Details

analyze6.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	49.7%	50.3%	0
0%	49.7%	50.3%	1
0%	49.7%	50.3%	2
24.8%	24.8%	50.3%	3
37.3%	12.4%	50.3%	4
43.5%	6.2%	50.3%	5
46.6%	3.1%	50.3%	6
48.1%	1.6%	50.3%	7
48.9%	0.8%	50.3%	8
49.3%	0.4%	50.3%	9
49.5%	0.2%	50.3%	10
49.6%	0.1%	50.3%	11
49.6%	0%	50.3%	12
49.7%	0%	50.3%	13
49.7%	0%	50.3%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample236.0ms (2.5%)

Algorithm

1×

intervals

Results

152.0ms	125×	body	2048	valid
39.0ms	67×	body	1024	valid
6.0ms	37×	body	512	valid
5.0ms	9×	body	4096	valid
4.0ms	256×	pre	128	true
1.0ms	13×	body	256	valid
0.0ms	5×	body	128	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify10.0ms (0.1%)

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 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	11	12
2	17	12
3	25	12
4	33	12
5	51	12
6	76	12
7	93	12
8	110	12
9	120	12
10	124	12
11	126	12
12	112	12

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

60.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	60.4b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (tan.f64 x))
✓	2.0b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

series24.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

14.0ms	(/.f64 1 (tan.f64 x))
10.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

rewrite51.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

288×	`times-frac_binary64`
239×	`add-sqr-sqrt_binary64`
231×	`*-un-lft-identity_binary64`
215×	`add-cube-cbrt_binary64`
182×	`prod-diff_binary64`

Counts

2 → 273

Calls

2 calls:

15.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
4.0ms	(/.f64 1 (tan.f64 x))

simplify247.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

770×	`fma-neg_binary64`
466×	`fma-def_binary64`
354×	`distribute-rgt-in_binary64`
331×	`cancel-sign-sub-inv_binary64`
277×	`associate-l_binary64`

Counts

297 → 302

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	171	8645
1	364	6130
2	911	4575
3	2803	4281
4	4238	4246
5	4940	4246
6	4768	4246

prune183.0ms (1.9%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	301	1	302
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	302	1	303

Error

0.3b

Counts

303 → 1

Alt Table

Status	Error	Program
▶	0.3b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 1/3 x))

Compiler

Compiled 10336 to 6487 computations (37.2% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 1/45 (pow.f64 x 3))
✓	0.3b	(*.f64 1/3 x)

series5.0ms (0%)

Counts

2 → 0

Calls

2 calls:

3.0ms	(*.f64 1/45 (pow.f64 x 3))
2.0ms	(*.f64 1/3 x)

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
15×	`associate-r_binary64`
9×	`add-exp-log_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`

Counts

2 → 53

Calls

2 calls:

7.0ms	(*.f64 1/45 (pow.f64 x 3))
3.0ms	(*.f64 1/3 x)

simplify91.0ms (1%)

Algorithm

1×	egg-herbie

Rules

629×	`associate-l_binary64`
574×	`associate-r_binary64`
469×	`fma-def_binary64`
366×	`log-prod_binary64`
326×	`cube-prod_binary64`

Counts

53 → 70

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	85	496
1	156	444
2	392	443
3	2007	443
4	3157	411
5	4364	411
6	4951	411
7	4911	411

prune52.0ms (0.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	64	6	70
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	64	7	71

Error

0.1b

Counts

71 → 7

Alt Table

Status	Error	Program
	34.4b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (sqrt.f64 (.f64 1/3 x)) (sqrt.f64 (.f64 1/3 x))))
✓	0.3b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 1/3 x))
	34.4b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (*.f64 1/3 (sqrt.f64 x)) (sqrt.f64 x)))
	1.6b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (*.f64 1/3 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x)))
▶	0.7b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (sqrt.f64 1/3) (*.f64 (sqrt.f64 1/3) x)))
	40.7b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (cbrt.f64 (.f64 (.f64 (.f64 1/3 1/3) 1/3) (.f64 (.f64 x x) x))))
	1.5b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (.f64 (cbrt.f64 (.f64 1/3 x)) (cbrt.f64 (.f64 1/3 x))) (cbrt.f64 (.f64 1/3 x))))

Compiler

Compiled 1187 to 930 computations (21.7% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(*.f64 1/45 (pow.f64 x 3))
✓	0.3b	(.f64 (sqrt.f64 1/3) (.f64 (sqrt.f64 1/3) x))
✓	0.4b	(*.f64 (sqrt.f64 1/3) x)

series11.0ms (0.1%)

Counts

2 → 12

Calls

2 calls:

8.0ms	(.f64 (sqrt.f64 1/3) (.f64 (sqrt.f64 1/3) x))
3.0ms	(*.f64 (sqrt.f64 1/3) x)

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`associate-l_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`

Counts

2 → 47

Calls

2 calls:

8.0ms	(.f64 (sqrt.f64 1/3) (.f64 (sqrt.f64 1/3) x))
4.0ms	(*.f64 (sqrt.f64 1/3) x)

simplify76.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

981×	`fma-def_binary64`
332×	`associate-l_binary64`
332×	`unswap-sqr_binary64`
263×	`associate-*r/_binary64`
234×	`associate-*l/_binary64`

Counts

59 → 59

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	57	459
1	121	420
2	338	419
3	628	411
4	824	411
5	1265	411
6	3215	411
7	4671	411
8	4933	411

prune197.0ms (2.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	101	4	105
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	103	9	112

Error

0.1b

Counts

112 → 9

Alt Table

Status	Error	Program
	34.4b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (sqrt.f64 (.f64 1/3 x)) (sqrt.f64 (.f64 1/3 x))))
✓	0.3b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 1/3 x))
▶	0.4b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (*.f64 x (pow.f64 (sqrt.f64 1/3) 3/2))))
	40.7b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (cbrt.f64 (.f64 (.f64 (.f64 1/3 1/3) 1/3) (.f64 (.f64 x x) x))))
	0.5b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 1/3) x))))
	0.5b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (sqrt.f64 1/3) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) x))))
	1.6b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (sqrt.f64 1/3) (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 1/3) x)) (cbrt.f64 (.f64 (sqrt.f64 1/3) x))) (cbrt.f64 (*.f64 (sqrt.f64 1/3) x)))))
	34.4b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (*.f64 1/3 (sqrt.f64 x)) (sqrt.f64 x)))
	1.5b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (.f64 (cbrt.f64 (.f64 1/3 x)) (cbrt.f64 (.f64 1/3 x))) (cbrt.f64 (.f64 1/3 x))))

Compiler

Compiled 2185 to 1838 computations (15.9% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(*.f64 1/45 (pow.f64 x 3))
✓	0.2b	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)))
✓	0.4b	(*.f64 x (pow.f64 (sqrt.f64 1/3) 3/2))

series27.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

17.0ms	(*.f64 x (pow.f64 (sqrt.f64 1/3) 3/2))
10.0ms	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-exp-log_binary64`
16×	`add-sqr-sqrt_binary64`
13×	`sqrt-prod_binary64`
12×	`associate-l_binary64`
11×	`associate-r_binary64`

Counts

2 → 58

Calls

2 calls:

7.0ms	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)))
5.0ms	(*.f64 x (pow.f64 (sqrt.f64 1/3) 3/2))

simplify73.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

564×	`associate-/r/_binary64`
560×	`associate-/l/_binary64`
541×	`fma-def_binary64`
480×	`*-commutative_binary64`
276×	`sqr-pow_binary64`

Counts

82 → 85

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	95	1147
1	190	997
2	602	971
3	873	779
4	1358	728
5	2345	713
6	4971	713

prune132.0ms (1.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	128	3	131
Fresh	6	1	7
Picked	1	0	1
Done	0	1	1
Total	135	5	140

Error

Counts

140 → 5

Alt Table

Status	Error	Program
	0.5b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (*.f64 (sqrt.f64 (sqrt.f64 1/3)) x) (pow.f64 (sqrt.f64 1/3) 3/2)))
	0.4b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 1/3))) (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)))))
✓	0.3b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 1/3 x))
	0.3b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (.f64 x (pow.f64 (sqrt.f64 1/3) 3/4)) (pow.f64 (sqrt.f64 (sqrt.f64 1/3)) 3/2))))
	1.5b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 (.f64 (cbrt.f64 (.f64 1/3 x)) (cbrt.f64 (.f64 1/3 x))) (cbrt.f64 (.f64 1/3 x))))

Compiler

Compiled 2867 to 2483 computations (13.4% saved)

regimes199.0ms (2.1%)

Accuracy

Total 0.4b remaining (82.5%)

Threshold costs 0.4b (82.5%)

Counts

103 → 1

Compiler

Compiled 3772 to 3238 computations (14.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	35
1	22	35
2	22	35

end1.0ms (0%)

Compiler: Compiled 23 to 21 computations (8.7% saved)

sample7.7s (82%)

Algorithm

1×

intervals

Results

5.8s	3929×	body	2048	valid
883.0ms	2076×	body	1024	valid
199.0ms	8000×	pre	128	true
187.0ms	1027×	body	512	valid
133.0ms	220×	body	4096	valid
59.0ms	525×	body	256	valid
13.0ms	223×	body	128	valid

Compiler

Compiled 134 to 116 computations (13.4% saved)

Iter	Nodes	Cost
0	7	12
1	11	12
2	17	12
3	25	12
4	33	12
5	51	12
6	76	12
7	93	12
8	110	12
9	120	12
10	124	12
11	126	12
12	112	12

Iter	Nodes	Cost
0	7	12
1	11	12
2	17	12
3	25	12
4	33	12
5	51	12
6	76	12
7	93	12
8	110	12
9	120	12
10	124	12
11	126	12
12	112	12

Details

analyze6.0ms (0.1%)

sample236.0ms (2.5%)

simplify10.0ms (0.1%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series24.0ms (0.3%)

rewrite51.0ms (0.5%)

simplify247.0ms (2.6%)

prune183.0ms (1.9%)

localize5.0ms (0.1%)

series5.0ms (0%)

rewrite11.0ms (0.1%)

simplify91.0ms (1%)

prune52.0ms (0.6%)

localize7.0ms (0.1%)

series11.0ms (0.1%)

rewrite13.0ms (0.1%)

simplify76.0ms (0.8%)

prune197.0ms (2.1%)

localize11.0ms (0.1%)

series27.0ms (0.3%)

rewrite15.0ms (0.2%)

simplify73.0ms (0.8%)

prune132.0ms (1.4%)

regimes199.0ms (2.1%)

simplify3.0ms (0%)

end1.0ms (0%)

sample7.7s (82%)

Profiling

Iter	Nodes	Cost
0	7	12
1	11	12
2	17	12
3	25	12
4	33	12
5	51	12
6	76	12
7	93	12
8	110	12
9	120	12
10	124	12
11	126	12
12	112	12