Details

analyze364.0ms (6.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50%	13
49.9%	0%	50%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample88.0ms (1.5%)

Algorithm

1×

intervals

Results

52.0ms	126×	body	1024	valid
15.0ms	71×	body	512	valid
8.0ms	16×	body	2048	valid
3.0ms	24×	body	256	valid
1.0ms	19×	body	128	valid

Compiler

Compiled 20 to 16 computations (20% saved)

simplify373.0ms (6.5%)

Algorithm

1×	egg-herbie

Rules

2648×	`associate--r-_binary64`
1079×	`distribute-rgt-in_binary64`
753×	`distribute-lft-in_binary64`
705×	`unsub-neg_binary64`
642×	`distribute-neg-in_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	18	12
2	26	12
3	38	12
4	64	12
5	82	12
6	123	12
7	219	12
8	360	12
9	441	12
10	505	12
11	673	12
12	1029	12
13	1080	12
14	1073	12
15	1086	12
16	1084	12
17	1084	12
18	2524	12
19	1534	12
20	1612	12
21	1620	12
22	1628	12
23	1628	12
24	1828	12
25	2320	12
26	2368	12
27	2342	12
28	2408	12
29	2452	12
30	2452	12
31	2540	12
32	2548	12
33	3248	12
34	3360	12
35	3320	12
36	3392	12
37	3416	12
38	3416	12
39	3440	12
40	6078	12

prune2.0ms (0%)

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

58.2b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	58.2b	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 1 eps) (+.f64 1 eps))
4.5b	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))

rewrite139.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

57.9b

Rules

78×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
48×	`times-frac_binary64`
30×	`log-prod_binary64`
25×	`add-cube-cbrt_binary64`

Counts

2 → 92

Calls

2 calls:

6.0ms	(/.f64 (-.f64 1 eps) (+.f64 1 eps))
6.0ms	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))

Compiler

Compiled 1251 to 969 computations (22.5% saved)

series20.0ms (0.4%)

Error

0.0b

Counts

2 → 14

Calls

2 calls:

7.0ms	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
6.0ms	(/.f64 (-.f64 1 eps) (+.f64 1 eps))

Compiler

Compiled 279 to 238 computations (14.7% saved)

simplify120.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

497×	`cancel-sign-sub-inv_binary64`
468×	`div-sub_binary64`
441×	`distribute-rgt-in_binary64`
339×	`distribute-lft-in_binary64`
230×	`sub-neg_binary64`

Counts

106 → 94

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	149	2054
1	349	1960
2	848	1915
3	2130	1911
4	4274	1911
5	5264	1911

prune37.0ms (0.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	3	95

Error

Counts

95 → 3

Alt Table

Status	Error	Program
	58.2b	(log.f64 (/.f64 1 (/.f64 (+.f64 eps 1) (-.f64 1 eps))))
	58.3b	(+.f64 (+.f64 (log.f64 (sqrt.f64 (-.f64 1 eps))) (*.f64 -2 (log.f64 (cbrt.f64 (+.f64 eps 1))))) (log.f64 (/.f64 (sqrt.f64 (-.f64 1 eps)) (cbrt.f64 (+.f64 eps 1)))))
▶	0.1b	(-.f64 (-.f64 (.f64 -2 eps) (+.f64 (.f64 2/3 (pow.f64 eps 3)) (.f64 2/5 (pow.f64 eps 5)))) (.f64 2/7 (pow.f64 eps 7)))

Compiler

Compiled 1135 to 883 computations (22.2% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (-.f64 (.f64 -2 eps) (+.f64 (.f64 2/3 (pow.f64 eps 3)) (.f64 2/5 (pow.f64 eps 5)))) (.f64 2/7 (pow.f64 eps 7)))
0.0b	(*.f64 2/5 (pow.f64 eps 5))
0.1b	(*.f64 2/7 (pow.f64 eps 7))
0.1b	(*.f64 2/3 (pow.f64 eps 3))

rewrite121.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

32×	`add-sqr-sqrt_binary64`
26×	`associate-r_binary64`
19×	`add-exp-log_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`

Counts

4 → 100

Calls

4 calls:

12.0ms	(-.f64 (-.f64 (.f64 -2 eps) (+.f64 (.f64 2/3 (pow.f64 eps 3)) (.f64 2/5 (pow.f64 eps 5)))) (.f64 2/7 (pow.f64 eps 7)))
5.0ms	(*.f64 2/3 (pow.f64 eps 3))
4.0ms	(*.f64 2/5 (pow.f64 eps 5))
4.0ms	(*.f64 2/7 (pow.f64 eps 7))

Compiler

Compiled 2650 to 2165 computations (18.3% saved)

series36.0ms (0.6%)

Error

Counts

4 → 15

Calls

4 calls:

9.0ms	(*.f64 2/7 (pow.f64 eps 7))
8.0ms	(-.f64 (-.f64 (.f64 -2 eps) (+.f64 (.f64 2/3 (pow.f64 eps 3)) (.f64 2/5 (pow.f64 eps 5)))) (.f64 2/7 (pow.f64 eps 7)))
8.0ms	(*.f64 2/5 (pow.f64 eps 5))
7.0ms	(*.f64 2/3 (pow.f64 eps 3))

Compiler

Compiled 567 to 464 computations (18.2% saved)

simplify137.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

592×	`unswap-sqr_binary64`
391×	`log-prod_binary64`
377×	`*-commutative_binary64`
288×	`unsub-neg_binary64`
202×	`exp-prod_binary64`

Counts

115 → 71

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	204	1814
1	424	1685
2	1107	1625
3	2779	1625
4	4720	1625
5	4910	1625
6	4978	1625

prune41.0ms (0.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	71	3	74

Error

Counts

74 → 3

Alt Table

Status	Error	Program
▶	58.2b	(log.f64 (/.f64 1 (/.f64 (+.f64 eps 1) (-.f64 1 eps))))
	58.3b	(+.f64 (+.f64 (log.f64 (sqrt.f64 (-.f64 1 eps))) (*.f64 -2 (log.f64 (cbrt.f64 (+.f64 eps 1))))) (log.f64 (/.f64 (sqrt.f64 (-.f64 1 eps)) (cbrt.f64 (+.f64 eps 1)))))
✓	0.1b	(-.f64 (-.f64 (.f64 -2 eps) (+.f64 (.f64 2/3 (pow.f64 eps 3)) (.f64 2/5 (pow.f64 eps 5)))) (.f64 2/7 (pow.f64 eps 7)))

Compiler

Compiled 1226 to 996 computations (18.8% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 1 (/.f64 (+.f64 eps 1) (-.f64 1 eps)))
0.0b	(/.f64 (+.f64 eps 1) (-.f64 1 eps))
4.5b	(log.f64 (/.f64 1 (/.f64 (+.f64 eps 1) (-.f64 1 eps))))

rewrite177.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

372×	`times-frac_binary64`
351×	`*-un-lft-identity_binary64`
253×	`add-sqr-sqrt_binary64`
154×	`add-cube-cbrt_binary64`
95×	`log-prod_binary64`

Counts

3 → 308

Calls

3 calls:

11.0ms	(log.f64 (/.f64 1 (/.f64 (+.f64 eps 1) (-.f64 1 eps))))
10.0ms	(/.f64 1 (/.f64 (+.f64 eps 1) (-.f64 1 eps)))
6.0ms	(/.f64 (+.f64 eps 1) (-.f64 1 eps))

Compiler

Compiled 5248 to 4297 computations (18.1% saved)

series29.0ms (0.5%)

Error

Counts

3 → 22

Calls

3 calls:

9.0ms	(/.f64 (+.f64 eps 1) (-.f64 1 eps))
7.0ms	(log.f64 (/.f64 1 (/.f64 (+.f64 eps 1) (-.f64 1 eps))))
6.0ms	(/.f64 1 (/.f64 (+.f64 eps 1) (-.f64 1 eps)))

Compiler

Compiled 464 to 404 computations (12.9% saved)

simplify276.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

555×	`div-sub_binary64`
284×	`times-frac_binary64`
259×	`log-div_binary64`
245×	`distribute-rgt-in_binary64`
222×	`associate-l_binary64`

Counts

330 → 276

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	212	7386
1	500	6807
2	1334	6423
3	3462	6423
4	4316	6423
5	5436	6423

prune52.0ms (0.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	276	0	276
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	276	3	279

Error

Counts

279 → 3

Alt Table

Status	Error	Program
✓	58.2b	(log.f64 (/.f64 1 (/.f64 (+.f64 eps 1) (-.f64 1 eps))))
▶	58.3b	(+.f64 (+.f64 (log.f64 (sqrt.f64 (-.f64 1 eps))) (*.f64 -2 (log.f64 (cbrt.f64 (+.f64 eps 1))))) (log.f64 (/.f64 (sqrt.f64 (-.f64 1 eps)) (cbrt.f64 (+.f64 eps 1)))))
✓	0.1b	(-.f64 (-.f64 (.f64 -2 eps) (+.f64 (.f64 2/3 (pow.f64 eps 3)) (.f64 2/5 (pow.f64 eps 5)))) (.f64 2/7 (pow.f64 eps 7)))

Compiler

Compiled 1723 to 1338 computations (22.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (sqrt.f64 (-.f64 1 eps)) (cbrt.f64 (+.f64 eps 1)))
4.6b	(log.f64 (/.f64 (sqrt.f64 (-.f64 1 eps)) (cbrt.f64 (+.f64 eps 1))))
4.6b	(log.f64 (sqrt.f64 (-.f64 1 eps)))
4.7b	(log.f64 (cbrt.f64 (+.f64 eps 1)))

rewrite174.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

165×	`*-un-lft-identity_binary64`
126×	`times-frac_binary64`
125×	`add-sqr-sqrt_binary64`
96×	`sqrt-prod_binary64`
85×	`log-prod_binary64`

Counts

4 → 216

Calls

4 calls:

8.0ms	(log.f64 (/.f64 (sqrt.f64 (-.f64 1 eps)) (cbrt.f64 (+.f64 eps 1))))
8.0ms	(/.f64 (sqrt.f64 (-.f64 1 eps)) (cbrt.f64 (+.f64 eps 1)))
3.0ms	(log.f64 (sqrt.f64 (-.f64 1 eps)))
3.0ms	(log.f64 (cbrt.f64 (+.f64 eps 1)))

Compiler

Compiled 5763 to 4802 computations (16.7% saved)

series61.0ms (1.1%)

Error

Counts

4 → 25

Calls

4 calls:

14.0ms	(/.f64 (sqrt.f64 (-.f64 1 eps)) (cbrt.f64 (+.f64 eps 1)))
13.0ms	(log.f64 (cbrt.f64 (+.f64 eps 1)))
12.0ms	(log.f64 (/.f64 (sqrt.f64 (-.f64 1 eps)) (cbrt.f64 (+.f64 eps 1))))
9.0ms	(log.f64 (sqrt.f64 (-.f64 1 eps)))

Compiler

Compiled 1567 to 1320 computations (15.8% saved)

simplify290.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

389×	`sub-neg_binary64`
243×	`distribute-rgt-neg-in_binary64`
208×	`distribute-lft-neg-in_binary64`
206×	`times-frac_binary64`
179×	`associate-l_binary64`

Counts

241 → 164

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	300	6108
1	555	5845
2	1254	5781
3	2954	5757
4	4515	5751
5	4952	5751
6	4866	5751

prune69.0ms (1.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

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

Error

Counts

167 → 3

Alt Table

Status	Error	Program
	58.2b	(log.f64 (/.f64 1 (/.f64 (+.f64 eps 1) (-.f64 1 eps))))
	58.3b	(+.f64 (+.f64 (log.f64 (sqrt.f64 (-.f64 1 eps))) (*.f64 -2 (log.f64 (cbrt.f64 (+.f64 eps 1))))) (log.f64 (/.f64 (sqrt.f64 (-.f64 1 eps)) (cbrt.f64 (+.f64 eps 1)))))
	0.1b	(-.f64 (-.f64 (.f64 -2 eps) (+.f64 (.f64 2/3 (pow.f64 eps 3)) (.f64 2/5 (pow.f64 eps 5)))) (.f64 2/7 (pow.f64 eps 7)))

Compiler

Compiled 2927 to 2424 computations (17.2% saved)

regimes164.0ms (2.9%)

Accuracy

Total 0.1b remaining (94.3%)

Threshold costs 0.1b (94.3%)

Compiler

Compiled 3192 to 2548 computations (20.2% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
10×	`+-commutative_binary64`
9×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	31
1	32	31
2	47	31
3	73	31
4	85	31
5	92	31
6	94	31
7	91	31

end1.0ms (0%)

Compiler: Compiled 22 to 18 computations (18.2% saved)

sample2.9s (50.7%)

Algorithm

1×

intervals

Results

1.7s	4005×	body	1024	valid
495.0ms	2001×	body	512	valid
238.0ms	409×	body	2048	valid
129.0ms	998×	body	256	valid
40.0ms	587×	body	128	valid

Compiler

Compiled 91 to 75 computations (17.6% saved)

Details

analyze364.0ms (6.4%)

sample88.0ms (1.5%)

simplify373.0ms (6.5%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite139.0ms (2.4%)

series20.0ms (0.4%)

simplify120.0ms (2.1%)

prune37.0ms (0.6%)

localize15.0ms (0.3%)

rewrite121.0ms (2.1%)

series36.0ms (0.6%)

simplify137.0ms (2.4%)

prune41.0ms (0.7%)

localize8.0ms (0.1%)

rewrite177.0ms (3.1%)

series29.0ms (0.5%)

simplify276.0ms (4.8%)

prune52.0ms (0.9%)

localize14.0ms (0.2%)

rewrite174.0ms (3%)

series61.0ms (1.1%)

simplify290.0ms (5.1%)

prune69.0ms (1.2%)

regimes164.0ms (2.9%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample2.9s (50.7%)

Profiling