Details

analyze452.0ms (10.2%)

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)

sample61.0ms (1.4%)

Algorithm

1×

intervals

Results

25.0ms	132×	body	2048	nan
11.0ms	256×	body	128	valid
6.0ms	49×	body	1024	nan
3.0ms	29×	body	512	nan
1.0ms	22×	body	256	nan
0.0ms	13×	body	128	nan

Compiler

Compiled 22 to 16 computations (27.3% saved)

simplify145.0ms (3.3%)

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%)

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

34.9b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	34.9b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))

Compiler

Compiled 20 to 14 computations (30% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (*.f64 x x) 1)
0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
0.2b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
32.4b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite95.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

13×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64`
6×	`pow1_binary64` `sqrt-prod_binary64`

Counts

4 → 62

Calls

4 calls:

7.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
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 978 to 598 computations (38.9% saved)

series67.0ms (1.5%)

Error

0.0b

Counts

4 → 25

Calls

4 calls:

14.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
12.0ms	(-.f64 (*.f64 x x) 1)
12.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))
10.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))

Compiler

Compiled 655 to 538 computations (17.9% saved)

simplify91.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

436×	`sub-neg_binary64`
257×	`unsub-neg_binary64`
208×	`cancel-sign-sub-inv_binary64`
201×	`times-frac_binary64`
180×	`associate--l+_binary64`

Counts

87 → 68

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	140	1265
1	287	1175
2	709	1127
3	2228	1121
4	4322	1121
5	4859	1121

prune63.0ms (1.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	65	3	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	3	69

Error

0.0b

Counts

69 → 3

Alt Table

Status	Error	Program
▶	0.3b	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 -1 x)))))
	34.9b	(log.f64 (+.f64 x (.f64 (fabs.f64 (cbrt.f64 (+.f64 -1 (.f64 x x)))) (sqrt.f64 (cbrt.f64 (+.f64 -1 (*.f64 x x)))))))
	0.9b	(+.f64 (log.f64 2) (log.f64 x))

Compiler

Compiled 860 to 559 computations (35% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 -1 x))))
0.2b	(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)))

rewrite115.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

21×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64` `sqrt-prod_binary64`
14×	`sqrt-div_binary64`
10×	`pow1_binary64` `add-cube-cbrt_binary64`
9×	`flip3-+_binary64` `flip-+_binary64`

Counts

4 → 82

Calls

4 calls:

12.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 -1 x)))
3.0ms	(sqrt.f64 (+.f64 x 1))
3.0ms	(+.f64 x (*.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 1576 to 1215 computations (22.9% saved)

series65.0ms (1.5%)

Error

0.0b

Counts

4 → 22

Calls

4 calls:

16.0ms	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 -1 x)))))
12.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 -1 x)))
11.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 -1 x))))
8.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 638 to 523 computations (18% saved)

simplify115.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

466×	`neg-mul-1_binary64`
303×	`sub-neg_binary64`
299×	`associate-l_binary64`
250×	`unsub-neg_binary64`
238×	`associate-r_binary64`

Counts

104 → 70

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	177	1924
1	389	1821
2	964	1549
3	2841	1549
4	4455	1549
5	4873	1549

prune67.0ms (1.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	70	3	73

Error

0.0b

Counts

73 → 3

Alt Table

Status	Error	Program
✓	0.3b	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 -1 x)))))
▶	0.6b	(+.f64 (log.f64 2) (-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))))
	34.9b	(log.f64 (+.f64 x (.f64 (fabs.f64 (cbrt.f64 (+.f64 -1 (.f64 x x)))) (sqrt.f64 (cbrt.f64 (+.f64 -1 (*.f64 x x)))))))

Compiler

Compiled 1108 to 757 computations (31.7% saved)

localize12.0ms (0.3%)

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))))
0.3b	(/.f64 1/4 (*.f64 x x))

rewrite110.0ms (2.5%)

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)

series62.0ms (1.4%)

Error

0.0b

Counts

3 → 13

Calls

3 calls:

24.0ms	(+.f64 (log.f64 2) (-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x))))
17.0ms	(-.f64 (log.f64 x) (/.f64 1/4 (*.f64 x x)))
8.0ms	(/.f64 1/4 (*.f64 x x))

Compiler

Compiled 405 to 349 computations (13.8% saved)

simplify86.0ms (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

prune59.0ms (1.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	75	3	78

Error

Counts

78 → 3

Alt Table

Status	Error	Program
✓	0.3b	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 -1 x)))))
	34.9b	(log.f64 (+.f64 x (.f64 (fabs.f64 (cbrt.f64 (+.f64 -1 (.f64 x x)))) (sqrt.f64 (cbrt.f64 (+.f64 -1 (*.f64 x x)))))))
▶	0.7b	(+.f64 (+.f64 (log.f64 2) (.f64 2 (log.f64 (cbrt.f64 x)))) (-.f64 (log.f64 (cbrt.f64 x)) (/.f64 1/4 (.f64 x x))))

Compiler

Compiled 919 to 582 computations (36.7% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(+.f64 (+.f64 (log.f64 2) (.f64 2 (log.f64 (cbrt.f64 x)))) (-.f64 (log.f64 (cbrt.f64 x)) (/.f64 1/4 (.f64 x x))))
0.3b	(/.f64 1/4 (*.f64 x x))
0.5b	(cbrt.f64 x)
0.5b	(cbrt.f64 x)

rewrite126.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

19×	`*-un-lft-identity_binary64`
14×	`associate-+r+_binary64`
12×	`add-log-exp_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `cbrt-prod_binary64`
7×	`cancel-sign-sub-inv_binary64`

Counts

4 → 80

Calls

4 calls:

14.0ms	(+.f64 (+.f64 (log.f64 2) (.f64 2 (log.f64 (cbrt.f64 x)))) (-.f64 (log.f64 (cbrt.f64 x)) (/.f64 1/4 (.f64 x x))))
4.0ms	(/.f64 1/4 (*.f64 x x))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

Compiler

Compiled 2228 to 1198 computations (46.2% saved)

series99.0ms (2.2%)

Error

Counts

4 → 14

Calls

4 calls:

38.0ms	(+.f64 (+.f64 (log.f64 2) (.f64 2 (log.f64 (cbrt.f64 x)))) (-.f64 (log.f64 (cbrt.f64 x)) (/.f64 1/4 (.f64 x x))))
20.0ms	(cbrt.f64 x)
19.0ms	(cbrt.f64 x)
9.0ms	(/.f64 1/4 (*.f64 x x))

Compiler

Compiled 677 to 547 computations (19.2% saved)

simplify72.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

558×	`associate-/r*_binary64`
501×	`times-frac_binary64`
448×	`associate-*l/_binary64`
171×	`associate-/l*_binary64`
135×	`distribute-rgt-in_binary64`

Counts

94 → 67

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	163	2100
1	468	1711
2	1727	1533
3	4920	1533

prune63.0ms (1.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	67	3	70

Error

Counts

70 → 3

Alt Table

Status	Error	Program
	0.3b	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 -1 x)))))
	34.9b	(log.f64 (+.f64 x (.f64 (fabs.f64 (cbrt.f64 (+.f64 -1 (.f64 x x)))) (sqrt.f64 (cbrt.f64 (+.f64 -1 (*.f64 x x)))))))
	0.7b	(+.f64 (+.f64 (log.f64 2) (.f64 2 (log.f64 (cbrt.f64 x)))) (-.f64 (log.f64 (cbrt.f64 x)) (/.f64 1/4 (.f64 x x))))

Compiler

Compiled 1234 to 760 computations (38.4% saved)

regimes361.0ms (8.1%)

Accuracy

Total 0.1b remaining (97.8%)

Threshold costs 0.1b (97.8%)

Compiler

Compiled 3453 to 2536 computations (26.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	17	19
2	16	19

end1.0ms (0%)

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

sample2.0s (45.2%)

Algorithm

1×

intervals

Results

684.0ms	4093×	body	2048	nan
356.0ms	8000×	body	128	valid
263.0ms	2036×	body	1024	nan
103.0ms	1049×	body	512	nan
33.0ms	510×	body	256	nan
17.0ms	505×	body	128	nan
2.0ms	9×	body	4096	nan

Compiler

Compiled 76 to 55 computations (27.6% saved)

Details

analyze452.0ms (10.2%)

sample61.0ms (1.4%)

simplify145.0ms (3.3%)

prune2.0ms (0%)

localize8.0ms (0.2%)

rewrite95.0ms (2.1%)

series67.0ms (1.5%)

simplify91.0ms (2.1%)

prune63.0ms (1.4%)

localize10.0ms (0.2%)

rewrite115.0ms (2.6%)

series65.0ms (1.5%)

simplify115.0ms (2.6%)

prune67.0ms (1.5%)

localize12.0ms (0.3%)

rewrite110.0ms (2.5%)

series62.0ms (1.4%)

simplify86.0ms (2%)

prune59.0ms (1.3%)

localize16.0ms (0.4%)

rewrite126.0ms (2.9%)

series99.0ms (2.2%)

simplify72.0ms (1.6%)

prune63.0ms (1.4%)

regimes361.0ms (8.1%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample2.0s (45.2%)

Profiling