (pow.f64 (pow.f64 (log.f64 N) 4) 1/18)) (cbrt.f64 (pow.f64 (cbrt.f64 -1) 4))) 1) (.f64 (.f64 N N) (fma.f64 -1/3 (fma.f64 1/3 (.f64 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/18) (pow.f64 (/.f64 1 (log.f64 N)) 1/18)) (cbrt.f64 (/.f64 1 (cbrt.f64 -1)))) 1/2) (fma.f64 2/9 (.f64 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/18) (pow.f64 (/.f64 1 (log.f64 N)) 1/18)) (cbrt.f64 (/.f64 1 (cbrt.f64 -1)))) (.f64 (cbrt.f64 (log.f64 N)) (.f64 (cbrt.f64 -1) (fma.f64 -2/3 (.f64 (cbrt.f64 (/.f64 1 (log.f64 N))) (/.f64 (fma.f64 1/3 (.f64 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/18) (pow.f64 (/.f64 1 (log.f64 N)) 1/18)) (cbrt.f64 (/.f64 1 (cbrt.f64 -1)))) 1/2) (cbrt.f64 -1))) (.f64 1/9 (.f64 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 4)) 1/18) (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 4)) 1/18)) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 4)))))))))))))
(-.f64 (fma.f64 (.f64 N N) (fma.f64 -1/3 (fma.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/18) (pow.f64 (/.f64 1 (log.f64 N)) 1/18))) (cbrt.f64 (/.f64 1 (cbrt.f64 -1))) 1/2) (fma.f64 (.f64 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/18) (pow.f64 (/.f64 1 (log.f64 N)) 1/18)) (cbrt.f64 (/.f64 1 (cbrt.f64 -1)))) 2/9 (.f64 (fma.f64 1/9 (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 4)) 1/18) (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 4)) 1/18)) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 4)))) (.f64 (cbrt.f64 (/.f64 1 (log.f64 N))) (.f64 (/.f64 (fma.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/18) (pow.f64 (/.f64 1 (log.f64 N)) 1/18))) (cbrt.f64 (/.f64 1 (cbrt.f64 -1))) 1/2) (cbrt.f64 -1)) -2/3))) (.f64 (cbrt.f64 -1) (cbrt.f64 (log.f64 N)))))) (.f64 N (.f64 (.f64 (pow.f64 (pow.f64 (log.f64 N) 4) 1/18) (pow.f64 (pow.f64 (log.f64 N) 4) 1/18)) (cbrt.f64 (pow.f64 (cbrt.f64 -1) 4))))) (log.f64 N))
(-.f64 (.f64 N (+.f64 (.f64 (.f64 (pow.f64 (pow.f64 (log.f64 N) 4) 1/18) (pow.f64 (pow.f64 (log.f64 N) 4) 1/18)) (cbrt.f64 (.f64 -1 (cbrt.f64 -1)))) (.f64 (fma.f64 (cbrt.f64 -1) (.f64 (fma.f64 -2/3 (.f64 (/.f64 (cbrt.f64 (/.f64 1 (log.f64 N))) (cbrt.f64 -1)) (fma.f64 1/3 (.f64 (.f64 (cbrt.f64 (/.f64 1 (cbrt.f64 -1))) (pow.f64 (/.f64 1 (log.f64 N)) 1/18)) (pow.f64 (/.f64 1 (log.f64 N)) 1/18)) 1/2)) (.f64 1/9 (.f64 (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 4)) 1/18) (.f64 (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 4)) 1/18) (cbrt.f64 (/.f64 -1 (cbrt.f64 -1))))))) (cbrt.f64 (log.f64 N))) (+.f64 -1/6 (.f64 (.f64 (*.f64 (cbrt.f64 (/.f64 1 (cbrt.f64 -1))) (pow.f64 (/.f64 1 (log.f64 N)) 1/18)) (pow.f64 (/.f64 1 (log.f64 N)) 1/18)) 1/9))) N))) (log.f64 N))
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(+.f64 (.f64 1/3 (.f64 N (.f64 (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 2)) 1/9) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)) 1/3)))) (+.f64 (.f64 -1/3 (.f64 (/.f64 (.f64 (pow.f64 N 2) (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3))) 1/2)) (pow.f64 (cbrt.f64 -1) 2)) (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 2)) 1/3))) (*.f64 (pow.f64 (log.f64 N) 1/3) (cbrt.f64 -1))))
(fma.f64 1/3 (.f64 N (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 2)) 1/18) (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 2)) 1/18)) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))))) (fma.f64 -1/3 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (log.f64 N) 2))) (/.f64 (.f64 N N) (/.f64 (pow.f64 (cbrt.f64 -1) 2) (fma.f64 1/3 (.f64 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/18) (pow.f64 (/.f64 1 (log.f64 N)) 1/18)) (cbrt.f64 (/.f64 1 (cbrt.f64 -1)))) 1/2)))) (.f64 (cbrt.f64 -1) (cbrt.f64 (log.f64 N)))))
(fma.f64 1/3 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))) (.f64 N (.f64 (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 2)) 1/18) (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 2)) 1/18)))) (fma.f64 (/.f64 (.f64 (.f64 N N) (+.f64 -1/6 (.f64 (.f64 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/18) (pow.f64 (/.f64 1 (log.f64 N)) 1/18)) (cbrt.f64 (/.f64 1 (cbrt.f64 -1)))) -1/9))) (pow.f64 (cbrt.f64 -1) 2)) (cbrt.f64 (/.f64 1 (pow.f64 (log.f64 N) 2))) (*.f64 (cbrt.f64 -1) (cbrt.f64 (log.f64 N)))))
(fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 (log.f64 N) 2))) (/.f64 (.f64 N N) (/.f64 (pow.f64 (cbrt.f64 -1) 2) (fma.f64 (.f64 (.f64 (cbrt.f64 (/.f64 1 (cbrt.f64 -1))) (pow.f64 (/.f64 1 (log.f64 N)) 1/18)) (pow.f64 (/.f64 1 (log.f64 N)) 1/18)) -1/9 -1/6))) (fma.f64 (cbrt.f64 -1) (cbrt.f64 (log.f64 N)) (.f64 (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 2)) 1/18) (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 2)) 1/18)) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)))) (*.f64 N 1/3))))
(+.f64 (.f64 1/3 (.f64 N (.f64 (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 2)) 1/9) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)) 1/3)))) (+.f64 (.f64 -1/3 (.f64 (/.f64 (.f64 (pow.f64 N 2) (+.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3))) 1/2)) (pow.f64 (cbrt.f64 -1) 2)) (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 2)) 1/3))) (+.f64 (.f64 1/3 (.f64 (/.f64 (.f64 (pow.f64 N 3) (-.f64 1/3 (+.f64 (.f64 1/27 (.f64 (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 2)) 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)))) (.f64 -2/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 5)) 1/9) (.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 1/3) (+.f64 1/2 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/9) (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3)))))))))) (pow.f64 (cbrt.f64 -1) 2)) (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 2)) 1/3))) (*.f64 (pow.f64 (log.f64 N) 1/3) (cbrt.f64 -1)))))
(fma.f64 1/3 (.f64 N (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 2)) 1/18) (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 2)) 1/18)) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))))) (fma.f64 -1/3 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (log.f64 N) 2))) (/.f64 (.f64 N N) (/.f64 (pow.f64 (cbrt.f64 -1) 2) (fma.f64 1/3 (.f64 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/18) (pow.f64 (/.f64 1 (log.f64 N)) 1/18)) (cbrt.f64 (/.f64 1 (cbrt.f64 -1)))) 1/2)))) (fma.f64 1/3 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (log.f64 N) 2))) (/.f64 (pow.f64 N 3) (/.f64 (pow.f64 (cbrt.f64 -1) 2) (-.f64 1/3 (fma.f64 1/27 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (log.f64 N) 2))) (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))) (.f64 -2/3 (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 5)) 1/18) (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 5)) 1/18)) (.f64 (fma.f64 1/3 (.f64 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/18) (pow.f64 (/.f64 1 (log.f64 N)) 1/18)) (cbrt.f64 (/.f64 1 (cbrt.f64 -1)))) 1/2) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))))))))))) (.f64 (cbrt.f64 -1) (cbrt.f64 (log.f64 N))))))
(+.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (log.f64 N) 2))) (+.f64 (/.f64 (.f64 (.f64 N N) (+.f64 -1/6 (.f64 (.f64 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/18) (pow.f64 (/.f64 1 (log.f64 N)) 1/18)) (cbrt.f64 (/.f64 1 (cbrt.f64 -1)))) -1/9))) (pow.f64 (cbrt.f64 -1) 2)) (.f64 1/3 (.f64 (/.f64 (pow.f64 N 3) (pow.f64 (cbrt.f64 -1) 2)) (-.f64 1/3 (fma.f64 -2/3 (.f64 (fma.f64 (.f64 1/3 (.f64 (pow.f64 (/.f64 1 (log.f64 N)) 1/18) (pow.f64 (/.f64 1 (log.f64 N)) 1/18))) (cbrt.f64 (/.f64 1 (cbrt.f64 -1))) 1/2) (.f64 (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 5)) 1/18) (.f64 (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 5)) 1/18) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)))))) (.f64 1/27 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (log.f64 N) 2))) (pow.f64 (cbrt.f64 -1) 2))))))))) (fma.f64 1/3 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))) (.f64 N (.f64 (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 2)) 1/18) (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 2)) 1/18)))) (.f64 (cbrt.f64 -1) (cbrt.f64 (log.f64 N)))))
(fma.f64 N (.f64 (.f64 (.f64 (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 2)) 1/18) (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 2)) 1/18)) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)))) 1/3) (fma.f64 (cbrt.f64 -1) (cbrt.f64 (log.f64 N)) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (log.f64 N) 2))) (+.f64 (/.f64 (.f64 N N) (/.f64 (pow.f64 (cbrt.f64 -1) 2) (fma.f64 (.f64 (.f64 (cbrt.f64 (/.f64 1 (cbrt.f64 -1))) (pow.f64 (/.f64 1 (log.f64 N)) 1/18)) (pow.f64 (/.f64 1 (log.f64 N)) 1/18)) -1/9 -1/6))) (.f64 1/3 (.f64 (/.f64 (pow.f64 N 3) (pow.f64 (cbrt.f64 -1) 2)) (-.f64 1/3 (fma.f64 (.f64 (.f64 -2/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 5)) 1/18) (pow.f64 (/.f64 1 (pow.f64 (log.f64 N) 5)) 1/18))) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)))) (fma.f64 1/3 (.f64 (.f64 (cbrt.f64 (/.f64 1 (cbrt.f64 -1))) (pow.f64 (/.f64 1 (log.f64 N)) 1/18)) (pow.f64 (/.f64 1 (log.f64 N)) 1/18)) 1/2) (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (log.f64 N) 2))) (/.f64 1/27 (pow.f64 (cbrt.f64 -1) 2)))))))))))

prune149.0ms (4.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	134	5	139

Error

0.0b

Counts

139 → 5

Alt Table

Status	Error	Program
	32.9b	(+.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))))
✓	29.2b	(pow.f64 (cbrt.f64 (-.f64 (log1p.f64 N) (log.f64 N))) 3)
	29.6b	(+.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)))
✓	28.5b	(+.f64 (log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N))) (log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N))))
✓	28.4b	(log.f64 (/.f64 (+.f64 N 1) N))

Compiler

Compiled 3586 to 2249 computations (37.3% saved)

regimes22.0ms (0.7%)

Accuracy

Total -62.0b remaining (-139325.9%)

Threshold costs -62.0b (-139325.9%)

Counts

8 → 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))))
(+.f64 (log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N))) (log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N))))
(pow.f64 (cbrt.f64 (-.f64 (log1p.f64 N) (log.f64 N))) 3)
(+.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)))
(+.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))))
(log.f64 (/.f64 (+.f64 N 1) N))

Results

12.0ms	0.0b	`N`
7.0ms	0.0b	`(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))`

Compiler

Compiled 112 to 71 computations (36.6% 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
0.0005	∈ [	0.00026903495324681614	,	0.020652677403006248	]

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	28	56
1	37	56
2	46	56
3	55	56
4	59	56
5	60	56

Stop Event

1×

saturated

Calls

Call 1

Inputs

(if (<=.f64 (-.f64 (log.f64 (+.f64 N 1)) (log.f64 N)) 9223372036854776/18446744073709551616) (+.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)))) (log.f64 (/.f64 (+.f64 N 1) N)))

Outputs

(if (<=.f64 (-.f64 (log.f64 (+.f64 N 1)) (log.f64 N)) 9223372036854776/18446744073709551616) (+.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)))) (log.f64 (/.f64 (+.f64 N 1) N)))

(if (<=.f64 (-.f64 (log.f64 (+.f64 N 1)) (log.f64 N)) 1152921504606847/2305843009213693952) (+.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)))) (log.f64 (/.f64 (+.f64 N 1) N)))

(if (<=.f64 (-.f64 (log.f64 (+.f64 N 1)) (log.f64 N)) 1152921504606847/2305843009213693952) (+.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)))) (log.f64 (/.f64 (+.f64 N 1) N)))

end28.0ms (0.8%)

Stop Event

1×

fuel

Compiler

Compiled 76 to 58 computations (23.7% saved)

Details

analyze3.0ms (0.1%)

sample2.1s (61.1%)

preprocess19.0ms (0.6%)

simplify10.0ms (0.3%)

prune2.0ms (0.1%)

localize5.0ms (0.1%)

series2.0ms (0.1%)

rewrite36.0ms (1.1%)

simplify24.0ms (0.7%)

prune86.0ms (2.5%)

localize4.0ms (0.1%)

series3.0ms (0.1%)

rewrite42.0ms (1.2%)

simplify27.0ms (0.8%)

prune143.0ms (4.2%)

localize6.0ms (0.2%)

series4.0ms (0.1%)

rewrite43.0ms (1.2%)

simplify25.0ms (0.7%)

prune534.0ms (15.7%)

localize7.0ms (0.2%)

series17.0ms (0.5%)

rewrite41.0ms (1.2%)

simplify38.0ms (1.1%)

prune149.0ms (4.4%)

regimes22.0ms (0.7%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end28.0ms (0.8%)

Profiling