Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	0%	50%	4

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample2.0s (52%)

Results

889.0ms	2092×	body	1024	valid
531.0ms	4378×	body	128	valid
311.0ms	1038×	body	512	valid
155.0ms	259×	body	2048	valid
105.0ms	489×	body	256	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	8
2	17	8
3	24	8
4	31	8
5	48	8
6	73	8
7	93	8
8	110	8
9	120	8
10	124	8
11	126	8
12	112	8

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

28.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	28.1b	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))

Compiler

Compiled 29 to 20 computations (31% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.9b	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
✓	2.9b	(log.f64 (+.f64 N 1))

series6.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
3.0ms	(log.f64 (+.f64 N 1))

rewrite38.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
17×	`pow1_binary64`
16×	`prod-diff_binary64`
15×	`add-cube-cbrt_binary64`

Counts

2 → 68

Calls

2 calls:

32.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
2.0ms	(log.f64 (+.f64 N 1))

simplify126.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

594×	`fma-def_binary64`
411×	`sub-neg_binary64`
349×	`associate-l_binary64`
292×	`associate-r_binary64`
272×	`unswap-sqr_binary64`

Counts

92 → 115

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	150	1267
1	325	980
2	951	974
3	3284	974
4	4236	974
5	4663	968
6	4951	968
7	4833	968

prune63.0ms (1.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	112	3	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	113	3	116

Error

0.0b

Counts

116 → 3

Alt Table

Status	Error	Program
	28.1b	(/.f64 (-.f64 (.f64 (log.f64 (+.f64 N 1)) (log.f64 (+.f64 N 1))) (.f64 (log.f64 N) (log.f64 N))) (+.f64 (log.f64 (+.f64 N 1)) (log.f64 N)))
	33.8b	(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
▶	28.1b	(+.f64 (log.f64 (sqrt.f64 (+.f64 N 1))) (-.f64 (*.f64 1/2 (log1p.f64 N)) (log.f64 N)))

Compiler

Compiled 1820 to 1016 computations (44.2% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 1/2 (log1p.f64 N)) (log.f64 N))
✓	2.4b	(+.f64 (log.f64 (sqrt.f64 (+.f64 N 1))) (-.f64 (*.f64 1/2 (log1p.f64 N)) (log.f64 N)))
✓	2.9b	(log.f64 (sqrt.f64 (+.f64 N 1)))

series21.0ms (0.5%)

Counts

3 → 20

Calls

3 calls:

10.0ms	(+.f64 (log.f64 (sqrt.f64 (+.f64 N 1))) (-.f64 (*.f64 1/2 (log1p.f64 N)) (log.f64 N)))
7.0ms	(log.f64 (sqrt.f64 (+.f64 N 1)))
3.0ms	(-.f64 (*.f64 1/2 (log1p.f64 N)) (log.f64 N))

rewrite19.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
17×	`log-prod_binary64`
13×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`pow1_binary64`

Counts

3 → 88

Calls

3 calls:

8.0ms	(+.f64 (log.f64 (sqrt.f64 (+.f64 N 1))) (-.f64 (*.f64 1/2 (log1p.f64 N)) (log.f64 N)))
4.0ms	(-.f64 (*.f64 1/2 (log1p.f64 N)) (log.f64 N))
3.0ms	(log.f64 (sqrt.f64 (+.f64 N 1)))

simplify206.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

1881×	`fma-neg_binary64`
482×	`associate-l_binary64`
404×	`associate-r_binary64`
267×	`times-frac_binary64`
265×	`distribute-rgt-in_binary64`

Counts

108 → 164

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	190	1764
1	466	1631
2	1382	1609
3	4524	1490
4	4741	1319
5	4809	1319
6	4890	1295
7	4983	1295
8	4992	1279
9	6395	1279

prune99.0ms (2.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	164	3	167

Error

0.0b

Counts

167 → 3

Alt Table

Status	Error	Program
▶	28.1b	(/.f64 (-.f64 (.f64 (log.f64 (+.f64 N 1)) (log.f64 (+.f64 N 1))) (.f64 (log.f64 N) (log.f64 N))) (+.f64 (log.f64 (+.f64 N 1)) (log.f64 N)))
	33.8b	(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
✓	28.1b	(+.f64 (log.f64 (sqrt.f64 (+.f64 N 1))) (-.f64 (*.f64 1/2 (log1p.f64 N)) (log.f64 N)))

Compiler

Compiled 3287 to 1992 computations (39.4% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (-.f64 (.f64 (log.f64 (+.f64 N 1)) (log.f64 (+.f64 N 1))) (.f64 (log.f64 N) (log.f64 N))) (+.f64 (log.f64 (+.f64 N 1)) (log.f64 N)))
✓	0.5b	(*.f64 (log.f64 N) (log.f64 N))
✓	1.9b	(-.f64 (.f64 (log.f64 (+.f64 N 1)) (log.f64 (+.f64 N 1))) (.f64 (log.f64 N) (log.f64 N)))
	2.9b	(log.f64 (+.f64 N 1))

series59.0ms (1.5%)

Counts

3 → 36

Calls

3 calls:

33.0ms

(*.f64 (log.f64 N) (log.f64 N))

20.0ms

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

7.0ms

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

rewrite60.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64`
36×	`pow1_binary64`
28×	`times-frac_binary64`
28×	`add-sqr-sqrt_binary64`
26×	`log-pow_binary64`

Counts

3 → 127

Calls

3 calls:

40.0ms

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

6.0ms

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

3.0ms

(*.f64 (log.f64 N) (log.f64 N))

simplify154.0ms (4%)

Algorithm

1×	egg-herbie

Rules

365×	`fma-neg_binary64`
309×	`sub-neg_binary64`
253×	`fma-def_binary64`
240×	`associate-+r+_binary64`
212×	`+-commutative_binary64`

Counts

163 → 216

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	367	6363
1	1035	5193
2	3860	4862
3	4955	4861
4	5052	4861

prune286.0ms (7.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	352	2	354
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	353	4	357

Error

0.0b

Counts

357 → 4

Alt Table

Status	Error	Program
	33.8b	(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
▶	28.7b	(exp.f64 (log.f64 (/.f64 (-.f64 (.f64 (log.f64 (+.f64 N 1)) (log.f64 (+.f64 N 1))) (.f64 (log.f64 N) (log.f64 N))) (+.f64 (log.f64 (+.f64 N 1)) (log.f64 N)))))
	33.9b	(/.f64 (+.f64 (.f64 2 (/.f64 (log.f64 N) N)) (-.f64 (/.f64 1 (.f64 N N)) (/.f64 (log.f64 N) (*.f64 N N)))) (+.f64 (log.f64 (+.f64 N 1)) (log.f64 N)))
✓	28.1b	(+.f64 (log.f64 (sqrt.f64 (+.f64 N 1))) (-.f64 (*.f64 1/2 (log1p.f64 N)) (log.f64 N)))

Compiler

Compiled 12582 to 7734 computations (38.5% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(*.f64 (log.f64 N) (log.f64 N))
✓	0.7b	(exp.f64 (log.f64 (/.f64 (-.f64 (.f64 (log.f64 (+.f64 N 1)) (log.f64 (+.f64 N 1))) (.f64 (log.f64 N) (log.f64 N))) (+.f64 (log.f64 (+.f64 N 1)) (log.f64 N)))))
	1.9b	(-.f64 (.f64 (log.f64 (+.f64 N 1)) (log.f64 (+.f64 N 1))) (.f64 (log.f64 N) (log.f64 N)))
	2.9b	(log.f64 (+.f64 N 1))

series22.0ms (0.6%)

Counts

1 → 12

Calls

1 calls:

22.0ms

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

rewrite18.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`exp-sum_binary64`
34×	`log-prod_binary64`
30×	`*-un-lft-identity_binary64`
28×	`times-frac_binary64`
18×	`pow1_binary64`

Counts

1 → 49

Calls

1 calls:

9.0ms

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

simplify120.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

724×	`times-frac_binary64`
375×	`fma-neg_binary64`
203×	`cancel-sign-sub-inv_binary64`
194×	`sub-neg_binary64`
187×	`associate-+r+_binary64`

Counts

61 → 80

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	281	4373
1	728	3618
2	2500	3306
3	4817	3305
4	5066	3305

prune244.0ms (6.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	341	1	342
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	342	4	346

Error

0.0b

Counts

346 → 4

Alt Table

Status	Error	Program
	33.9b	(/.f64 (+.f64 (.f64 2 (/.f64 (log.f64 N) N)) (-.f64 (/.f64 1 (.f64 N N)) (/.f64 (log.f64 N) (*.f64 N N)))) (+.f64 (log.f64 (+.f64 N 1)) (log.f64 N)))
	28.8b	(pow.f64 (E.f64) (log.f64 (/.f64 (-.f64 (.f64 (log.f64 (+.f64 N 1)) (log.f64 (+.f64 N 1))) (.f64 (log.f64 N) (log.f64 N))) (+.f64 (log.f64 (+.f64 N 1)) (log.f64 N)))))
	33.8b	(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
✓	28.1b	(+.f64 (log.f64 (sqrt.f64 (+.f64 N 1))) (-.f64 (*.f64 1/2 (log1p.f64 N)) (log.f64 N)))

Compiler

Compiled 12747 to 7928 computations (37.8% saved)

regimes185.0ms (4.8%)

Accuracy

Total 0.1b remaining (51.4%)

Threshold costs 0.1b (51.4%)

Counts

46 → 2

Compiler

Compiled 1331 to 927 computations (30.4% saved)

bsearch1.0ms (0%)

Compiler: Compiled 8 to 6 computations (25% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	48
1	30	48
2	41	48
3	45	48
4	47	48
5	45	48

end84.0ms (2.2%)

Compiler: Compiled 143 to 97 computations (32.2% saved)

Iter	Nodes	Cost
0	7	11
1	12	8
2	17	8
3	24	8
4	31	8
5	48	8
6	73	8
7	93	8
8	110	8
9	120	8
10	124	8
11	126	8
12	112	8

Iter	Nodes	Cost
0	7	11
1	12	8
2	17	8
3	24	8
4	31	8
5	48	8
6	73	8
7	93	8
8	110	8
9	120	8
10	124	8
11	126	8
12	112	8

Details

analyze1.0ms (0%)

sample2.0s (52%)

simplify10.0ms (0.2%)

prune2.0ms (0.1%)

localize6.0ms (0.1%)

series6.0ms (0.1%)

rewrite38.0ms (1%)

simplify126.0ms (3.2%)

prune63.0ms (1.6%)

localize10.0ms (0.3%)

series21.0ms (0.5%)

rewrite19.0ms (0.5%)

simplify206.0ms (5.3%)

prune99.0ms (2.6%)

localize10.0ms (0.3%)

series59.0ms (1.5%)

rewrite60.0ms (1.5%)

simplify154.0ms (4%)

prune286.0ms (7.3%)

localize13.0ms (0.3%)

series22.0ms (0.6%)

rewrite18.0ms (0.5%)

simplify120.0ms (3.1%)

prune244.0ms (6.3%)

regimes185.0ms (4.8%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end84.0ms (2.2%)

Profiling

Iter	Nodes	Cost
0	7	11
1	12	8
2	17	8
3	24	8
4	31	8
5	48	8
6	73	8
7	93	8
8	110	8
9	120	8
10	124	8
11	126	8
12	112	8