Details

analyze3.0ms (0%)

Algorithm

1×

Search

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample2.2s (34.8%)

Results

832.0ms	2056×	body	1024	valid
782.0ms	4871×	body	256	valid
349.0ms	276×	body	2048	valid
239.0ms	1053×	body	512	valid

preprocess22.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

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

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

30.3b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	30.3b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize10.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 11 to 4 computations (63.6% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite64.0ms (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	1453	8

Stop Event

1×	node limit

Counts

1 → 35

Calls

Call 1

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

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

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 log1p.f64 (expm1.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)))))))

simplify96.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

47 → 50

Calls

Call 1

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

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

eval11.0ms (0.2%)

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

prune17.0ms (0.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	40	10	50
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	40	11	51

Error

0.1b

Counts

51 → 11

Alt Table

Click to see full alt table

Status	Error	Program
▶	30.7b	(exp.f64 (log.f64 (-.f64 (log1p.f64 N) (log.f64 N))))
	30.5b	(/.f64 1 (/.f64 (+.f64 (log1p.f64 N) (log.f64 N)) (-.f64 (pow.f64 (log1p.f64 N) 2) (pow.f64 (log.f64 N) 2))))
	30.6b	(+.f64 (/.f64 1 N) (+.f64 (/.f64 -1/2 (.f64 N N)) (.f64 (/.f64 1 (pow.f64 N 3)) (+.f64 (/.f64 -1/4 N) 1/3))))
▶	30.1b	(log.f64 (/.f64 (+.f64 N 1) N))
▶	30.9b	(-.f64 (/.f64 1 N) (/.f64 (/.f64 1/2 N) N))
▶	29.9b	(/.f64 1 N)
	32.4b	(-.f64 N (log.f64 N))
▶	33.3b	(neg.f64 (log.f64 N))
	30.3b	(/.f64 (-.f64 (pow.f64 (log1p.f64 N) 2) (pow.f64 (log.f64 N) 2)) (+.f64 (log1p.f64 N) (log.f64 N)))
	30.2b	(+.f64 (/.f64 1 N) (.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2)))
✓	30.3b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 226 to 160 computations (29.2% saved)

localize3.0ms (0%)

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

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 24 to 16 computations (33.3% saved)

series3.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite116.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 294

Calls

Call 1

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

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

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N) (/.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 N (/.f64 (*.f64 N 1/2) N)) (pow.f64 N -2) (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 fma.f64 (-.f64 N (/.f64 (*.f64 N 1/2) N)) (pow.f64 N -2) (fma.f64 (/.f64 (/.f64 -1/2 N) N) 1 (*.f64 1/2 (pow.f64 N -2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 N (/.f64 (*.f64 N 1/2) N)) (pow.f64 N -2) (fma.f64 (neg.f64 (cbrt.f64 (*.f64 1/2 (pow.f64 N -2)))) (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 1/2) N) 4)) (*.f64 1/2 (pow.f64 N -2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 N (/.f64 (*.f64 N 1/2) N)) (pow.f64 N -2) (+.f64 (/.f64 (/.f64 -1/2 N) N) (*.f64 1/2 (pow.f64 N -2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 1 (/.f64 -1/2 N)) (/.f64 1 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 fma.f64 (+.f64 1 (/.f64 -1/2 N)) (/.f64 1 N) (fma.f64 (/.f64 (/.f64 -1/2 N) N) 1 (*.f64 1/2 (pow.f64 N -2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 1 (/.f64 -1/2 N)) (/.f64 1 N) (fma.f64 (neg.f64 (cbrt.f64 (*.f64 1/2 (pow.f64 N -2)))) (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 1/2) N) 4)) (*.f64 1/2 (pow.f64 N -2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 1 (/.f64 -1/2 N)) (/.f64 1 N) (+.f64 (/.f64 (/.f64 -1/2 N) N) (*.f64 1/2 (pow.f64 N -2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 N -3) (/.f64 1/8 (pow.f64 N 6))) (/.f64 1 (fma.f64 (*.f64 1/2 (pow.f64 N -2)) (fma.f64 1/2 (pow.f64 N -2) (/.f64 1 N)) (pow.f64 N -2))) (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 fma.f64 (-.f64 (pow.f64 N -3) (/.f64 1/8 (pow.f64 N 6))) (/.f64 1 (fma.f64 (*.f64 1/2 (pow.f64 N -2)) (fma.f64 1/2 (pow.f64 N -2) (/.f64 1 N)) (pow.f64 N -2))) (fma.f64 (/.f64 (/.f64 -1/2 N) N) 1 (*.f64 1/2 (pow.f64 N -2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 N -3) (/.f64 1/8 (pow.f64 N 6))) (/.f64 1 (fma.f64 (*.f64 1/2 (pow.f64 N -2)) (fma.f64 1/2 (pow.f64 N -2) (/.f64 1 N)) (pow.f64 N -2))) (fma.f64 (neg.f64 (cbrt.f64 (*.f64 1/2 (pow.f64 N -2)))) (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 1/2) N) 4)) (*.f64 1/2 (pow.f64 N -2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 N -3) (/.f64 1/8 (pow.f64 N 6))) (/.f64 1 (fma.f64 (*.f64 1/2 (pow.f64 N -2)) (fma.f64 1/2 (pow.f64 N -2) (/.f64 1 N)) (pow.f64 N -2))) (+.f64 (/.f64 (/.f64 -1/2 N) N) (*.f64 1/2 (pow.f64 N -2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 N -2) (pow.f64 (/.f64 (sqrt.f64 1/2) N) 4)) (/.f64 1 (fma.f64 1/2 (pow.f64 N -2) (/.f64 1 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 fma.f64 (-.f64 (pow.f64 N -2) (pow.f64 (/.f64 (sqrt.f64 1/2) N) 4)) (/.f64 1 (fma.f64 1/2 (pow.f64 N -2) (/.f64 1 N))) (fma.f64 (/.f64 (/.f64 -1/2 N) N) 1 (*.f64 1/2 (pow.f64 N -2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 N -2) (pow.f64 (/.f64 (sqrt.f64 1/2) N) 4)) (/.f64 1 (fma.f64 1/2 (pow.f64 N -2) (/.f64 1 N))) (fma.f64 (neg.f64 (cbrt.f64 (*.f64 1/2 (pow.f64 N -2)))) (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 1/2) N) 4)) (*.f64 1/2 (pow.f64 N -2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 N -2) (pow.f64 (/.f64 (sqrt.f64 1/2) N) 4)) (/.f64 1 (fma.f64 1/2 (pow.f64 N -2) (/.f64 1 N))) (+.f64 (/.f64 (/.f64 -1/2 N) N) (*.f64 1/2 (pow.f64 N -2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (/.f64 (/.f64 -1/2 N) N)) 2) (cbrt.f64 (/.f64 (/.f64 -1/2 N) N)) (/.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 (/.f64 -1/2 N) N)) (sqrt.f64 (/.f64 (/.f64 -1/2 N) N)) (/.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (/.f64 (sqrt.f64 1/2) N)) (/.f64 (sqrt.f64 1/2) N) (/.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 N) -2) (/.f64 1 (cbrt.f64 N)) (/.f64 (/.f64 -1/2 N) N))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 N) -2) (/.f64 1 (cbrt.f64 N)) (*.f64 (/.f64 (/.f64 -1/2 N) N) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (pow.f64 N -1/2) (/.f64 (sqrt.f64 1/2) N)) (-.f64 (pow.f64 N -1/2) (/.f64 (sqrt.f64 1/2) 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 fma.f64 (+.f64 (pow.f64 N -1/2) (/.f64 (sqrt.f64 1/2) N)) (-.f64 (pow.f64 N -1/2) (/.f64 (sqrt.f64 1/2) N)) (fma.f64 (/.f64 (/.f64 -1/2 N) N) 1 (*.f64 1/2 (pow.f64 N -2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (pow.f64 N -1/2) (/.f64 (sqrt.f64 1/2) N)) (-.f64 (pow.f64 N -1/2) (/.f64 (sqrt.f64 1/2) N)) (fma.f64 (neg.f64 (cbrt.f64 (*.f64 1/2 (pow.f64 N -2)))) (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 1/2) N) 4)) (*.f64 1/2 (pow.f64 N -2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (pow.f64 N -1/2) (/.f64 (sqrt.f64 1/2) N)) (-.f64 (pow.f64 N -1/2) (/.f64 (sqrt.f64 1/2) N)) (+.f64 (/.f64 (/.f64 -1/2 N) N) (*.f64 1/2 (pow.f64 N -2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 1/2) N) 4))) (cbrt.f64 (*.f64 1/2 (pow.f64 N -2))) (/.f64 1 N))))))

simplify53.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

318 → 300

Calls

Call 1

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

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

localize5.0ms (0.1%)

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

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 N 1) N)
✓	2.6b	(log.f64 (/.f64 (+.f64 N 1) N))

Compiler

Compiled 17 to 11 computations (35.3% saved)

series3.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite53.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 60

Calls

Call 1

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

Outputs

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

simplify54.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

84 → 77

Calls

Call 1

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

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

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (-.f64 (log1p.f64 N) (log.f64 N)))
✓	0.7b	(exp.f64 (log.f64 (-.f64 (log1p.f64 N) (log.f64 N))))
	2.8b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 24 to 6 computations (75% saved)

series3.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	N	@	0	(log.f64 (-.f64 (log1p.f64 N) (log.f64 N)))
0.0ms	N	@	inf	(log.f64 (-.f64 (log1p.f64 N) (log.f64 N)))
0.0ms	N	@	-inf	(log.f64 (-.f64 (log1p.f64 N) (log.f64 N)))
0.0ms	N	@	0	(exp.f64 (log.f64 (-.f64 (log1p.f64 N) (log.f64 N))))
0.0ms	N	@	inf	(exp.f64 (log.f64 (-.f64 (log1p.f64 N) (log.f64 N))))

rewrite153.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

650×	`pow1_binary64`
603×	`add-log-exp_binary64`
603×	`expm1-log1p-u_binary64`
602×	`log1p-expm1-u_binary64`
589×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	18
1	130	18
2	1639	18

Stop Event

1×	node limit

Counts

2 → 62

Calls

Call 1

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

simplify47.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

377×	`associate-/r*_binary64`
344×	`distribute-rgt-in_binary64`
318×	`distribute-lft-in_binary64`
305×	`associate-+l-_binary64`
277×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	79	495
1	234	482
2	694	474
3	2510	460

Stop Event

1×	node limit

Counts

86 → 98

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)))))
(log.f64 (neg.f64 (log.f64 N)))
(+.f64 (log.f64 (neg.f64 (log.f64 N))) (*.f64 -1 (/.f64 N (log.f64 N))))
(+.f64 (log.f64 (neg.f64 (log.f64 N))) (+.f64 (.f64 -1 (/.f64 N (log.f64 N))) (.f64 1/2 (*.f64 (pow.f64 N 2) (-.f64 (/.f64 1 (log.f64 N)) (/.f64 1 (pow.f64 (log.f64 N) 2)))))))
(+.f64 (.f64 1/6 (.f64 (pow.f64 N 3) (-.f64 (.f64 3 (/.f64 1 (pow.f64 (log.f64 N) 2))) (+.f64 (.f64 2 (/.f64 1 (pow.f64 (log.f64 N) 3))) (.f64 2 (/.f64 1 (log.f64 N))))))) (+.f64 (log.f64 (neg.f64 (log.f64 N))) (+.f64 (.f64 -1 (/.f64 N (log.f64 N))) (.f64 1/2 (.f64 (pow.f64 N 2) (-.f64 (/.f64 1 (log.f64 N)) (/.f64 1 (pow.f64 (log.f64 N) 2))))))))
(log.f64 (/.f64 1 N))
(-.f64 (log.f64 (/.f64 1 N)) (*.f64 1/2 (/.f64 1 N)))
(-.f64 (+.f64 (.f64 5/24 (/.f64 1 (pow.f64 N 2))) (log.f64 (/.f64 1 N))) (.f64 1/2 (/.f64 1 N)))
(-.f64 (+.f64 (.f64 5/24 (/.f64 1 (pow.f64 N 2))) (log.f64 (/.f64 1 N))) (+.f64 (.f64 1/2 (/.f64 1 N)) (*.f64 1/8 (/.f64 1 (pow.f64 N 3)))))
(+.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))
(-.f64 (+.f64 (log.f64 -1) (log.f64 (/.f64 -1 N))) (*.f64 1/2 (/.f64 1 N)))
(-.f64 (+.f64 (.f64 5/24 (/.f64 1 (pow.f64 N 2))) (+.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))) (.f64 1/2 (/.f64 1 N)))
(-.f64 (+.f64 (.f64 5/24 (/.f64 1 (pow.f64 N 2))) (+.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))) (+.f64 (.f64 1/2 (/.f64 1 N)) (*.f64 1/8 (/.f64 1 (pow.f64 N 3)))))

Outputs
(*.f64 -1 (log.f64 N))
(neg.f64 (log.f64 N))
(+.f64 N (*.f64 -1 (log.f64 N)))
(+.f64 N (neg.f64 (log.f64 N)))
(-.f64 N (log.f64 N))
(+.f64 N (+.f64 (.f64 -1 (log.f64 N)) (.f64 -1/2 (pow.f64 N 2))))
(+.f64 N (fma.f64 -1 (log.f64 N) (.f64 -1/2 (.f64 N N))))
(+.f64 N (-.f64 (.f64 N (.f64 N -1/2)) (log.f64 N)))
(-.f64 (fma.f64 -1/2 (*.f64 N N) N) (log.f64 N))
(-.f64 (fma.f64 N (*.f64 N -1/2) 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 (.f64 N N) (+.f64 -1/2 (*.f64 N 1/3))) (-.f64 N (log.f64 N)))
(fma.f64 N (.f64 N (+.f64 (.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 (/.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 N) (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 -1/2 (*.f64 N N))))
(-.f64 (+.f64 (/.f64 1 N) (.f64 1/3 (/.f64 1 (pow.f64 N 3)))) (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 N 4))) (*.f64 1/2 (/.f64 1 (pow.f64 N 2)))))
(+.f64 (/.f64 1 N) (-.f64 (/.f64 1/3 (pow.f64 N 3)) (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4)))))
(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4))))
(+.f64 (/.f64 1 N) (+.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 -1/4 (pow.f64 N 4))) (/.f64 -1/2 (*.f64 N N))))
(+.f64 (+.f64 (/.f64 1 N) (/.f64 -1/2 (*.f64 N N))) (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 -1/4 (pow.f64 N 4))))
(/.f64 1 N)
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
(+.f64 (/.f64 1 N) (/.f64 -1/2 (*.f64 N N)))
(-.f64 (+.f64 (/.f64 1 N) (.f64 1/3 (/.f64 1 (pow.f64 N 3)))) (.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(+.f64 (/.f64 1 N) (-.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1/2 (*.f64 N N))))
(+.f64 (/.f64 1/3 (pow.f64 N 3)) (-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N))))
(+.f64 (/.f64 1 N) (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 -1/2 (*.f64 N N))))
(-.f64 (+.f64 (/.f64 1 N) (.f64 1/3 (/.f64 1 (pow.f64 N 3)))) (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 N 4))) (*.f64 1/2 (/.f64 1 (pow.f64 N 2)))))
(+.f64 (/.f64 1 N) (-.f64 (/.f64 1/3 (pow.f64 N 3)) (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4)))))
(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4))))
(+.f64 (/.f64 1 N) (+.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 -1/4 (pow.f64 N 4))) (/.f64 -1/2 (*.f64 N N))))
(+.f64 (+.f64 (/.f64 1 N) (/.f64 -1/2 (*.f64 N N))) (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 -1/4 (pow.f64 N 4))))
(log.f64 (neg.f64 (log.f64 N)))
(+.f64 (log.f64 (neg.f64 (log.f64 N))) (*.f64 -1 (/.f64 N (log.f64 N))))
(+.f64 (log.f64 (neg.f64 (log.f64 N))) (neg.f64 (/.f64 N (log.f64 N))))
(-.f64 (log.f64 (neg.f64 (log.f64 N))) (/.f64 N (log.f64 N)))
(+.f64 (log.f64 (neg.f64 (log.f64 N))) (+.f64 (.f64 -1 (/.f64 N (log.f64 N))) (.f64 1/2 (*.f64 (pow.f64 N 2) (-.f64 (/.f64 1 (log.f64 N)) (/.f64 1 (pow.f64 (log.f64 N) 2)))))))
(+.f64 (log.f64 (neg.f64 (log.f64 N))) (fma.f64 -1 (/.f64 N (log.f64 N)) (.f64 (.f64 1/2 (*.f64 N N)) (-.f64 (/.f64 1 (log.f64 N)) (/.f64 1 (pow.f64 (log.f64 N) 2))))))
(+.f64 (log.f64 (neg.f64 (log.f64 N))) (-.f64 (.f64 1/2 (.f64 (*.f64 N N) (-.f64 (/.f64 1 (log.f64 N)) (/.f64 1 (pow.f64 (log.f64 N) 2))))) (/.f64 N (log.f64 N))))
(fma.f64 (+.f64 (/.f64 1 (log.f64 N)) (/.f64 -1 (pow.f64 (log.f64 N) 2))) (.f64 N (.f64 N 1/2)) (-.f64 (log.f64 (neg.f64 (log.f64 N))) (/.f64 N (log.f64 N))))
(fma.f64 N (*.f64 N (+.f64 (/.f64 -1/2 (pow.f64 (log.f64 N) 2)) (/.f64 1/2 (log.f64 N)))) (-.f64 (log.f64 (neg.f64 (log.f64 N))) (/.f64 N (log.f64 N))))
(+.f64 (.f64 1/6 (.f64 (pow.f64 N 3) (-.f64 (.f64 3 (/.f64 1 (pow.f64 (log.f64 N) 2))) (+.f64 (.f64 2 (/.f64 1 (pow.f64 (log.f64 N) 3))) (.f64 2 (/.f64 1 (log.f64 N))))))) (+.f64 (log.f64 (neg.f64 (log.f64 N))) (+.f64 (.f64 -1 (/.f64 N (log.f64 N))) (.f64 1/2 (.f64 (pow.f64 N 2) (-.f64 (/.f64 1 (log.f64 N)) (/.f64 1 (pow.f64 (log.f64 N) 2))))))))
(fma.f64 1/6 (.f64 (pow.f64 N 3) (-.f64 (/.f64 3 (pow.f64 (log.f64 N) 2)) (+.f64 (/.f64 2 (pow.f64 (log.f64 N) 3)) (/.f64 2 (log.f64 N))))) (+.f64 (log.f64 (neg.f64 (log.f64 N))) (fma.f64 -1 (/.f64 N (log.f64 N)) (.f64 (.f64 1/2 (.f64 N N)) (-.f64 (/.f64 1 (log.f64 N)) (/.f64 1 (pow.f64 (log.f64 N) 2)))))))
(+.f64 (-.f64 (.f64 1/2 (.f64 (.f64 N N) (-.f64 (/.f64 1 (log.f64 N)) (/.f64 1 (pow.f64 (log.f64 N) 2))))) (/.f64 N (log.f64 N))) (fma.f64 1/6 (.f64 (pow.f64 N 3) (-.f64 (/.f64 3 (pow.f64 (log.f64 N) 2)) (+.f64 (/.f64 2 (pow.f64 (log.f64 N) 3)) (/.f64 2 (log.f64 N))))) (log.f64 (neg.f64 (log.f64 N)))))
(fma.f64 1/6 (.f64 (pow.f64 N 3) (+.f64 (/.f64 3 (pow.f64 (log.f64 N) 2)) (+.f64 (/.f64 -2 (pow.f64 (log.f64 N) 3)) (/.f64 -2 (log.f64 N))))) (fma.f64 (+.f64 (/.f64 1 (log.f64 N)) (/.f64 -1 (pow.f64 (log.f64 N) 2))) (.f64 N (*.f64 N 1/2)) (-.f64 (log.f64 (neg.f64 (log.f64 N))) (/.f64 N (log.f64 N)))))
(fma.f64 (pow.f64 N 3) (+.f64 (.f64 1/6 (+.f64 (/.f64 3 (pow.f64 (log.f64 N) 2)) (/.f64 -2 (pow.f64 (log.f64 N) 3)))) (/.f64 -1/3 (log.f64 N))) (fma.f64 N (.f64 N (+.f64 (/.f64 -1/2 (pow.f64 (log.f64 N) 2)) (/.f64 1/2 (log.f64 N)))) (-.f64 (log.f64 (neg.f64 (log.f64 N))) (/.f64 N (log.f64 N)))))
(log.f64 (/.f64 1 N))
(neg.f64 (log.f64 N))
(-.f64 (log.f64 (/.f64 1 N)) (*.f64 1/2 (/.f64 1 N)))
(-.f64 (neg.f64 (log.f64 N)) (/.f64 1/2 N))
(fma.f64 -1 (log.f64 N) (/.f64 -1/2 N))
(-.f64 (/.f64 -1/2 N) (log.f64 N))
(-.f64 (+.f64 (.f64 5/24 (/.f64 1 (pow.f64 N 2))) (log.f64 (/.f64 1 N))) (.f64 1/2 (/.f64 1 N)))
(+.f64 (/.f64 5/24 (*.f64 N N)) (-.f64 (neg.f64 (log.f64 N)) (/.f64 1/2 N)))
(+.f64 (-.f64 (/.f64 5/24 (*.f64 N N)) (log.f64 N)) (/.f64 -1/2 N))
(+.f64 (-.f64 (/.f64 -1/2 N) (log.f64 N)) (/.f64 5/24 (*.f64 N N)))
(-.f64 (/.f64 5/24 (*.f64 N N)) (+.f64 (log.f64 N) (/.f64 1/2 N)))
(-.f64 (+.f64 (.f64 5/24 (/.f64 1 (pow.f64 N 2))) (log.f64 (/.f64 1 N))) (+.f64 (.f64 1/2 (/.f64 1 N)) (*.f64 1/8 (/.f64 1 (pow.f64 N 3)))))
(-.f64 (+.f64 (/.f64 5/24 (*.f64 N N)) (-.f64 (neg.f64 (log.f64 N)) (/.f64 1/2 N))) (/.f64 1/8 (pow.f64 N 3)))
(+.f64 (-.f64 (/.f64 5/24 (*.f64 N N)) (log.f64 N)) (-.f64 (/.f64 -1/2 N) (/.f64 1/8 (pow.f64 N 3))))
(+.f64 (-.f64 (/.f64 -1/2 N) (log.f64 N)) (+.f64 (/.f64 5/24 (*.f64 N N)) (/.f64 -1/8 (pow.f64 N 3))))
(-.f64 (+.f64 (/.f64 5/24 (*.f64 N N)) (/.f64 -1/2 N)) (-.f64 (log.f64 N) (/.f64 -1/8 (pow.f64 N 3))))
(+.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))
(-.f64 (+.f64 (log.f64 -1) (log.f64 (/.f64 -1 N))) (*.f64 1/2 (/.f64 1 N)))
(+.f64 (log.f64 -1) (-.f64 (log.f64 (/.f64 -1 N)) (/.f64 1/2 N)))
(+.f64 (log.f64 (/.f64 -1 N)) (-.f64 (log.f64 -1) (/.f64 1/2 N)))
(fma.f64 2 (log.f64 -1) (-.f64 (/.f64 -1/2 N) (log.f64 N)))
(-.f64 (+.f64 (.f64 5/24 (/.f64 1 (pow.f64 N 2))) (+.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))) (.f64 1/2 (/.f64 1 N)))
(+.f64 (/.f64 5/24 (*.f64 N N)) (+.f64 (log.f64 -1) (-.f64 (log.f64 (/.f64 -1 N)) (/.f64 1/2 N))))
(+.f64 (/.f64 5/24 (*.f64 N N)) (+.f64 (log.f64 (/.f64 -1 N)) (-.f64 (log.f64 -1) (/.f64 1/2 N))))
(+.f64 (log.f64 -1) (-.f64 (+.f64 (/.f64 5/24 (*.f64 N N)) (log.f64 (/.f64 -1 N))) (/.f64 1/2 N)))
(fma.f64 2 (log.f64 -1) (-.f64 (/.f64 5/24 (*.f64 N N)) (+.f64 (log.f64 N) (/.f64 1/2 N))))
(-.f64 (+.f64 (.f64 5/24 (/.f64 1 (pow.f64 N 2))) (+.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))) (+.f64 (.f64 1/2 (/.f64 1 N)) (*.f64 1/8 (/.f64 1 (pow.f64 N 3)))))
(-.f64 (+.f64 (/.f64 5/24 (*.f64 N N)) (+.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))) (+.f64 (/.f64 1/2 N) (/.f64 1/8 (pow.f64 N 3))))
(+.f64 (/.f64 5/24 (*.f64 N N)) (+.f64 (log.f64 -1) (-.f64 (log.f64 (/.f64 -1 N)) (+.f64 (/.f64 1/2 N) (/.f64 1/8 (pow.f64 N 3))))))
(+.f64 (/.f64 5/24 (.f64 N N)) (-.f64 (.f64 2 (log.f64 -1)) (-.f64 (log.f64 N) (+.f64 (/.f64 -1/2 N) (/.f64 -1/8 (pow.f64 N 3))))))
(fma.f64 2 (log.f64 -1) (-.f64 (+.f64 (/.f64 5/24 (*.f64 N N)) (/.f64 -1/2 N)) (-.f64 (log.f64 N) (/.f64 -1/8 (pow.f64 N 3)))))

eval284.0ms (4.5%)

Compiler: Compiled 11418 to 7696 computations (32.6% saved)

prune88.0ms (1.4%)

Pruning

12 alts after pruning (8 fresh and 4 done)

	Pruned	Kept	Total
New	519	6	525
Fresh	3	2	5
Picked	0	1	1
Done	2	3	5
Total	524	12	536

Error

0.1b

Counts

536 → 12

Alt Table

Click to see full alt table

Status	Error	Program
	30.2b	(+.f64 (/.f64 1 N) (.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2)))
▶	30.1b	(log.f64 (+.f64 1 (/.f64 1 N)))
	30.6b	(+.f64 (+.f64 (/.f64 1 N) (/.f64 -1/2 (.f64 N N))) (.f64 (/.f64 1 (pow.f64 N 3)) (-.f64 1/3 (/.f64 1/4 N))))
✓	30.3b	(-.f64 (log1p.f64 N) (log.f64 N))
▶	30.9b	(/.f64 (+.f64 1 (/.f64 -1/2 N)) N)
✓	29.9b	(/.f64 1 N)
	30.9b	(/.f64 1 (/.f64 N (+.f64 1 (/.f64 -1/2 N))))
▶	33.1b	(exp.f64 (-.f64 (+.f64 (/.f64 5/24 (*.f64 N N)) (/.f64 -1/2 N)) (-.f64 (log.f64 N) (/.f64 -1/8 (pow.f64 N 3)))))
▶	32.4b	(-.f64 N (log.f64 N))
✓	33.3b	(neg.f64 (log.f64 N))
✓	30.7b	(exp.f64 (log.f64 (-.f64 (log1p.f64 N) (log.f64 N))))
▶	46.2b	(/.f64 (-.f64 N (/.f64 (.f64 N 1/2) N)) (.f64 N N))

Compiler

Compiled 222 to 164 computations (26.1% saved)

localize144.0ms (2.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.6b	(log.f64 (+.f64 1 (/.f64 1 N)))

Compiler

Compiled 17 to 13 computations (23.5% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite41.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

585×	`pow1_binary64`
545×	`add-log-exp_binary64`
545×	`log1p-expm1-u_binary64`
545×	`expm1-log1p-u_binary64`
534×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6
1	125	6
2	1529	6

Stop Event

1×	node limit

Counts

1 → 20

Calls

Call 1

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

Outputs

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

simplify38.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

32 → 35

Calls

Call 1

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

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

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 19 to 14 computations (26.3% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite58.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 31

Calls

Call 1

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

Outputs

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

simplify42.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

43 → 36

Calls

Call 1

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

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

localize12.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	15.3b	(/.f64 (-.f64 N (/.f64 (.f64 N 1/2) N)) (.f64 N N))

Compiler

Compiled 32 to 17 computations (46.9% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite140.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 199

Calls

Call 1

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

Outputs

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

simplify128.0ms (2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

211 → 204

Calls

Call 1

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

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

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 8 to 3 computations (62.5% saved)

series8.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite44.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 35

Calls

Call 1

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

Outputs

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

simplify160.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

47 → 42

Calls

Call 1

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

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

localize32.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 -1/8 (pow.f64 N 3))
✓	1.0b	(/.f64 5/24 (*.f64 N N))
✓	3.0b	(exp.f64 (-.f64 (+.f64 (/.f64 5/24 (*.f64 N N)) (/.f64 -1/2 N)) (-.f64 (log.f64 N) (/.f64 -1/8 (pow.f64 N 3)))))
✓	13.8b	(-.f64 (+.f64 (/.f64 5/24 (*.f64 N N)) (/.f64 -1/2 N)) (-.f64 (log.f64 N) (/.f64 -1/8 (pow.f64 N 3))))

Compiler

Compiled 81 to 50 computations (38.3% saved)

series6.0ms (0.1%)

Counts

4 → 36

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	N	@	0	(/.f64 -1/8 (pow.f64 N 3))
1.0ms	N	@	inf	(exp.f64 (-.f64 (+.f64 (/.f64 5/24 (*.f64 N N)) (/.f64 -1/2 N)) (-.f64 (log.f64 N) (/.f64 -1/8 (pow.f64 N 3)))))
1.0ms	N	@	-inf	(exp.f64 (-.f64 (+.f64 (/.f64 5/24 (*.f64 N N)) (/.f64 -1/2 N)) (-.f64 (log.f64 N) (/.f64 -1/8 (pow.f64 N 3)))))
1.0ms	N	@	0	(-.f64 (+.f64 (/.f64 5/24 (*.f64 N N)) (/.f64 -1/2 N)) (-.f64 (log.f64 N) (/.f64 -1/8 (pow.f64 N 3))))
0.0ms	N	@	0	(/.f64 5/24 (*.f64 N N))

rewrite153.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

493×	`fma-neg_binary64`
319×	`expm1-udef_binary64`
319×	`log1p-udef_binary64`
252×	`log-pow_binary64`
192×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	70
1	383	66
2	5711	66

Stop Event

1×	node limit

Counts

4 → 181

Calls

Call 1

Inputs
(-.f64 (+.f64 (/.f64 5/24 (*.f64 N N)) (/.f64 -1/2 N)) (-.f64 (log.f64 N) (/.f64 -1/8 (pow.f64 N 3))))
(exp.f64 (-.f64 (+.f64 (/.f64 5/24 (*.f64 N N)) (/.f64 -1/2 N)) (-.f64 (log.f64 N) (/.f64 -1/8 (pow.f64 N 3)))))
(/.f64 5/24 (*.f64 N N))
(/.f64 -1/8 (pow.f64 N 3))

Outputs
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(expm1.f64 (/.f64 (exp.f64 (fma.f64 5/24 (pow.f64 N -2) (/.f64 -1/2 N))) (/.f64 N (pow.f64 (exp.f64 -1/8) (pow.f64 N -3))))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 5/24 (pow.f64 N -2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 5/24 (pow.f64 N -2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 5/24 (pow.f64 N -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 5/24 (pow.f64 N -2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 5/24 (pow.f64 N -2))) (cbrt.f64 (/.f64 25/576 (pow.f64 N 4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 25/576 (pow.f64 N 4))) (cbrt.f64 (.f64 5/24 (pow.f64 N -2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 5/24) N) (/.f64 (sqrt.f64 5/24) N))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -5/24 (/.f64 1 (.f64 N (neg.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 N -2) 5/24)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 5/24 N) (pow.f64 N -1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 5/24 (pow.f64 N -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 5/24 (pow.f64 N -2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 5/24) N) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 125/13824 (pow.f64 N 6)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (.f64 N N) 24/5) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 25/576 (pow.f64 N 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 5/24) (pow.f64 N -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 5/24 (pow.f64 N -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 125/13824 (pow.f64 N 6)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 5/24 (pow.f64 N -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 5/24 (pow.f64 N -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 5/24 (pow.f64 N -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (*.f64 5/24 (pow.f64 N -2))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 -1/8 (pow.f64 N -3)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 -1/2 N) (/.f64 1/4 (.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1/8 (pow.f64 N -3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1/8 (pow.f64 (pow.f64 N -1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 -1/8 (pow.f64 N -3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 -1/8 (pow.f64 N -3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/4 (.f64 N N)) (/.f64 -1/2 N))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 -1/8) (pow.f64 N 3/2)) (/.f64 (sqrt.f64 -1/8) (pow.f64 N 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/8 (/.f64 1 (neg.f64 (pow.f64 N 3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 N -3) -1/8)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 -1/2 N)) 2) 3) (/.f64 -1/2 N))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (/.f64 -1/2 N)) 3) (pow.f64 (sqrt.f64 (/.f64 -1/2 N)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (/.f64 -1/2 N) 3/2) (pow.f64 (/.f64 -1/2 N) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (/.f64 1/4 (.f64 N N)) -1/2) (pow.f64 N -1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (/.f64 1/4 (.f64 N N)) 1) (/.f64 -1/2 N))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (/.f64 1/4 (.f64 N N)) (pow.f64 (cbrt.f64 (/.f64 -1/2 N)) 2)) (cbrt.f64 (/.f64 -1/2 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (/.f64 1/4 (.f64 N N)) (sqrt.f64 (/.f64 -1/2 N))) (sqrt.f64 (/.f64 -1/2 N)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 -1/2 N) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 -1/8 (pow.f64 N -3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 -1/8) (pow.f64 N 3/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 -1/512 (pow.f64 (pow.f64 N 3) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 N 3) -8) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1/64 (pow.f64 N 6)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 -1/8) (pow.f64 N -3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 -1/8 (pow.f64 N -3)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 -1/512 (pow.f64 (pow.f64 N 3) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 -1/8 (pow.f64 N -3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 -1/8 (pow.f64 N -3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 3 (log.f64 (/.f64 -1/2 N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 -1/2 N)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log.f64 (/.f64 -1/2 N))) 1))))))

simplify53.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

750×	`times-frac_binary64`
519×	`associate-/r*_binary64`
330×	`associate-/l*_binary64`
279×	`associate-/l/_binary64`
252×	`associate-*l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	75	706
1	220	622
2	626	522
3	2163	522

Stop Event

1×	node limit

Counts

217 → 215

Calls

Call 1

Inputs
(/.f64 -1/8 (pow.f64 N 3))
(-.f64 (.f64 5/24 (/.f64 1 (pow.f64 N 2))) (.f64 1/8 (/.f64 1 (pow.f64 N 3))))
(-.f64 (.f64 5/24 (/.f64 1 (pow.f64 N 2))) (+.f64 (.f64 1/2 (/.f64 1 N)) (*.f64 1/8 (/.f64 1 (pow.f64 N 3)))))
(-.f64 (+.f64 (.f64 5/24 (/.f64 1 (pow.f64 N 2))) (.f64 -1 (log.f64 N))) (+.f64 (.f64 1/2 (/.f64 1 N)) (.f64 1/8 (/.f64 1 (pow.f64 N 3)))))
(log.f64 (/.f64 1 N))
(-.f64 (log.f64 (/.f64 1 N)) (*.f64 1/2 (/.f64 1 N)))
(-.f64 (+.f64 (.f64 5/24 (/.f64 1 (pow.f64 N 2))) (log.f64 (/.f64 1 N))) (.f64 1/2 (/.f64 1 N)))
(-.f64 (+.f64 (.f64 5/24 (/.f64 1 (pow.f64 N 2))) (log.f64 (/.f64 1 N))) (+.f64 (.f64 1/2 (/.f64 1 N)) (*.f64 1/8 (/.f64 1 (pow.f64 N 3)))))
(.f64 -1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))
(-.f64 (.f64 -1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))) (*.f64 1/2 (/.f64 1 N)))
(-.f64 (+.f64 (.f64 5/24 (/.f64 1 (pow.f64 N 2))) (.f64 -1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))) (.f64 1/2 (/.f64 1 N)))
(-.f64 (+.f64 (.f64 5/24 (/.f64 1 (pow.f64 N 2))) (.f64 -1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))) (+.f64 (.f64 1/2 (/.f64 1 N)) (*.f64 1/8 (/.f64 1 (pow.f64 N 3)))))
(exp.f64 (-.f64 (.f64 5/24 (/.f64 1 (pow.f64 N 2))) (+.f64 (log.f64 N) (+.f64 (.f64 1/2 (/.f64 1 N)) (*.f64 1/8 (/.f64 1 (pow.f64 N 3)))))))
(exp.f64 (-.f64 (.f64 5/24 (/.f64 1 (pow.f64 N 2))) (+.f64 (log.f64 N) (+.f64 (.f64 1/2 (/.f64 1 N)) (*.f64 1/8 (/.f64 1 (pow.f64 N 3)))))))
(exp.f64 (-.f64 (.f64 5/24 (/.f64 1 (pow.f64 N 2))) (+.f64 (log.f64 N) (+.f64 (.f64 1/2 (/.f64 1 N)) (*.f64 1/8 (/.f64 1 (pow.f64 N 3)))))))
(exp.f64 (-.f64 (.f64 5/24 (/.f64 1 (pow.f64 N 2))) (+.f64 (log.f64 N) (+.f64 (.f64 1/2 (/.f64 1 N)) (*.f64 1/8 (/.f64 1 (pow.f64 N 3)))))))
(exp.f64 (neg.f64 (*.f64 -1 (log.f64 (/.f64 1 N)))))
(+.f64 (exp.f64 (neg.f64 (.f64 -1 (log.f64 (/.f64 1 N))))) (.f64 -1/2 (/.f64 (exp.f64 (neg.f64 (*.f64 -1 (log.f64 (/.f64 1 N))))) N)))
(+.f64 (exp.f64 (neg.f64 (.f64 -1 (log.f64 (/.f64 1 N))))) (+.f64 (.f64 -1/2 (/.f64 (exp.f64 (neg.f64 (.f64 -1 (log.f64 (/.f64 1 N))))) N)) (.f64 1/3 (/.f64 (exp.f64 (neg.f64 (*.f64 -1 (log.f64 (/.f64 1 N))))) (pow.f64 N 2)))))
(+.f64 (.f64 -1/4 (/.f64 (exp.f64 (neg.f64 (.f64 -1 (log.f64 (/.f64 1 N))))) (pow.f64 N 3))) (+.f64 (exp.f64 (neg.f64 (.f64 -1 (log.f64 (/.f64 1 N))))) (+.f64 (.f64 -1/2 (/.f64 (exp.f64 (neg.f64 (.f64 -1 (log.f64 (/.f64 1 N))))) N)) (.f64 1/3 (/.f64 (exp.f64 (neg.f64 (*.f64 -1 (log.f64 (/.f64 1 N))))) (pow.f64 N 2))))))
(exp.f64 (neg.f64 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 N))))))
(+.f64 (exp.f64 (neg.f64 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))) (.f64 -1/2 (/.f64 (exp.f64 (neg.f64 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 N)))))) N)))
(+.f64 (exp.f64 (neg.f64 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))) (+.f64 (.f64 1/3 (/.f64 (exp.f64 (neg.f64 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))) (pow.f64 N 2))) (.f64 -1/2 (/.f64 (exp.f64 (neg.f64 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 N)))))) N))))
(+.f64 (exp.f64 (neg.f64 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))) (+.f64 (.f64 1/3 (/.f64 (exp.f64 (neg.f64 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))) (pow.f64 N 2))) (+.f64 (.f64 -1/2 (/.f64 (exp.f64 (neg.f64 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))) N)) (.f64 -1/4 (/.f64 (exp.f64 (neg.f64 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 N)))))) (pow.f64 N 3))))))
(/.f64 5/24 (pow.f64 N 2))
(/.f64 5/24 (pow.f64 N 2))
(/.f64 5/24 (pow.f64 N 2))
(/.f64 5/24 (pow.f64 N 2))
(/.f64 5/24 (pow.f64 N 2))
(/.f64 5/24 (pow.f64 N 2))
(/.f64 5/24 (pow.f64 N 2))
(/.f64 5/24 (pow.f64 N 2))
(/.f64 5/24 (pow.f64 N 2))
(/.f64 5/24 (pow.f64 N 2))
(/.f64 5/24 (pow.f64 N 2))
(/.f64 5/24 (pow.f64 N 2))

Outputs
(/.f64 -1/8 (pow.f64 N 3))
(-.f64 (.f64 5/24 (/.f64 1 (pow.f64 N 2))) (.f64 1/8 (/.f64 1 (pow.f64 N 3))))
(-.f64 (/.f64 5/24 (*.f64 N N)) (/.f64 1/8 (pow.f64 N 3)))
(+.f64 (/.f64 5/24 (*.f64 N N)) (/.f64 -1/8 (pow.f64 N 3)))
(-.f64 (.f64 5/24 (/.f64 1 (pow.f64 N 2))) (+.f64 (.f64 1/2 (/.f64 1 N)) (*.f64 1/8 (/.f64 1 (pow.f64 N 3)))))
(-.f64 (/.f64 5/24 (*.f64 N N)) (+.f64 (/.f64 1/8 (pow.f64 N 3)) (/.f64 1/2 N)))
(+.f64 (+.f64 (/.f64 5/24 (*.f64 N N)) (/.f64 -1/2 N)) (/.f64 -1/8 (pow.f64 N 3)))
(+.f64 (/.f64 5/24 (*.f64 N N)) (+.f64 (/.f64 -1/2 N) (/.f64 -1/8 (pow.f64 N 3))))
(-.f64 (+.f64 (.f64 5/24 (/.f64 1 (pow.f64 N 2))) (.f64 -1 (log.f64 N))) (+.f64 (.f64 1/2 (/.f64 1 N)) (.f64 1/8 (/.f64 1 (pow.f64 N 3)))))
(+.f64 (/.f64 5/24 (*.f64 N N)) (-.f64 (neg.f64 (log.f64 N)) (+.f64 (/.f64 1/8 (pow.f64 N 3)) (/.f64 1/2 N))))
(-.f64 (-.f64 (/.f64 5/24 (*.f64 N N)) (+.f64 (/.f64 1/2 N) (log.f64 N))) (/.f64 1/8 (pow.f64 N 3)))
(+.f64 (+.f64 (/.f64 5/24 (*.f64 N N)) (-.f64 (/.f64 -1/2 N) (log.f64 N))) (/.f64 -1/8 (pow.f64 N 3)))
(+.f64 (/.f64 5/24 (*.f64 N N)) (+.f64 (-.f64 (/.f64 -1/2 N) (log.f64 N)) (/.f64 -1/8 (pow.f64 N 3))))
(log.f64 (/.f64 1 N))
(neg.f64 (log.f64 N))
(-.f64 (log.f64 (/.f64 1 N)) (*.f64 1/2 (/.f64 1 N)))
(-.f64 (neg.f64 (log.f64 N)) (/.f64 1/2 N))
(fma.f64 -1 (log.f64 N) (/.f64 -1/2 N))
(-.f64 (/.f64 -1/2 N) (log.f64 N))
(-.f64 (+.f64 (.f64 5/24 (/.f64 1 (pow.f64 N 2))) (log.f64 (/.f64 1 N))) (.f64 1/2 (/.f64 1 N)))
(+.f64 (/.f64 5/24 (*.f64 N N)) (-.f64 (neg.f64 (log.f64 N)) (/.f64 1/2 N)))
(+.f64 (-.f64 (/.f64 5/24 (*.f64 N N)) (log.f64 N)) (/.f64 -1/2 N))
(+.f64 (/.f64 5/24 (*.f64 N N)) (-.f64 (/.f64 -1/2 N) (log.f64 N)))
(-.f64 (+.f64 (.f64 5/24 (/.f64 1 (pow.f64 N 2))) (log.f64 (/.f64 1 N))) (+.f64 (.f64 1/2 (/.f64 1 N)) (*.f64 1/8 (/.f64 1 (pow.f64 N 3)))))
(+.f64 (/.f64 5/24 (*.f64 N N)) (-.f64 (neg.f64 (log.f64 N)) (+.f64 (/.f64 1/8 (pow.f64 N 3)) (/.f64 1/2 N))))
(-.f64 (-.f64 (/.f64 5/24 (*.f64 N N)) (+.f64 (/.f64 1/2 N) (log.f64 N))) (/.f64 1/8 (pow.f64 N 3)))
(+.f64 (+.f64 (/.f64 5/24 (*.f64 N N)) (-.f64 (/.f64 -1/2 N) (log.f64 N))) (/.f64 -1/8 (pow.f64 N 3)))
(+.f64 (/.f64 5/24 (*.f64 N N)) (+.f64 (-.f64 (/.f64 -1/2 N) (log.f64 N)) (/.f64 -1/8 (pow.f64 N 3))))
(.f64 -1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))
(neg.f64 (log.f64 N))
(-.f64 (.f64 -1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))) (*.f64 1/2 (/.f64 1 N)))
(-.f64 (neg.f64 (log.f64 N)) (/.f64 1/2 N))
(fma.f64 -1 (log.f64 N) (/.f64 -1/2 N))
(-.f64 (/.f64 -1/2 N) (log.f64 N))
(-.f64 (+.f64 (.f64 5/24 (/.f64 1 (pow.f64 N 2))) (.f64 -1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))) (.f64 1/2 (/.f64 1 N)))
(+.f64 (/.f64 5/24 (*.f64 N N)) (-.f64 (neg.f64 (log.f64 N)) (/.f64 1/2 N)))
(+.f64 (-.f64 (/.f64 5/24 (*.f64 N N)) (log.f64 N)) (/.f64 -1/2 N))
(+.f64 (/.f64 5/24 (*.f64 N N)) (-.f64 (/.f64 -1/2 N) (log.f64 N)))
(-.f64 (+.f64 (.f64 5/24 (/.f64 1 (pow.f64 N 2))) (.f64 -1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))) (+.f64 (.f64 1/2 (/.f64 1 N)) (*.f64 1/8 (/.f64 1 (pow.f64 N 3)))))
(+.f64 (/.f64 5/24 (*.f64 N N)) (-.f64 (neg.f64 (log.f64 N)) (+.f64 (/.f64 1/8 (pow.f64 N 3)) (/.f64 1/2 N))))
(-.f64 (-.f64 (/.f64 5/24 (*.f64 N N)) (+.f64 (/.f64 1/2 N) (log.f64 N))) (/.f64 1/8 (pow.f64 N 3)))
(+.f64 (+.f64 (/.f64 5/24 (*.f64 N N)) (-.f64 (/.f64 -1/2 N) (log.f64 N))) (/.f64 -1/8 (pow.f64 N 3)))
(+.f64 (/.f64 5/24 (*.f64 N N)) (+.f64 (-.f64 (/.f64 -1/2 N) (log.f64 N)) (/.f64 -1/8 (pow.f64 N 3))))
(exp.f64 (-.f64 (.f64 5/24 (/.f64 1 (pow.f64 N 2))) (+.f64 (log.f64 N) (+.f64 (.f64 1/2 (/.f64 1 N)) (*.f64 1/8 (/.f64 1 (pow.f64 N 3)))))))
(exp.f64 (-.f64 (/.f64 5/24 (*.f64 N N)) (+.f64 (+.f64 (log.f64 N) (/.f64 1/2 N)) (/.f64 1/8 (pow.f64 N 3)))))
(exp.f64 (-.f64 (-.f64 (/.f64 5/24 (*.f64 N N)) (+.f64 (/.f64 1/2 N) (log.f64 N))) (/.f64 1/8 (pow.f64 N 3))))
(/.f64 (exp.f64 (+.f64 (/.f64 5/24 (*.f64 N N)) (+.f64 (/.f64 -1/2 N) (/.f64 -1/8 (pow.f64 N 3))))) N)
(exp.f64 (-.f64 (.f64 5/24 (/.f64 1 (pow.f64 N 2))) (+.f64 (log.f64 N) (+.f64 (.f64 1/2 (/.f64 1 N)) (*.f64 1/8 (/.f64 1 (pow.f64 N 3)))))))
(exp.f64 (-.f64 (/.f64 5/24 (*.f64 N N)) (+.f64 (+.f64 (log.f64 N) (/.f64 1/2 N)) (/.f64 1/8 (pow.f64 N 3)))))
(exp.f64 (-.f64 (-.f64 (/.f64 5/24 (*.f64 N N)) (+.f64 (/.f64 1/2 N) (log.f64 N))) (/.f64 1/8 (pow.f64 N 3))))
(/.f64 (exp.f64 (+.f64 (/.f64 5/24 (*.f64 N N)) (+.f64 (/.f64 -1/2 N) (/.f64 -1/8 (pow.f64 N 3))))) N)
(exp.f64 (-.f64 (.f64 5/24 (/.f64 1 (pow.f64 N 2))) (+.f64 (log.f64 N) (+.f64 (.f64 1/2 (/.f64 1 N)) (*.f64 1/8 (/.f64 1 (pow.f64 N 3)))))))
(exp.f64 (-.f64 (/.f64 5/24 (*.f64 N N)) (+.f64 (+.f64 (log.f64 N) (/.f64 1/2 N)) (/.f64 1/8 (pow.f64 N 3)))))
(exp.f64 (-.f64 (-.f64 (/.f64 5/24 (*.f64 N N)) (+.f64 (/.f64 1/2 N) (log.f64 N))) (/.f64 1/8 (pow.f64 N 3))))
(/.f64 (exp.f64 (+.f64 (/.f64 5/24 (*.f64 N N)) (+.f64 (/.f64 -1/2 N) (/.f64 -1/8 (pow.f64 N 3))))) N)
(exp.f64 (-.f64 (.f64 5/24 (/.f64 1 (pow.f64 N 2))) (+.f64 (log.f64 N) (+.f64 (.f64 1/2 (/.f64 1 N)) (*.f64 1/8 (/.f64 1 (pow.f64 N 3)))))))
(exp.f64 (-.f64 (/.f64 5/24 (*.f64 N N)) (+.f64 (+.f64 (log.f64 N) (/.f64 1/2 N)) (/.f64 1/8 (pow.f64 N 3)))))
(exp.f64 (-.f64 (-.f64 (/.f64 5/24 (*.f64 N N)) (+.f64 (/.f64 1/2 N) (log.f64 N))) (/.f64 1/8 (pow.f64 N 3))))
(/.f64 (exp.f64 (+.f64 (/.f64 5/24 (*.f64 N N)) (+.f64 (/.f64 -1/2 N) (/.f64 -1/8 (pow.f64 N 3))))) N)
(exp.f64 (neg.f64 (*.f64 -1 (log.f64 (/.f64 1 N)))))
(exp.f64 (*.f64 1 (neg.f64 (log.f64 N))))
(exp.f64 (neg.f64 (log.f64 N)))
(/.f64 1 N)
(+.f64 (exp.f64 (neg.f64 (.f64 -1 (log.f64 (/.f64 1 N))))) (.f64 -1/2 (/.f64 (exp.f64 (neg.f64 (*.f64 -1 (log.f64 (/.f64 1 N))))) N)))
(+.f64 (exp.f64 (.f64 1 (neg.f64 (log.f64 N)))) (.f64 -1/2 (/.f64 (exp.f64 (*.f64 1 (neg.f64 (log.f64 N)))) N)))
(fma.f64 -1/2 (/.f64 (exp.f64 (neg.f64 (log.f64 N))) N) (exp.f64 (neg.f64 (log.f64 N))))
(+.f64 (/.f64 1 N) (/.f64 -1/2 (*.f64 N N)))
(+.f64 (exp.f64 (neg.f64 (.f64 -1 (log.f64 (/.f64 1 N))))) (+.f64 (.f64 -1/2 (/.f64 (exp.f64 (neg.f64 (.f64 -1 (log.f64 (/.f64 1 N))))) N)) (.f64 1/3 (/.f64 (exp.f64 (neg.f64 (*.f64 -1 (log.f64 (/.f64 1 N))))) (pow.f64 N 2)))))
(+.f64 (exp.f64 (.f64 1 (neg.f64 (log.f64 N)))) (fma.f64 -1/2 (/.f64 (exp.f64 (.f64 1 (neg.f64 (log.f64 N)))) N) (.f64 1/3 (/.f64 (exp.f64 (.f64 1 (neg.f64 (log.f64 N)))) (*.f64 N N)))))
(+.f64 (exp.f64 (neg.f64 (log.f64 N))) (fma.f64 -1/2 (/.f64 (exp.f64 (neg.f64 (log.f64 N))) N) (/.f64 (/.f64 1/3 (exp.f64 (log.f64 N))) (*.f64 N N))))
(+.f64 (/.f64 1 N) (.f64 (/.f64 1 (.f64 N N)) (+.f64 -1/2 (/.f64 1/3 N))))
(+.f64 (/.f64 1 N) (+.f64 (/.f64 -1/2 (*.f64 N N)) (/.f64 1/3 (pow.f64 N 3))))
(+.f64 (.f64 -1/4 (/.f64 (exp.f64 (neg.f64 (.f64 -1 (log.f64 (/.f64 1 N))))) (pow.f64 N 3))) (+.f64 (exp.f64 (neg.f64 (.f64 -1 (log.f64 (/.f64 1 N))))) (+.f64 (.f64 -1/2 (/.f64 (exp.f64 (neg.f64 (.f64 -1 (log.f64 (/.f64 1 N))))) N)) (.f64 1/3 (/.f64 (exp.f64 (neg.f64 (*.f64 -1 (log.f64 (/.f64 1 N))))) (pow.f64 N 2))))))
(fma.f64 -1/4 (/.f64 (exp.f64 (.f64 1 (neg.f64 (log.f64 N)))) (pow.f64 N 3)) (+.f64 (exp.f64 (.f64 1 (neg.f64 (log.f64 N)))) (fma.f64 -1/2 (/.f64 (exp.f64 (.f64 1 (neg.f64 (log.f64 N)))) N) (.f64 1/3 (/.f64 (exp.f64 (.f64 1 (neg.f64 (log.f64 N)))) (.f64 N N))))))
(+.f64 (fma.f64 -1/2 (/.f64 (exp.f64 (neg.f64 (log.f64 N))) N) (/.f64 (/.f64 1/3 (exp.f64 (log.f64 N))) (*.f64 N N))) (fma.f64 -1/4 (/.f64 (exp.f64 (neg.f64 (log.f64 N))) (pow.f64 N 3)) (exp.f64 (neg.f64 (log.f64 N)))))
(+.f64 (/.f64 1 N) (+.f64 (/.f64 -1/2 (.f64 N N)) (.f64 (/.f64 1 (pow.f64 N 3)) (+.f64 1/3 (/.f64 -1/4 N)))))
(+.f64 (/.f64 -1/2 (.f64 N N)) (+.f64 (/.f64 (.f64 1 (+.f64 1/3 (/.f64 -1/4 N))) (pow.f64 N 3)) (/.f64 1 N)))
(exp.f64 (neg.f64 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 N))))))
(exp.f64 (*.f64 1 (neg.f64 (log.f64 N))))
(exp.f64 (neg.f64 (log.f64 N)))
(/.f64 1 N)
(+.f64 (exp.f64 (neg.f64 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))) (.f64 -1/2 (/.f64 (exp.f64 (neg.f64 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 N)))))) N)))
(+.f64 (exp.f64 (.f64 1 (neg.f64 (log.f64 N)))) (.f64 -1/2 (/.f64 (exp.f64 (*.f64 1 (neg.f64 (log.f64 N)))) N)))
(fma.f64 -1/2 (/.f64 (exp.f64 (neg.f64 (log.f64 N))) N) (exp.f64 (neg.f64 (log.f64 N))))
(+.f64 (/.f64 1 N) (/.f64 -1/2 (*.f64 N N)))
(+.f64 (exp.f64 (neg.f64 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))) (+.f64 (.f64 1/3 (/.f64 (exp.f64 (neg.f64 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))) (pow.f64 N 2))) (.f64 -1/2 (/.f64 (exp.f64 (neg.f64 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 N)))))) N))))
(+.f64 (exp.f64 (.f64 1 (neg.f64 (log.f64 N)))) (fma.f64 -1/2 (/.f64 (exp.f64 (.f64 1 (neg.f64 (log.f64 N)))) N) (.f64 1/3 (/.f64 (exp.f64 (.f64 1 (neg.f64 (log.f64 N)))) (*.f64 N N)))))
(+.f64 (exp.f64 (neg.f64 (log.f64 N))) (fma.f64 -1/2 (/.f64 (exp.f64 (neg.f64 (log.f64 N))) N) (/.f64 (/.f64 1/3 (exp.f64 (log.f64 N))) (*.f64 N N))))
(+.f64 (/.f64 1 N) (.f64 (/.f64 1 (.f64 N N)) (+.f64 -1/2 (/.f64 1/3 N))))
(+.f64 (/.f64 1 N) (+.f64 (/.f64 -1/2 (*.f64 N N)) (/.f64 1/3 (pow.f64 N 3))))
(+.f64 (exp.f64 (neg.f64 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))) (+.f64 (.f64 1/3 (/.f64 (exp.f64 (neg.f64 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))) (pow.f64 N 2))) (+.f64 (.f64 -1/2 (/.f64 (exp.f64 (neg.f64 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))) N)) (.f64 -1/4 (/.f64 (exp.f64 (neg.f64 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 N)))))) (pow.f64 N 3))))))
(fma.f64 -1/4 (/.f64 (exp.f64 (.f64 1 (neg.f64 (log.f64 N)))) (pow.f64 N 3)) (+.f64 (exp.f64 (.f64 1 (neg.f64 (log.f64 N)))) (fma.f64 -1/2 (/.f64 (exp.f64 (.f64 1 (neg.f64 (log.f64 N)))) N) (.f64 1/3 (/.f64 (exp.f64 (.f64 1 (neg.f64 (log.f64 N)))) (.f64 N N))))))
(+.f64 (fma.f64 -1/2 (/.f64 (exp.f64 (neg.f64 (log.f64 N))) N) (/.f64 (/.f64 1/3 (exp.f64 (log.f64 N))) (*.f64 N N))) (fma.f64 -1/4 (/.f64 (exp.f64 (neg.f64 (log.f64 N))) (pow.f64 N 3)) (exp.f64 (neg.f64 (log.f64 N)))))
(+.f64 (/.f64 1 N) (+.f64 (/.f64 -1/2 (.f64 N N)) (.f64 (/.f64 1 (pow.f64 N 3)) (+.f64 1/3 (/.f64 -1/4 N)))))
(+.f64 (/.f64 -1/2 (.f64 N N)) (+.f64 (/.f64 (.f64 1 (+.f64 1/3 (/.f64 -1/4 N))) (pow.f64 N 3)) (/.f64 1 N)))
(/.f64 5/24 (pow.f64 N 2))
(/.f64 5/24 (*.f64 N N))
(/.f64 5/24 (pow.f64 N 2))
(/.f64 5/24 (*.f64 N N))
(/.f64 5/24 (pow.f64 N 2))
(/.f64 5/24 (*.f64 N N))
(/.f64 5/24 (pow.f64 N 2))
(/.f64 5/24 (*.f64 N N))
(/.f64 5/24 (pow.f64 N 2))
(/.f64 5/24 (*.f64 N N))
(/.f64 5/24 (pow.f64 N 2))
(/.f64 5/24 (*.f64 N N))
(/.f64 5/24 (pow.f64 N 2))
(/.f64 5/24 (*.f64 N N))
(/.f64 5/24 (pow.f64 N 2))
(/.f64 5/24 (*.f64 N N))
(/.f64 5/24 (pow.f64 N 2))
(/.f64 5/24 (*.f64 N N))
(/.f64 5/24 (pow.f64 N 2))
(/.f64 5/24 (*.f64 N N))
(/.f64 5/24 (pow.f64 N 2))
(/.f64 5/24 (*.f64 N N))
(/.f64 5/24 (pow.f64 N 2))
(/.f64 5/24 (*.f64 N N))

eval361.0ms (5.7%)

Compiler: Compiled 17197 to 11552 computations (32.8% saved)

prune112.0ms (1.8%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	528	4	532
Fresh	1	2	3
Picked	1	0	1
Done	4	4	8
Total	534	10	544

Error

Counts

544 → 10

Alt Table

Click to see full alt table

Status	Error	Program
✓	29.9b	(/.f64 1 N)
▶	0.0b	(log1p.f64 (/.f64 1 N))
▶	30.9b	(/.f64 1 (/.f64 N (+.f64 1 (/.f64 -1/2 N))))
▶	19.2b	(cbrt.f64 (pow.f64 (log1p.f64 (/.f64 1 N)) 3))
✓	33.3b	(neg.f64 (log.f64 N))
	61.0b	N
▶	60.8b	(-.f64 (+.f64 1 (/.f64 (+.f64 1 (/.f64 -1/2 N)) N)) 1)
▶	30.2b	(+.f64 (/.f64 1 N) (.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2)))
✓	30.9b	(/.f64 (+.f64 1 (/.f64 -1/2 N)) N)
✓	46.2b	(/.f64 (-.f64 N (/.f64 (.f64 N 1/2) N)) (.f64 N N))

Compiler

Compiled 132 to 102 computations (22.7% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (/.f64 1 N))

Compiler

Compiled 10 to 7 computations (30% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	N	@	0	(log1p.f64 (/.f64 1 N))
0.0ms	N	@	inf	(log1p.f64 (/.f64 1 N))
0.0ms	N	@	-inf	(log1p.f64 (/.f64 1 N))

rewrite41.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

397×	`pow1_binary64`
383×	`add-sqr-sqrt_binary64`
375×	`*-un-lft-identity_binary64`
366×	`add-log-exp_binary64`
366×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	96	6
2	1059	6

Stop Event

1×	node limit

Counts

1 → 27

Calls

Call 1

Inputs
(log1p.f64 (/.f64 1 N))

Outputs

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

simplify41.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

39 → 42

Calls

Call 1

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

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

localize12.0ms (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)))

Compiler

Compiled 28 to 21 computations (25% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite69.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

937×	`pow1_binary64`
877×	`add-log-exp_binary64`
876×	`log1p-expm1-u_binary64`
876×	`expm1-log1p-u_binary64`
90×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	182	20
2	2461	20

Stop Event

1×	node limit

Counts

2 → 75

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 (+.f64 -1 (neg.f64 (/.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 (+.f64 -1 (neg.f64 (/.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 log1p.f64 (expm1.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 +.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)) (+.f64 -1 (neg.f64 (/.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 log1p.f64 (expm1.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)))))))

simplify65.0ms (1%)

Algorithm

1×	egg-herbie

Rules

887×	`fma-def_binary64`
648×	`times-frac_binary64`
500×	`associate-*l/_binary64`
482×	`fma-neg_binary64`
427×	`associate-*r/_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	42	270
1	105	270
2	232	268
3	626	261
4	1674	255
5	4149	255
6	7758	255

Stop Event

1×	node limit

Counts

99 → 94

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

localize15.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (/.f64 (+.f64 1 (/.f64 -1/2 N)) N))
	0.1b	(/.f64 (+.f64 1 (/.f64 -1/2 N)) N)
✓	2.6b	(-.f64 (+.f64 1 (/.f64 (+.f64 1 (/.f64 -1/2 N)) N)) 1)

Compiler

Compiled 39 to 30 computations (23.1% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite87.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	29
1	215	23
2	3184	23

Stop Event

1×	node limit

Counts

2 → 168

Calls

Call 1

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

Outputs

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

simplify50.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

730×	`times-frac_binary64`
535×	`associate-/r*_binary64`
492×	`associate-/l/_binary64`
434×	`unswap-sqr_binary64`
353×	`distribute-neg-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	264
1	32	264
2	59	264
3	129	264
4	322	264
5	1055	264
6	5343	264

Stop Event

1×	node limit

Counts

192 → 177

Calls

Call 1

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

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

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1 N) (.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2)))
✓	0.1b	(.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2))
✓	0.4b	(/.f64 1/3 N)
✓	1.1b	(/.f64 1 (*.f64 N N))

Compiler

Compiled 50 to 32 computations (36% saved)

series5.0ms (0.1%)

Counts

4 → 36

Calls

12 calls:

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

rewrite93.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	43
1	274	38
2	3774	38

Stop Event

1×	node limit

Counts

4 → 193

Calls

Call 1

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

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

simplify94.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 5 (0.0ms)

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

Stop Event

1×	node limit

Counts

229 → 206

Calls

Call 1

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

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

localize38.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(log1p.f64 (/.f64 1 N))
✓	0.4b	(pow.f64 (log1p.f64 (/.f64 1 N)) 3)
✓	19.2b	(cbrt.f64 (pow.f64 (log1p.f64 (/.f64 1 N)) 3))

Compiler

Compiled 24 to 19 computations (20.8% saved)

series5.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	N	@	0	(pow.f64 (log1p.f64 (/.f64 1 N)) 3)
1.0ms	N	@	inf	(pow.f64 (log1p.f64 (/.f64 1 N)) 3)
1.0ms	N	@	-inf	(pow.f64 (log1p.f64 (/.f64 1 N)) 3)
1.0ms	N	@	0	(cbrt.f64 (pow.f64 (log1p.f64 (/.f64 1 N)) 3))
1.0ms	N	@	-inf	(cbrt.f64 (pow.f64 (log1p.f64 (/.f64 1 N)) 3))

rewrite65.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

565×	`pow1_binary64`
533×	`add-log-exp_binary64`
532×	`expm1-log1p-u_binary64`
531×	`log1p-expm1-u_binary64`
519×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	164	15
2	1563	15

Stop Event

1×	node limit

Counts

2 → 38

Calls

Call 1

Inputs
(cbrt.f64 (pow.f64 (log1p.f64 (/.f64 1 N)) 3))
(pow.f64 (log1p.f64 (/.f64 1 N)) 3)

Outputs

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

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

simplify88.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

643×	`distribute-rgt-in_binary64`
625×	`fma-neg_binary64`
617×	`distribute-lft-in_binary64`
506×	`fma-def_binary64`
319×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	83	536
1	257	526
2	821	499
3	3591	481

Stop Event

1×	node limit

Counts

62 → 68

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 (pow.f64 (log.f64 N) 3))
(+.f64 (.f64 -1 (pow.f64 (log.f64 N) 3)) (.f64 N (+.f64 (pow.f64 (log.f64 N) 2) (*.f64 2 (pow.f64 (log.f64 N) 2)))))
(+.f64 (.f64 -1 (pow.f64 (log.f64 N) 3)) (+.f64 (.f64 (pow.f64 N 2) (+.f64 (.f64 -1/2 (pow.f64 (log.f64 N) 2)) (+.f64 (.f64 -1 (.f64 (log.f64 N) (+.f64 (log.f64 N) 1))) (.f64 -2 (log.f64 N))))) (.f64 N (+.f64 (pow.f64 (log.f64 N) 2) (.f64 2 (pow.f64 (log.f64 N) 2))))))
(+.f64 (.f64 (pow.f64 N 3) (+.f64 1 (+.f64 (.f64 2 (log.f64 N)) (+.f64 (.f64 -1 (.f64 (log.f64 N) (-.f64 (.f64 -2/3 (log.f64 N)) 1))) (.f64 1/3 (pow.f64 (log.f64 N) 2)))))) (+.f64 (.f64 -1 (pow.f64 (log.f64 N) 3)) (+.f64 (.f64 (pow.f64 N 2) (+.f64 (.f64 -1/2 (pow.f64 (log.f64 N) 2)) (+.f64 (.f64 -1 (.f64 (log.f64 N) (+.f64 (log.f64 N) 1))) (.f64 -2 (log.f64 N))))) (.f64 N (+.f64 (pow.f64 (log.f64 N) 2) (.f64 2 (pow.f64 (log.f64 N) 2)))))))
(/.f64 1 (pow.f64 N 3))
(-.f64 (/.f64 1 (pow.f64 N 3)) (*.f64 3/2 (/.f64 1 (pow.f64 N 4))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 N 3)) (.f64 7/4 (/.f64 1 (pow.f64 N 5)))) (.f64 3/2 (/.f64 1 (pow.f64 N 4))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 N 3)) (.f64 7/4 (/.f64 1 (pow.f64 N 5)))) (+.f64 (.f64 3/2 (/.f64 1 (pow.f64 N 4))) (*.f64 15/8 (/.f64 1 (pow.f64 N 6)))))
(/.f64 1 (pow.f64 N 3))
(-.f64 (/.f64 1 (pow.f64 N 3)) (*.f64 3/2 (/.f64 1 (pow.f64 N 4))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 N 3)) (.f64 7/4 (/.f64 1 (pow.f64 N 5)))) (.f64 3/2 (/.f64 1 (pow.f64 N 4))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 N 3)) (.f64 7/4 (/.f64 1 (pow.f64 N 5)))) (+.f64 (.f64 3/2 (/.f64 1 (pow.f64 N 4))) (*.f64 15/8 (/.f64 1 (pow.f64 N 6)))))

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))
(+.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 N (-.f64 (.f64 (.f64 N N) (+.f64 (*.f64 N 1/3) -1/2)) (log.f64 N)))
(fma.f64 N (.f64 N (+.f64 -1/2 (.f64 N 1/3))) (-.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 (/.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 (/.f64 1 N) (/.f64 -1/2 (*.f64 N N))) (/.f64 1/3 (pow.f64 N 3)))
(-.f64 (+.f64 (/.f64 1 N) (.f64 1/3 (/.f64 1 (pow.f64 N 3)))) (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 N 4))) (*.f64 1/2 (/.f64 1 (pow.f64 N 2)))))
(+.f64 (/.f64 1 N) (-.f64 (/.f64 1/3 (pow.f64 N 3)) (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4)))))
(+.f64 (-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (/.f64 1/4 (pow.f64 N 4))) (/.f64 -1/2 (*.f64 N N)))
(+.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 1 N)
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
(+.f64 (/.f64 1 N) (/.f64 -1/2 (*.f64 N N)))
(-.f64 (+.f64 (/.f64 1 N) (.f64 1/3 (/.f64 1 (pow.f64 N 3)))) (.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(+.f64 (/.f64 1 N) (-.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1/2 (*.f64 N N))))
(+.f64 (/.f64 1 N) (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 -1/2 (*.f64 N N))))
(+.f64 (+.f64 (/.f64 1 N) (/.f64 -1/2 (*.f64 N N))) (/.f64 1/3 (pow.f64 N 3)))
(-.f64 (+.f64 (/.f64 1 N) (.f64 1/3 (/.f64 1 (pow.f64 N 3)))) (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 N 4))) (*.f64 1/2 (/.f64 1 (pow.f64 N 2)))))
(+.f64 (/.f64 1 N) (-.f64 (/.f64 1/3 (pow.f64 N 3)) (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4)))))
(+.f64 (-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (/.f64 1/4 (pow.f64 N 4))) (/.f64 -1/2 (*.f64 N N)))
(+.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 -1 (pow.f64 (log.f64 N) 3))
(neg.f64 (pow.f64 (log.f64 N) 3))
(+.f64 (.f64 -1 (pow.f64 (log.f64 N) 3)) (.f64 N (+.f64 (pow.f64 (log.f64 N) 2) (*.f64 2 (pow.f64 (log.f64 N) 2)))))
(fma.f64 -1 (pow.f64 (log.f64 N) 3) (.f64 N (.f64 3 (pow.f64 (log.f64 N) 2))))
(-.f64 (.f64 N (.f64 3 (pow.f64 (log.f64 N) 2))) (pow.f64 (log.f64 N) 3))
(.f64 (pow.f64 (log.f64 N) 2) (-.f64 (.f64 N 3) (log.f64 N)))
(+.f64 (.f64 -1 (pow.f64 (log.f64 N) 3)) (+.f64 (.f64 (pow.f64 N 2) (+.f64 (.f64 -1/2 (pow.f64 (log.f64 N) 2)) (+.f64 (.f64 -1 (.f64 (log.f64 N) (+.f64 (log.f64 N) 1))) (.f64 -2 (log.f64 N))))) (.f64 N (+.f64 (pow.f64 (log.f64 N) 2) (.f64 2 (pow.f64 (log.f64 N) 2))))))
(fma.f64 -1 (pow.f64 (log.f64 N) 3) (fma.f64 (.f64 N N) (fma.f64 -1/2 (pow.f64 (log.f64 N) 2) (fma.f64 -1 (.f64 (log.f64 N) (+.f64 (log.f64 N) 1)) (.f64 (log.f64 N) -2))) (.f64 N (*.f64 3 (pow.f64 (log.f64 N) 2)))))
(-.f64 (fma.f64 N (.f64 3 (pow.f64 (log.f64 N) 2)) (.f64 (.f64 N N) (fma.f64 -1/2 (pow.f64 (log.f64 N) 2) (-.f64 (.f64 (log.f64 N) -2) (+.f64 (log.f64 N) (pow.f64 (log.f64 N) 2)))))) (pow.f64 (log.f64 N) 3))
(fma.f64 N (.f64 N (fma.f64 -1/2 (pow.f64 (log.f64 N) 2) (.f64 (log.f64 N) (-.f64 -2 (+.f64 (log.f64 N) 1))))) (.f64 (pow.f64 (log.f64 N) 2) (-.f64 (.f64 N 3) (log.f64 N))))
(fma.f64 N (.f64 N (fma.f64 (log.f64 N) -2 (-.f64 (.f64 (pow.f64 (log.f64 N) 2) -3/2) (log.f64 N)))) (.f64 (pow.f64 (log.f64 N) 2) (-.f64 (.f64 N 3) (log.f64 N))))
(+.f64 (.f64 (pow.f64 N 3) (+.f64 1 (+.f64 (.f64 2 (log.f64 N)) (+.f64 (.f64 -1 (.f64 (log.f64 N) (-.f64 (.f64 -2/3 (log.f64 N)) 1))) (.f64 1/3 (pow.f64 (log.f64 N) 2)))))) (+.f64 (.f64 -1 (pow.f64 (log.f64 N) 3)) (+.f64 (.f64 (pow.f64 N 2) (+.f64 (.f64 -1/2 (pow.f64 (log.f64 N) 2)) (+.f64 (.f64 -1 (.f64 (log.f64 N) (+.f64 (log.f64 N) 1))) (.f64 -2 (log.f64 N))))) (.f64 N (+.f64 (pow.f64 (log.f64 N) 2) (.f64 2 (pow.f64 (log.f64 N) 2)))))))
(fma.f64 (pow.f64 N 3) (+.f64 1 (fma.f64 2 (log.f64 N) (fma.f64 -1 (.f64 (log.f64 N) (fma.f64 -2/3 (log.f64 N) -1)) (.f64 1/3 (pow.f64 (log.f64 N) 2))))) (fma.f64 -1 (pow.f64 (log.f64 N) 3) (fma.f64 (.f64 N N) (fma.f64 -1/2 (pow.f64 (log.f64 N) 2) (fma.f64 -1 (.f64 (log.f64 N) (+.f64 (log.f64 N) 1)) (.f64 (log.f64 N) -2))) (.f64 N (*.f64 3 (pow.f64 (log.f64 N) 2))))))
(fma.f64 (pow.f64 N 3) (+.f64 1 (fma.f64 (log.f64 N) 2 (fma.f64 (neg.f64 (log.f64 N)) (fma.f64 (log.f64 N) -2/3 -1) (.f64 1/3 (pow.f64 (log.f64 N) 2))))) (-.f64 (fma.f64 N (.f64 3 (pow.f64 (log.f64 N) 2)) (.f64 (.f64 N N) (fma.f64 -1/2 (pow.f64 (log.f64 N) 2) (-.f64 (*.f64 (log.f64 N) -2) (+.f64 (log.f64 N) (pow.f64 (log.f64 N) 2)))))) (pow.f64 (log.f64 N) 3)))
(fma.f64 (pow.f64 N 3) (+.f64 1 (fma.f64 1/3 (pow.f64 (log.f64 N) 2) (.f64 (log.f64 N) (-.f64 2 (fma.f64 (log.f64 N) -2/3 -1))))) (fma.f64 N (.f64 N (fma.f64 -1/2 (pow.f64 (log.f64 N) 2) (.f64 (log.f64 N) (-.f64 -2 (+.f64 (log.f64 N) 1))))) (.f64 (pow.f64 (log.f64 N) 2) (-.f64 (*.f64 N 3) (log.f64 N)))))
(fma.f64 (pow.f64 N 3) (+.f64 1 (.f64 (log.f64 N) (-.f64 (+.f64 (log.f64 N) 1) -2))) (fma.f64 N (.f64 N (fma.f64 (log.f64 N) -2 (-.f64 (.f64 (pow.f64 (log.f64 N) 2) -3/2) (log.f64 N)))) (.f64 (pow.f64 (log.f64 N) 2) (-.f64 (*.f64 N 3) (log.f64 N)))))
(/.f64 1 (pow.f64 N 3))
(-.f64 (/.f64 1 (pow.f64 N 3)) (*.f64 3/2 (/.f64 1 (pow.f64 N 4))))
(-.f64 (/.f64 1 (pow.f64 N 3)) (/.f64 3/2 (pow.f64 N 4)))
(+.f64 (/.f64 1 (pow.f64 N 3)) (/.f64 -3/2 (pow.f64 N 4)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 N 3)) (.f64 7/4 (/.f64 1 (pow.f64 N 5)))) (.f64 3/2 (/.f64 1 (pow.f64 N 4))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 N 3)) (/.f64 7/4 (pow.f64 N 5))) (/.f64 3/2 (pow.f64 N 4)))
(+.f64 (/.f64 7/4 (pow.f64 N 5)) (+.f64 (/.f64 1 (pow.f64 N 3)) (/.f64 -3/2 (pow.f64 N 4))))
(+.f64 (/.f64 1 (pow.f64 N 3)) (+.f64 (/.f64 7/4 (pow.f64 N 5)) (/.f64 -3/2 (pow.f64 N 4))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 N 3)) (.f64 7/4 (/.f64 1 (pow.f64 N 5)))) (+.f64 (.f64 3/2 (/.f64 1 (pow.f64 N 4))) (*.f64 15/8 (/.f64 1 (pow.f64 N 6)))))
(+.f64 (/.f64 1 (pow.f64 N 3)) (-.f64 (/.f64 7/4 (pow.f64 N 5)) (+.f64 (/.f64 3/2 (pow.f64 N 4)) (/.f64 15/8 (pow.f64 N 6)))))
(+.f64 (/.f64 7/4 (pow.f64 N 5)) (-.f64 (/.f64 1 (pow.f64 N 3)) (+.f64 (/.f64 3/2 (pow.f64 N 4)) (/.f64 15/8 (pow.f64 N 6)))))
(+.f64 (/.f64 1 (pow.f64 N 3)) (+.f64 (+.f64 (/.f64 7/4 (pow.f64 N 5)) (/.f64 -3/2 (pow.f64 N 4))) (/.f64 -15/8 (pow.f64 N 6))))
(/.f64 1 (pow.f64 N 3))
(-.f64 (/.f64 1 (pow.f64 N 3)) (*.f64 3/2 (/.f64 1 (pow.f64 N 4))))
(-.f64 (/.f64 1 (pow.f64 N 3)) (/.f64 3/2 (pow.f64 N 4)))
(+.f64 (/.f64 1 (pow.f64 N 3)) (/.f64 -3/2 (pow.f64 N 4)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 N 3)) (.f64 7/4 (/.f64 1 (pow.f64 N 5)))) (.f64 3/2 (/.f64 1 (pow.f64 N 4))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 N 3)) (/.f64 7/4 (pow.f64 N 5))) (/.f64 3/2 (pow.f64 N 4)))
(+.f64 (/.f64 7/4 (pow.f64 N 5)) (+.f64 (/.f64 1 (pow.f64 N 3)) (/.f64 -3/2 (pow.f64 N 4))))
(+.f64 (/.f64 1 (pow.f64 N 3)) (+.f64 (/.f64 7/4 (pow.f64 N 5)) (/.f64 -3/2 (pow.f64 N 4))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 N 3)) (.f64 7/4 (/.f64 1 (pow.f64 N 5)))) (+.f64 (.f64 3/2 (/.f64 1 (pow.f64 N 4))) (*.f64 15/8 (/.f64 1 (pow.f64 N 6)))))
(+.f64 (/.f64 1 (pow.f64 N 3)) (-.f64 (/.f64 7/4 (pow.f64 N 5)) (+.f64 (/.f64 3/2 (pow.f64 N 4)) (/.f64 15/8 (pow.f64 N 6)))))
(+.f64 (/.f64 7/4 (pow.f64 N 5)) (-.f64 (/.f64 1 (pow.f64 N 3)) (+.f64 (/.f64 3/2 (pow.f64 N 4)) (/.f64 15/8 (pow.f64 N 6)))))
(+.f64 (/.f64 1 (pow.f64 N 3)) (+.f64 (+.f64 (/.f64 7/4 (pow.f64 N 5)) (/.f64 -3/2 (pow.f64 N 4))) (/.f64 -15/8 (pow.f64 N 6))))

eval434.0ms (6.8%)

Compiler: Compiled 11070 to 8710 computations (21.3% saved)

prune93.0ms (1.5%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	663	2	665
Fresh	0	1	1
Picked	0	1	1
Done	5	3	8
Total	668	7	675

Error

Counts

675 → 7

Alt Table

Click to see full alt table

Status	Error	Program
✓	29.9b	(/.f64 1 N)
✓	0.0b	(log1p.f64 (/.f64 1 N))
✓	19.2b	(cbrt.f64 (pow.f64 (log1p.f64 (/.f64 1 N)) 3))
	30.2b	(+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N))
✓	33.3b	(neg.f64 (log.f64 N))
	61.0b	N
	26.6b	(/.f64 1 (+.f64 N 1/2))

Compiler

Compiled 43 to 33 computations (23.3% saved)

regimes25.0ms (0.4%)

Counts

24 → 1

Calls

Call 1

Inputs
N
(/.f64 1 N)
(/.f64 1 (+.f64 N 1/2))
(/.f64 (+.f64 1 (/.f64 -1/2 N)) N)
(/.f64 1 (/.f64 N (+.f64 1 (/.f64 -1/2 N))))
(-.f64 (/.f64 1 N) (/.f64 (/.f64 1/2 N) N))
(-.f64 (+.f64 1 (/.f64 (+.f64 1 (/.f64 -1/2 N)) N)) 1)
(/.f64 (-.f64 N (/.f64 (.f64 N 1/2) N)) (.f64 N N))
(+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N))
(+.f64 (/.f64 1 N) (.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2)))
(neg.f64 (log.f64 N))
(log1p.f64 (/.f64 1 N))
(-.f64 N (log.f64 N))
(log.f64 (+.f64 1 (/.f64 1 N)))
(log.f64 (/.f64 (+.f64 N 1) N))
(+.f64 (+.f64 (/.f64 1 N) (/.f64 -1/2 (.f64 N N))) (.f64 (/.f64 1 (pow.f64 N 3)) (-.f64 1/3 (/.f64 1/4 N))))
(+.f64 (/.f64 1 N) (+.f64 (/.f64 -1/2 (.f64 N N)) (.f64 (/.f64 1 (pow.f64 N 3)) (+.f64 (/.f64 -1/4 N) 1/3))))
(-.f64 (log1p.f64 N) (log.f64 N))
(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
(cbrt.f64 (pow.f64 (log1p.f64 (/.f64 1 N)) 3))
(exp.f64 (-.f64 (+.f64 (/.f64 5/24 (*.f64 N N)) (/.f64 -1/2 N)) (-.f64 (log.f64 N) (/.f64 -1/8 (pow.f64 N 3)))))
(exp.f64 (log.f64 (-.f64 (log1p.f64 N) (log.f64 N))))
(/.f64 (-.f64 (pow.f64 (log1p.f64 N) 2) (pow.f64 (log.f64 N) 2)) (+.f64 (log1p.f64 N) (log.f64 N)))
(/.f64 1 (/.f64 (+.f64 (log1p.f64 N) (log.f64 N)) (-.f64 (pow.f64 (log1p.f64 N) 2) (pow.f64 (log.f64 N) 2))))

Outputs
(log1p.f64 (/.f64 1 N))

Calls

2 calls:

13.0ms	N
6.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))

Results

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

Compiler

Compiled 237 to 152 computations (35.9% saved)

regimes15.0ms (0.2%)

Counts

11 → 2

Calls

Call 1

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

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

Calls

1 calls:

12.0ms

Results

Error	Segments	Branch
0.9b	2	`N`

Compiler

Compiled 90 to 62 computations (31.1% saved)

bsearch27.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
26.0ms	0.4213765771501462	21.002518204184227

Compiler

Compiled 12 to 9 computations (25% saved)

regimes10.0ms (0.2%)

Counts

10 → 1

Calls

Call 1

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

Outputs
(/.f64 1 (+.f64 N 1/2))

Calls

1 calls:

6.0ms

Results

Error	Segments	Branch
26.6b	1	`N`

Compiler

Compiled 87 to 60 computations (31% saved)

regimes4.0ms (0.1%)

Accuracy

Total -31.0b remaining (-103.7%)

Threshold costs -31.0b (-103.7%)

Counts

2 → 1

Calls

Call 1

Inputs
N
(/.f64 1 N)

Outputs
(/.f64 1 N)

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
29.9b	1	`N`

Compiler

Compiled 7 to 4 computations (42.9% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	48
1	29	48
2	31	48
3	32	48

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(log1p.f64 (/.f64 1 N))
(if (<=.f64 N 7773025877344475136/18446744073709551616) (neg.f64 (log.f64 N)) (+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N)))
(/.f64 1 (+.f64 N 1/2))
(/.f64 1 N)
N

Outputs
(log1p.f64 (/.f64 1 N))
(if (<=.f64 N 7773025877344475136/18446744073709551616) (neg.f64 (log.f64 N)) (+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N)))
(if (<=.f64 N 3795422791672107/9007199254740992) (neg.f64 (log.f64 N)) (+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N)))
(/.f64 1 (+.f64 N 1/2))
(/.f64 1 N)
N

Compiler

Compiled 38 to 28 computations (26.3% saved)

soundness15.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×

saturated

Compiler

Compiled 22 to 16 computations (27.3% saved)

end36.0ms (0.6%)

Compiler: Compiled 34 to 24 computations (29.4% saved)