Details

analyze422.0ms (11.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	50%	25%	4
25%	37.5%	37.5%	5
25%	31.2%	43.8%	6
25%	28.1%	46.9%	7
25%	26.5%	48.5%	8
25%	25.8%	49.2%	9
25%	25.4%	49.6%	10
25%	25.2%	49.8%	11
25%	25.1%	49.9%	12
25%	25%	50%	13
25%	25%	50%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample63.0ms (1.7%)

Algorithm

1×

intervals

Results

22.0ms	153×	body	2048	nan
12.0ms	78×	body	1024	nan
10.0ms	256×	body	128	valid
3.0ms	33×	body	512	nan
1.0ms	11×	body	256	nan
0.0ms	15×	body	128	nan

Compiler

Compiled 22 to 16 computations (27.3% saved)

simplify145.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

805×	`unsub-neg_binary64`
626×	`distribute-rgt-out--_binary64`
462×	`distribute-neg-in_binary64`
449×	`distribute-rgt-out_binary64`
439×	`sub-neg_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	17	14
2	21	14
3	36	14
4	57	14
5	94	14
6	185	14
7	360	14
8	1261	14
9	1616	14
10	2338	14
11	2722	14
12	2923	14
13	3093	14
14	3194	14
15	3511	14
16	3955	14
17	4851	14
18	4921	14

prune2.0ms (0.1%)

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

32.9b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	32.9b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))

Compiler

Compiled 20 to 14 computations (30% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (*.f64 x x) 1)
0.3b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
30.5b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite67.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

10×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
6×	`sqrt-prod_binary64`
6×	`add-cube-cbrt_binary64`
5×	`add-log-exp_binary64`

Counts

3 → 50

Calls

3 calls:

7.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
5.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))
4.0ms	(-.f64 (*.f64 x x) 1)

Compiler

Compiled 779 to 481 computations (38.3% saved)

series48.0ms (1.3%)

Error

0.0b

Counts

3 → 19

Calls

3 calls:

14.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
10.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))
9.0ms	(-.f64 (*.f64 x x) 1)

Compiler

Compiled 501 to 409 computations (18.4% saved)

simplify104.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

734×	`distribute-rgt-in_binary64`
609×	`distribute-lft-in_binary64`
214×	`sub-neg_binary64`
201×	`times-frac_binary64`
170×	`cancel-sign-sub-inv_binary64`

Counts

69 → 55

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	130	973
1	258	908
2	642	863
3	2023	860
4	4950	860
5	4984	860
6	4875	860

prune47.0ms (1.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	52	3	55
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	3	56

Error

Counts

56 → 3

Alt Table

Status	Error	Program
	1.0b	(+.f64 (log.f64 2) (log.f64 x))
	32.9b	(+.f64 (log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (+.f64 -1 (.f64 x x)))))) (log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (+.f64 -1 (.f64 x x)))))))
▶	0.3b	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 -1 x)))))

Compiler

Compiled 686 to 450 computations (34.4% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.3b	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 -1 x)))))
0.5b	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 -1 x)))

rewrite70.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

17×	`add-sqr-sqrt_binary64`
12×	`sqrt-prod_binary64`
12×	`sqrt-div_binary64`
11×	`*-un-lft-identity_binary64`
7×	`associate-r_binary64`

Counts

2 → 55

Calls

2 calls:

12.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 -1 x)))
2.0ms	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 -1 x)))))

Compiler

Compiled 1064 to 821 computations (22.8% saved)

series34.0ms (0.9%)

Error

Counts

2 → 12

Calls

2 calls:

12.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 -1 x)))
12.0ms	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 -1 x)))))

Compiler

Compiled 370 to 309 computations (16.5% saved)

simplify102.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

497×	`distribute-rgt-in_binary64`
270×	`sub-neg_binary64`
236×	`associate-l_binary64`
188×	`unsub-neg_binary64`
186×	`associate-r_binary64`

Counts

67 → 50

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	161	1407
1	350	1342
2	853	1138
3	2459	1135
4	4807	1135
5	4862	1135

prune45.0ms (1.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	49	1	50
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	50	3	53

Error

Counts

53 → 3

Alt Table

Status	Error	Program
	32.9b	(+.f64 (log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (+.f64 -1 (.f64 x x)))))) (log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (+.f64 -1 (.f64 x x)))))))
▶	0.7b	(+.f64 (log.f64 2) (-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))))
✓	0.3b	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 -1 x)))))

Compiler

Compiled 825 to 561 computations (32% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x)))
0.2b	(+.f64 (log.f64 2) (-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))))
0.6b	(/.f64 1/4 (*.f64 x x))

rewrite99.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

26×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
14×	`cancel-sign-sub-inv_binary64`
12×	`add-cube-cbrt_binary64`
11×	`associate-+r+_binary64`

Counts

3 → 79

Calls

3 calls:

11.0ms	(+.f64 (log.f64 2) (-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))))
7.0ms	(-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x)))
5.0ms	(/.f64 1/4 (*.f64 x x))

Compiler

Compiled 1292 to 784 computations (39.3% saved)

series51.0ms (1.3%)

Error

Counts

3 → 13

Calls

3 calls:

19.0ms	(+.f64 (log.f64 2) (-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))))
14.0ms	(-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x)))
7.0ms	(/.f64 1/4 (*.f64 x x))

Compiler

Compiled 405 to 349 computations (13.8% saved)

simplify84.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

473×	`associate-l_binary64`
399×	`associate-r_binary64`
392×	`distribute-rgt-in_binary64`
360×	`distribute-lft-in_binary64`
303×	`unsub-neg_binary64`

Counts

92 → 75

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	145	1315
1	341	1245
2	903	1222
3	4286	1210
4	4954	1210

prune51.0ms (1.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	75	3	78

Error

Counts

78 → 3

Alt Table

Status	Error	Program
▶	32.9b	(+.f64 (log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (+.f64 -1 (.f64 x x)))))) (log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (+.f64 -1 (.f64 x x)))))))
✓	0.7b	(+.f64 (log.f64 2) (-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))))
✓	0.3b	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 -1 x)))))

Compiler

Compiled 899 to 569 computations (36.7% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(sqrt.f64 (+.f64 x (sqrt.f64 (+.f64 -1 (*.f64 x x)))))
0.2b	(sqrt.f64 (+.f64 x (sqrt.f64 (+.f64 -1 (*.f64 x x)))))
30.5b	(sqrt.f64 (+.f64 -1 (*.f64 x x)))
30.5b	(sqrt.f64 (+.f64 -1 (*.f64 x x)))

rewrite87.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

14×	`sqrt-prod_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
8×	`sqrt-div_binary64`
8×	`add-cube-cbrt_binary64`

Counts

4 → 62

Calls

4 calls:

6.0ms	(sqrt.f64 (+.f64 x (sqrt.f64 (+.f64 -1 (*.f64 x x)))))
6.0ms	(sqrt.f64 (+.f64 x (sqrt.f64 (+.f64 -1 (*.f64 x x)))))
5.0ms	(sqrt.f64 (+.f64 -1 (*.f64 x x)))
3.0ms	(sqrt.f64 (+.f64 -1 (*.f64 x x)))

Compiler

Compiled 1685 to 1063 computations (36.9% saved)

series56.0ms (1.5%)

Error

Counts

4 → 20

Calls

4 calls:

15.0ms	(sqrt.f64 (+.f64 -1 (*.f64 x x)))
12.0ms	(sqrt.f64 (+.f64 -1 (*.f64 x x)))
7.0ms	(sqrt.f64 (+.f64 x (sqrt.f64 (+.f64 -1 (*.f64 x x)))))
7.0ms	(sqrt.f64 (+.f64 x (sqrt.f64 (+.f64 -1 (*.f64 x x)))))

Compiler

Compiled 1049 to 787 computations (25% saved)

simplify146.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

377×	`times-frac_binary64`
363×	`neg-sub0_binary64`
361×	`associate-l_binary64`
357×	`neg-mul-1_binary64`
289×	`associate-r_binary64`

Counts

82 → 38

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	85	1148
1	182	1108
2	397	1102
3	1026	1096
4	2848	1096
5	4198	1096
6	4986	1096
7	4993	1096
8	4786	1096

prune40.0ms (1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	38	3	41

Error

Counts

41 → 3

Alt Table

Status	Error	Program
	32.9b	(+.f64 (log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (+.f64 -1 (.f64 x x)))))) (log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (+.f64 -1 (.f64 x x)))))))
	0.7b	(+.f64 (log.f64 2) (-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))))
	0.3b	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 -1 x)))))

Compiler

Compiled 928 to 614 computations (33.8% saved)

regimes226.0ms (6%)

Accuracy

Total 0.1b remaining (97.9%)

Threshold costs 0.1b (97.9%)

Compiler

Compiled 2218 to 1627 computations (26.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	18	19
2	19	19
3	17	19

end1.0ms (0%)

Compiler: Compiled 13 to 10 computations (23.1% saved)

sample1.8s (46.6%)

Algorithm

1×

intervals

Results

569.0ms	3860×	body	2048	nan
329.0ms	8000×	body	128	valid
243.0ms	2001×	body	1024	nan
88.0ms	981×	body	512	nan
34.0ms	487×	body	256	nan
15.0ms	522×	body	128	nan
1.0ms	7×	body	4096	nan

Compiler

Compiled 72 to 53 computations (26.4% saved)

Details

analyze422.0ms (11.1%)

sample63.0ms (1.7%)

simplify145.0ms (3.8%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

rewrite67.0ms (1.8%)

series48.0ms (1.3%)

simplify104.0ms (2.8%)

prune47.0ms (1.3%)

localize9.0ms (0.2%)

rewrite70.0ms (1.8%)

series34.0ms (0.9%)

simplify102.0ms (2.7%)

prune45.0ms (1.2%)

localize9.0ms (0.2%)

rewrite99.0ms (2.6%)

series51.0ms (1.3%)

simplify84.0ms (2.2%)

prune51.0ms (1.4%)

localize9.0ms (0.2%)

rewrite87.0ms (2.3%)

series56.0ms (1.5%)

simplify146.0ms (3.9%)

prune40.0ms (1%)

regimes226.0ms (6%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.8s (46.6%)

Profiling