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 (72.7%)

Results

898.0ms	1999×	body	1024	valid
548.0ms	4418×	body	128	valid
346.0ms	1102×	body	512	valid
157.0ms	257×	body	2048	valid
102.0ms	480×	body	256	valid

preprocess16.0ms (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)

simplify9.0ms (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))

prune3.0ms (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

31.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	31.2b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 25 to 16 computations (36% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.9b	(-.f64 (log1p.f64 N) (log.f64 N))

series3.0ms (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	@	0	(-.f64 (log1p.f64 N) (log.f64 N))
1.0ms	N	@	-inf	(-.f64 (log1p.f64 N) (log.f64 N))

rewrite44.0ms (1.6%)

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))))))

simplify23.0ms (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	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))))

prune37.0ms (1.3%)

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
	31.1b	(log.f64 (/.f64 (+.f64 N 1) N))
	31.2b	(/.f64 (-.f64 (pow.f64 (log1p.f64 N) 2) (pow.f64 (log.f64 N) 2)) (+.f64 (log1p.f64 N) (log.f64 N)))
▶	30.5b	(-.f64 (/.f64 1 N) (/.f64 (/.f64 1/2 N) N))

Compiler

Compiled 697 to 330 computations (52.7% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series3.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite87.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

819×	`prod-diff_binary64`
187×	`egg-rr`
169×	`fma-neg_binary64`
160×	`expm1-udef_binary64`
160×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	186	17
2	2789	17

Stop Event

1×	node limit

Counts

2 → 224

Calls

Call 1

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

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

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

simplify24.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

730×	`times-frac_binary64`
530×	`associate-/r*_binary64`
494×	`associate-/l/_binary64`
308×	`associate-/l*_binary64`
283×	`associate-*l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	216
1	26	216
2	46	216
3	100	216
4	260	216
5	935	216

Stop Event

1×	node limit

Counts

248 → 230

Calls

Call 1

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

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

prune187.0ms (6.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	229	1	230
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	230	3	233

Error

0.0b

Counts

233 → 3

Alt Table

Status	Error	Program
	31.1b	(log.f64 (/.f64 (+.f64 N 1) N))
	31.2b	(/.f64 (-.f64 (pow.f64 (log1p.f64 N) 2) (pow.f64 (log.f64 N) 2)) (+.f64 (log1p.f64 N) (log.f64 N)))
▶	30.5b	(/.f64 1 (/.f64 N (+.f64 1 (/.f64 -1/2 N))))

Compiler

Compiled 7533 to 5448 computations (27.7% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series4.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite46.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

876×	`log1p-expm1-u_binary64`
876×	`expm1-log1p-u_binary64`
90×	`add-sqr-sqrt_binary64`
84×	`*-un-lft-identity_binary64`
84×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	182	20
2	2454	20

Stop Event

1×	node limit

Counts

2 → 79

Calls

Call 1

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

Outputs

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

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

simplify30.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

887×	`fma-def_binary64`
646×	`times-frac_binary64`
222×	`*-commutative_binary64`
206×	`unswap-sqr_binary64`
197×	`associate-/r*_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	42	270
1	105	270
2	232	268
3	630	261
4	1602	255
5	4029	255

Stop Event

1×	node limit

Counts

103 → 98

Calls

Call 1

Inputs
(*.f64 -2 (pow.f64 N 2))
(+.f64 (.f64 -4 (pow.f64 N 3)) (.f64 -2 (pow.f64 N 2)))
(+.f64 (.f64 -4 (pow.f64 N 3)) (+.f64 (.f64 -2 (pow.f64 N 2)) (*.f64 -8 (pow.f64 N 4))))
(+.f64 (.f64 -4 (pow.f64 N 3)) (+.f64 (.f64 -2 (pow.f64 N 2)) (+.f64 (.f64 -16 (pow.f64 N 5)) (.f64 -8 (pow.f64 N 4)))))
N
(+.f64 N 1/2)
(+.f64 N (+.f64 1/2 (*.f64 1/4 (/.f64 1 N))))
(+.f64 N (+.f64 1/2 (+.f64 (.f64 1/4 (/.f64 1 N)) (.f64 1/8 (/.f64 1 (pow.f64 N 2))))))
N
(+.f64 N 1/2)
(+.f64 N (+.f64 1/2 (*.f64 1/4 (/.f64 1 N))))
(+.f64 N (+.f64 1/2 (+.f64 (.f64 1/4 (/.f64 1 N)) (.f64 1/8 (/.f64 1 (pow.f64 N 2))))))
(/.f64 -1/2 (pow.f64 N 2))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(/.f64 1 N)
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(/.f64 1 N)
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))

Outputs
(*.f64 -2 (pow.f64 N 2))
(.f64 -2 (.f64 N N))
(+.f64 (.f64 -4 (pow.f64 N 3)) (.f64 -2 (pow.f64 N 2)))
(fma.f64 -4 (pow.f64 N 3) (.f64 -2 (.f64 N N)))
(fma.f64 -2 (.f64 N N) (.f64 -4 (pow.f64 N 3)))
(.f64 (.f64 N N) (+.f64 -2 (*.f64 N -4)))
(.f64 N (.f64 N (fma.f64 N -4 -2)))
(+.f64 (.f64 -4 (pow.f64 N 3)) (+.f64 (.f64 -2 (pow.f64 N 2)) (*.f64 -8 (pow.f64 N 4))))
(fma.f64 -4 (pow.f64 N 3) (fma.f64 -2 (.f64 N N) (.f64 -8 (pow.f64 N 4))))
(fma.f64 -8 (pow.f64 N 4) (.f64 (.f64 N N) (+.f64 -2 (*.f64 N -4))))
(fma.f64 (.f64 N N) (fma.f64 N -4 -2) (.f64 -8 (pow.f64 N 4)))
(.f64 (.f64 N N) (fma.f64 N (fma.f64 N -8 -4) -2))
(+.f64 (.f64 -4 (pow.f64 N 3)) (+.f64 (.f64 -2 (pow.f64 N 2)) (+.f64 (.f64 -16 (pow.f64 N 5)) (.f64 -8 (pow.f64 N 4)))))
(fma.f64 -4 (pow.f64 N 3) (fma.f64 -2 (.f64 N N) (fma.f64 -16 (pow.f64 N 5) (.f64 -8 (pow.f64 N 4)))))
(fma.f64 -4 (pow.f64 N 3) (fma.f64 -2 (.f64 N N) (fma.f64 -8 (pow.f64 N 4) (.f64 -16 (pow.f64 N 5)))))
(fma.f64 -4 (pow.f64 N 3) (fma.f64 -8 (pow.f64 N 4) (fma.f64 -16 (pow.f64 N 5) (.f64 -2 (.f64 N N)))))
(fma.f64 N (.f64 N (fma.f64 N -4 -2)) (fma.f64 -8 (pow.f64 N 4) (.f64 -16 (pow.f64 N 5))))
(fma.f64 (.f64 N N) (fma.f64 N (fma.f64 N -8 -4) -2) (.f64 -16 (pow.f64 N 5)))
N
(+.f64 N 1/2)
(+.f64 N (+.f64 1/2 (*.f64 1/4 (/.f64 1 N))))
(+.f64 (+.f64 N 1/2) (/.f64 1/4 N))
(+.f64 1/2 (+.f64 (/.f64 1/4 N) N))
(+.f64 N (+.f64 1/2 (/.f64 1/4 N)))
(+.f64 N (+.f64 1/2 (+.f64 (.f64 1/4 (/.f64 1 N)) (.f64 1/8 (/.f64 1 (pow.f64 N 2))))))
(+.f64 N (+.f64 1/2 (+.f64 (/.f64 1/4 N) (/.f64 1/8 (*.f64 N N)))))
(+.f64 N (+.f64 1/2 (+.f64 (/.f64 1/4 N) (/.f64 (/.f64 1/8 N) N))))
(+.f64 (+.f64 1/2 (/.f64 1/4 N)) (+.f64 N (/.f64 1/8 (*.f64 N N))))
(+.f64 1/2 (+.f64 (/.f64 1/4 N) (+.f64 N (/.f64 1/8 (*.f64 N N)))))
(+.f64 1/2 (+.f64 (/.f64 1/8 (*.f64 N N)) (+.f64 N (/.f64 1/4 N))))
N
(+.f64 N 1/2)
(+.f64 N (+.f64 1/2 (*.f64 1/4 (/.f64 1 N))))
(+.f64 (+.f64 N 1/2) (/.f64 1/4 N))
(+.f64 1/2 (+.f64 (/.f64 1/4 N) N))
(+.f64 N (+.f64 1/2 (/.f64 1/4 N)))
(+.f64 N (+.f64 1/2 (+.f64 (.f64 1/4 (/.f64 1 N)) (.f64 1/8 (/.f64 1 (pow.f64 N 2))))))
(+.f64 N (+.f64 1/2 (+.f64 (/.f64 1/4 N) (/.f64 1/8 (*.f64 N N)))))
(+.f64 N (+.f64 1/2 (+.f64 (/.f64 1/4 N) (/.f64 (/.f64 1/8 N) N))))
(+.f64 (+.f64 1/2 (/.f64 1/4 N)) (+.f64 N (/.f64 1/8 (*.f64 N N))))
(+.f64 1/2 (+.f64 (/.f64 1/4 N) (+.f64 N (/.f64 1/8 (*.f64 N N)))))
(+.f64 1/2 (+.f64 (/.f64 1/8 (*.f64 N N)) (+.f64 N (/.f64 1/4 N))))
(/.f64 -1/2 (pow.f64 N 2))
(/.f64 -1/2 (*.f64 N N))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
(+.f64 (/.f64 1 N) (/.f64 -1/2 (*.f64 N N)))
(-.f64 (/.f64 1 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 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 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 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 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 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 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 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)))

prune45.0ms (1.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	98	3	101

Error

0.0b

Counts

101 → 3

Alt Table

Status	Error	Program
▶	31.1b	(log.f64 (/.f64 (+.f64 N 1) N))
	31.2b	(/.f64 (-.f64 (pow.f64 (log1p.f64 N) 2) (pow.f64 (log.f64 N) 2)) (+.f64 (log1p.f64 N) (log.f64 N)))
✓	30.5b	(/.f64 1 (/.f64 N (+.f64 1 (/.f64 -1/2 N))))

Compiler

Compiled 1367 to 1059 computations (22.5% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 N 1) N)
✓	3.0b	(log.f64 (/.f64 (+.f64 N 1) N))

series2.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite42.0ms (1.5%)

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 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 (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 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)))))))

simplify24.0ms (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))

prune39.0ms (1.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

0.0b

Counts

80 → 3

Alt Table

Status	Error	Program
✓	31.1b	(log.f64 (/.f64 (+.f64 N 1) N))
	31.2b	(/.f64 (-.f64 (pow.f64 (log1p.f64 N) 2) (pow.f64 (log.f64 N) 2)) (+.f64 (log1p.f64 N) (log.f64 N)))
✓	30.5b	(/.f64 1 (/.f64 N (+.f64 1 (/.f64 -1/2 N))))

Compiler

Compiled 868 to 525 computations (39.5% saved)

regimes37.0ms (1.3%)

Accuracy

Total -61.2b remaining (-31760.6%)

Threshold costs -61.2b (-31760.6%)

Counts

26 → 2

Compiler

Compiled 237 to 133 computations (43.9% 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
5e-9	∈ [	3.073420629107204e-9	,	0.02593919919202392	]

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	32
1	24	32
2	28	32
3	30	32
4	31	32

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 (-.f64 (log.f64 (+.f64 N 1)) (log.f64 N)) 3022314549036573/604462909807314587353088) (/.f64 1 (+.f64 N 1/2)) (log.f64 (+.f64 1 (/.f64 1 N))))

Outputs
(if (<=.f64 (-.f64 (log.f64 (+.f64 N 1)) (log.f64 N)) 3022314549036573/604462909807314587353088) (/.f64 1 (+.f64 N 1/2)) (log.f64 (+.f64 1 (/.f64 1 N))))

end49.0ms (1.7%)

Stop Event

1×

fuel

Compiler

Compiled 74 to 55 computations (25.7% saved)

Details

analyze3.0ms (0.1%)

sample2.1s (72.7%)

preprocess16.0ms (0.6%)

simplify9.0ms (0.3%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series3.0ms (0.1%)

rewrite44.0ms (1.6%)

simplify23.0ms (0.8%)

prune37.0ms (1.3%)

localize5.0ms (0.2%)

series3.0ms (0.1%)

rewrite87.0ms (3%)

simplify24.0ms (0.8%)

prune187.0ms (6.6%)

localize5.0ms (0.2%)

series4.0ms (0.1%)

rewrite46.0ms (1.6%)

simplify30.0ms (1.1%)

prune45.0ms (1.6%)

localize4.0ms (0.1%)

series2.0ms (0.1%)

rewrite42.0ms (1.5%)

simplify24.0ms (0.8%)

prune39.0ms (1.4%)

regimes37.0ms (1.3%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end49.0ms (1.7%)

Profiling