Details

analyze22.0ms (0.8%)

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)

sample40.0ms (1.4%)

Algorithm

1×

intervals

Results

14.0ms	66×	body	1024	valid
7.0ms	128×	body	128	valid
5.0ms	35×	body	512	valid
4.0ms	12×	body	2048	valid
1.0ms	15×	body	256	valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify11.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

15×	`sub-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
10×	`distribute-rgt-in_binary64`
9×	`neg-mul-1_binary64`
8×	`associate--r+_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	22	11
4	28	11
5	43	11
6	65	11
7	77	11
8	89	11
9	91	11
10	85	11
11	71	11

prune6.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	0	0
Total	1	1

Error

31.0b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	31.0b	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))

Compiler

Compiled 16 to 12 computations (25% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

1.7b	(log.f64 (+.f64 N 1))
2.2b	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))

rewrite48.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

30.5b

Rules

14×	`*-un-lft-identity_binary64`
11×	`log-prod_binary64`
8×	`pow1_binary64` `add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64` `log-pow_binary64`
4×	`cancel-sign-sub-inv_binary64` `distribute-lft-out--_binary64` `log-div_binary64` `associate--l+_binary64`

Counts

2 → 44

Calls

2 calls:

7.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
3.0ms	(log.f64 (+.f64 N 1))

Compiler

Compiled 533 to 353 computations (33.8% saved)

series40.0ms (1.4%)

Error

0.0b

Counts

2 → 20

Calls

2 calls:

16.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
10.0ms	(log.f64 (+.f64 N 1))

Compiler

Compiled 515 to 399 computations (22.5% saved)

simplify102.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

424×	`distribute-rgt-in_binary64`
356×	`distribute-lft-in_binary64`
215×	`sub-neg_binary64`
194×	`neg-mul-1_binary64`
190×	`associate-+l-_binary64`

Counts

64 → 36

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	118	880
1	255	836
2	566	827
3	1671	827
4	4295	827
5	4930	827
6	4879	827

prune22.0ms (0.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	34	2	36
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	35	2	37

Error

0.0b

Counts

37 → 2

Alt Table

Status	Error	Program
	30.9b	(log.f64 (+.f64 1 (/.f64 1 N)))
▶	30.1b	(+.f64 (-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N))) (/.f64 1/3 (pow.f64 N 3)))

Compiler

Compiled 394 to 247 computations (37.3% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
0.4b	(/.f64 1/3 (pow.f64 N 3))
0.7b	(/.f64 1/2 (*.f64 N N))
13.8b	(+.f64 (-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N))) (/.f64 1/3 (pow.f64 N 3)))

rewrite171.0ms (6.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

52×	`times-frac_binary64`
49×	`add-sqr-sqrt_binary64`
47×	`*-un-lft-identity_binary64`
35×	`add-cube-cbrt_binary64`
14×	`add-exp-log_binary64` `cancel-sign-sub-inv_binary64`

Counts

4 → 140

Calls

4 calls:

34.0ms	(+.f64 (-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N))) (/.f64 1/3 (pow.f64 N 3)))
11.0ms	(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
5.0ms	(/.f64 1/3 (pow.f64 N 3))
4.0ms	(/.f64 1/2 (*.f64 N N))

Compiler

Compiled 2907 to 2029 computations (30.2% saved)

series51.0ms (1.8%)

Error

0.0b

Counts

4 → 19

Calls

4 calls:

14.0ms	(+.f64 (-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N))) (/.f64 1/3 (pow.f64 N 3)))
13.0ms	(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
8.0ms	(/.f64 1/3 (pow.f64 N 3))
8.0ms	(/.f64 1/2 (*.f64 N N))

Compiler

Compiled 572 to 464 computations (18.9% saved)

simplify178.0ms (6.3%)

Algorithm

1×	egg-herbie

Rules

436×	`unswap-sqr_binary64`
316×	`distribute-rgt-in_binary64`
286×	`log-prod_binary64`
243×	`cancel-sign-sub-inv_binary64`
204×	`associate-/r*_binary64`

Counts

159 → 109

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	231	2638
1	473	2538
2	1923	2496
3	4527	2440
4	4730	2440
5	4996	2440
6	4902	2440

prune48.0ms (1.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	109	2	111

Error

0.0b

Counts

111 → 2

Alt Table

Status	Error	Program
▶	30.9b	(log.f64 (+.f64 1 (/.f64 1 N)))
✓	30.1b	(+.f64 (-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N))) (/.f64 1/3 (pow.f64 N 3)))

Compiler

Compiled 1230 to 876 computations (28.8% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

2.3b	(log.f64 (+.f64 1 (/.f64 1 N)))

rewrite16.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

5×	`log-prod_binary64` `*-un-lft-identity_binary64`
2×	`pow1_binary64` `log-div_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `distribute-lft-out_binary64` `add-exp-log_binary64`
1×	`log-pow_binary64` `flip3-+_binary64` `flip-+_binary64` `div-inv_binary64` `rem-log-exp_binary64` `add-log-exp_binary64` `add-cbrt-cube_binary64`

Counts

1 → 16

Calls

1 calls:

6.0ms

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

Compiler

Compiled 192 to 166 computations (13.5% saved)

series20.0ms (0.7%)

Error

0.0b

Counts

1 → 12

Calls

1 calls:

15.0ms

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

Compiler

Compiled 261 to 208 computations (20.3% saved)

simplify78.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

291×	`distribute-rgt-neg-in_binary64`
279×	`neg-mul-1_binary64`
238×	`distribute-lft-neg-in_binary64`
232×	`distribute-neg-frac_binary64`
230×	`times-frac_binary64`

Counts

28 → 17

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	65	441
1	143	414
2	309	408
3	700	408
4	2274	396
5	4606	396
6	4913	396

prune13.0ms (0.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	16	1	17
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	16	3	19

Error

0.0b

Counts

19 → 3

Alt Table

Status	Error	Program
✓	30.9b	(log.f64 (+.f64 1 (/.f64 1 N)))
✓	30.1b	(+.f64 (-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N))) (/.f64 1/3 (pow.f64 N 3)))
▶	54.3b	(-.f64 (log.f64 (+.f64 1 (/.f64 1 (pow.f64 N 3)))) (log.f64 (+.f64 1 (/.f64 (+.f64 -1 (/.f64 1 N)) N))))

Compiler

Compiled 206 to 156 computations (24.3% saved)

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 1 (pow.f64 N 3))
0.4b	(-.f64 (log.f64 (+.f64 1 (/.f64 1 (pow.f64 N 3)))) (log.f64 (+.f64 1 (/.f64 (+.f64 -1 (/.f64 1 N)) N))))
19.3b	(log.f64 (+.f64 1 (/.f64 (+.f64 -1 (/.f64 1 N)) N)))
23.7b	(log.f64 (+.f64 1 (/.f64 1 (pow.f64 N 3))))

rewrite178.0ms (6.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

48×	`*-un-lft-identity_binary64`
36×	`add-sqr-sqrt_binary64` `times-frac_binary64`
34×	`add-cube-cbrt_binary64`
18×	`log-prod_binary64`
15×	`add-exp-log_binary64`

Counts

4 → 137

Calls

4 calls:

28.0ms	(-.f64 (log.f64 (+.f64 1 (/.f64 1 (pow.f64 N 3)))) (log.f64 (+.f64 1 (/.f64 (+.f64 -1 (/.f64 1 N)) N))))
15.0ms	(log.f64 (+.f64 1 (/.f64 1 (pow.f64 N 3))))
12.0ms	(log.f64 (+.f64 1 (/.f64 (+.f64 -1 (/.f64 1 N)) N)))
6.0ms	(/.f64 1 (pow.f64 N 3))

Compiler

Compiled 3180 to 2679 computations (15.8% saved)

series89.0ms (3.2%)

Error

0.0b

Counts

4 → 33

Calls

4 calls:

26.0ms	(log.f64 (+.f64 1 (/.f64 1 (pow.f64 N 3))))
19.0ms	(log.f64 (+.f64 1 (/.f64 (+.f64 -1 (/.f64 1 N)) N)))
16.0ms	(-.f64 (log.f64 (+.f64 1 (/.f64 1 (pow.f64 N 3)))) (log.f64 (+.f64 1 (/.f64 (+.f64 -1 (/.f64 1 N)) N))))
9.0ms	(/.f64 1 (pow.f64 N 3))

Compiler

Compiled 1140 to 940 computations (17.5% saved)

simplify159.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

725×	`times-frac_binary64`
590×	`associate-/r*_binary64`
206×	`cancel-sign-sub-inv_binary64`
205×	`associate-/l*_binary64`
192×	`log-div_binary64`

Counts

170 → 112

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	197	3015
1	414	2903
2	1124	2869
3	4721	2869
4	4970	2869
5	5011	2869

prune50.0ms (1.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	112	3	115

Error

0.0b

Counts

115 → 3

Alt Table

Status	Error	Program
	30.9b	(log.f64 (+.f64 1 (/.f64 1 N)))
	30.1b	(+.f64 (-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N))) (/.f64 1/3 (pow.f64 N 3)))
	56.2b	(/.f64 (-.f64 (pow.f64 (log.f64 (+.f64 1 (/.f64 1 (pow.f64 N 3)))) 3) (pow.f64 (log.f64 (+.f64 1 (/.f64 (+.f64 -1 (/.f64 1 N)) N))) 3)) (+.f64 (.f64 (log.f64 (+.f64 1 (/.f64 1 (pow.f64 N 3)))) (log.f64 (+.f64 1 (/.f64 1 (pow.f64 N 3))))) (.f64 (log.f64 (+.f64 1 (/.f64 (+.f64 -1 (/.f64 1 N)) N))) (+.f64 (log.f64 (+.f64 1 (/.f64 1 (pow.f64 N 3)))) (log.f64 (+.f64 1 (/.f64 (+.f64 -1 (/.f64 1 N)) N)))))))

Compiler

Compiled 1327 to 1069 computations (19.4% saved)

regimes100.0ms (3.6%)

Accuracy

Total 0.0b remaining (37.8%)

Threshold costs 0.0b (37.8%)

Compiler

Compiled 976 to 768 computations (21.3% saved)

bsearch1.0ms (0%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`neg-mul-1_binary64` `neg-sub0_binary64` `*-commutative_binary64`
1×	`1-exp_binary64` `distribute-neg-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	47
1	31	47
2	41	47
3	45	47
4	47	47
5	45	47

end1.0ms (0%)

Compiler: Compiled 32 to 24 computations (25% saved)

sample1.3s (47.2%)

Algorithm

1×

intervals

Results

462.0ms	2018×	body	1024	valid
243.0ms	4268×	body	128	valid
140.0ms	970×	body	512	valid
87.0ms	239×	body	2048	valid
52.0ms	505×	body	256	valid

Compiler

Compiled 138 to 113 computations (18.1% saved)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	22	11
4	28	11
5	43	11
6	65	11
7	77	11
8	89	11
9	91	11
10	85	11
11	71	11

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	22	11
4	28	11
5	43	11
6	65	11
7	77	11
8	89	11
9	91	11
10	85	11
11	71	11

Details

analyze22.0ms (0.8%)

sample40.0ms (1.4%)

simplify11.0ms (0.4%)

prune6.0ms (0.2%)

localize6.0ms (0.2%)

rewrite48.0ms (1.7%)

series40.0ms (1.4%)

simplify102.0ms (3.6%)

prune22.0ms (0.8%)

localize11.0ms (0.4%)

rewrite171.0ms (6.1%)

series51.0ms (1.8%)

simplify178.0ms (6.3%)

prune48.0ms (1.7%)

localize4.0ms (0.2%)

rewrite16.0ms (0.6%)

series20.0ms (0.7%)

simplify78.0ms (2.8%)

prune13.0ms (0.4%)

localize13.0ms (0.5%)

rewrite178.0ms (6.3%)

series89.0ms (3.2%)

simplify159.0ms (5.6%)

prune50.0ms (1.8%)

regimes100.0ms (3.6%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.3s (47.2%)

Profiling

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	22	11
4	28	11
5	43	11
6	65	11
7	77	11
8	89	11
9	91	11
10	85	11
11	71	11