Details

analyze27.0ms (0.3%)

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)

sample214.0ms (2.1%)

Algorithm

1×

intervals

Results

165.0ms	123×	body	2048	valid
24.0ms	61×	body	1024	valid
4.0ms	256×	pre	128	true
4.0ms	35×	body	512	valid
3.0ms	6×	body	4096	valid
2.0ms	19×	body	256	valid
1.0ms	12×	body	128	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify12.0ms (0.1%)

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	12
1	11	12
2	17	12
3	24	12
4	31	12
5	47	12
6	69	12
7	78	12
8	90	12
9	92	12
10	86	12
11	72	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

59.2b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	59.2b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 1 (tan.f64 x))
4.2b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

rewrite107.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

58.6b

Rules

43×	`add-sqr-sqrt_binary64`
36×	`times-frac_binary64`
35×	`*-un-lft-identity_binary64`
19×	`add-cube-cbrt_binary64`
14×	`cancel-sign-sub-inv_binary64`

Counts

2 → 74

Calls

2 calls:

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

Compiler

Compiled 1107 to 719 computations (35% saved)

series46.0ms (0.5%)

Error

0.4b

Counts

2 → 14

Calls

2 calls:

19.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
16.0ms	(/.f64 1 (tan.f64 x))

Compiler

Compiled 333 to 249 computations (25.2% saved)

simplify135.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

694×	`times-frac_binary64`
513×	`sub-neg_binary64`
441×	`div-sub_binary64`
347×	`associate-/l*_binary64`
338×	`unsub-neg_binary64`

Counts

88 → 57

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	109	1216
1	258	1182
2	552	1179
3	1458	1179
4	3628	1164
5	4209	1144
6	4585	1144
7	4996	1144

prune18.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	56	1	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	1	58

Error

0.4b

Counts

58 → 1

Alt Table

Status	Error	Program
▶	0.4b	(+.f64 (.f64 1/3 x) (+.f64 (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 2/945 (pow.f64 x 5))) (.f64 1/4725 (pow.f64 x 7))))

Compiler

Compiled 379 to 262 computations (30.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 1/4725 (pow.f64 x 7))
0.1b	(*.f64 2/945 (pow.f64 x 5))
0.1b	(*.f64 1/45 (pow.f64 x 3))
0.4b	(*.f64 1/3 x)

rewrite163.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

35×	`add-sqr-sqrt_binary64`
29×	`associate-r_binary64`
21×	`add-exp-log_binary64`
16×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
12×	`add-cbrt-cube_binary64` `associate-l_binary64` `unpow-prod-down_binary64`

Counts

4 → 99

Calls

4 calls:

6.0ms	(*.f64 1/45 (pow.f64 x 3))
5.0ms	(*.f64 1/4725 (pow.f64 x 7))
5.0ms	(*.f64 2/945 (pow.f64 x 5))
4.0ms	(*.f64 1/3 x)

Compiler

Compiled 2366 to 1918 computations (18.9% saved)

series42.0ms (0.4%)

Error

0.4b

Counts

4 → 12

Calls

4 calls:

12.0ms	(*.f64 1/4725 (pow.f64 x 7))
11.0ms	(*.f64 2/945 (pow.f64 x 5))
10.0ms	(*.f64 1/45 (pow.f64 x 3))
8.0ms	(*.f64 1/3 x)

Compiler

Compiled 550 to 450 computations (18.2% saved)

simplify160.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

544×	`unswap-sqr_binary64`
407×	`associate-+l+_binary64`
389×	`log-prod_binary64`
385×	`*-commutative_binary64`
369×	`exp-prod_binary64`

Counts

111 → 61

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	171	1091
1	322	1015
2	766	1002
3	1224	1002
4	2347	948
5	4677	945
6	4919	945
7	4986	945
8	4993	945
9	4842	945

prune56.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	58	3	61
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	58	4	62

Error

0.3b

Counts

62 → 4

Alt Table

Status	Error	Program
▶	0.7b	(+.f64 (.f64 (sqrt.f64 1/3) (.f64 x (sqrt.f64 1/3))) (+.f64 (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 2/945 (pow.f64 x 5))) (*.f64 1/4725 (pow.f64 x 7))))
	38.4b	(+.f64 (cbrt.f64 (pow.f64 (.f64 1/3 x) 3)) (+.f64 (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 2/945 (pow.f64 x 5))) (.f64 1/4725 (pow.f64 x 7))))
	1.5b	(+.f64 (.f64 (.f64 1/3 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x)) (+.f64 (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 2/945 (pow.f64 x 5))) (*.f64 1/4725 (pow.f64 x 7))))
✓	0.4b	(+.f64 (.f64 1/3 x) (+.f64 (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 2/945 (pow.f64 x 5))) (.f64 1/4725 (pow.f64 x 7))))

Compiler

Compiled 1105 to 896 computations (18.9% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 2/945 (pow.f64 x 5))
0.1b	(*.f64 1/45 (pow.f64 x 3))
0.4b	(.f64 (sqrt.f64 1/3) (.f64 x (sqrt.f64 1/3)))
0.4b	(*.f64 x (sqrt.f64 1/3))

rewrite176.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

32×	`add-sqr-sqrt_binary64`
26×	`associate-r_binary64`
21×	`add-exp-log_binary64`
16×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
15×	`add-cbrt-cube_binary64` `associate-l_binary64`

Counts

4 → 99

Calls

4 calls:

7.0ms	(.f64 (sqrt.f64 1/3) (.f64 x (sqrt.f64 1/3)))
6.0ms	(*.f64 1/45 (pow.f64 x 3))
5.0ms	(*.f64 2/945 (pow.f64 x 5))
5.0ms	(*.f64 x (sqrt.f64 1/3))

Compiler

Compiled 2604 to 2186 computations (16.1% saved)

series50.0ms (0.5%)

Error

0.3b

Counts

4 → 12

Calls

4 calls:

13.0ms	(.f64 (sqrt.f64 1/3) (.f64 x (sqrt.f64 1/3)))
12.0ms	(*.f64 x (sqrt.f64 1/3))
11.0ms	(*.f64 2/945 (pow.f64 x 5))
10.0ms	(*.f64 1/45 (pow.f64 x 3))

Compiler

Compiled 668 to 564 computations (15.6% saved)

simplify119.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

612×	`unswap-sqr_binary64`
380×	`*-commutative_binary64`
356×	`log-div_binary64`
278×	`sqr-pow_binary64`
270×	`associate-/l*_binary64`

Counts

111 → 68

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	150	1142
1	296	967
2	780	955
3	1279	946
4	2517	914
5	4216	911
6	4891	911
7	5173	911

prune80.0ms (0.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	63	5	68
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	63	9	72

Error

0.2b

Counts

72 → 9

Alt Table

Status	Error	Program
	1.6b	(+.f64 (.f64 (sqrt.f64 1/3) (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (sqrt.f64 1/3) (cbrt.f64 x)))) (+.f64 (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 2/945 (pow.f64 x 5))) (*.f64 1/4725 (pow.f64 x 7))))
✓	0.7b	(+.f64 (.f64 (sqrt.f64 1/3) (.f64 x (sqrt.f64 1/3))) (+.f64 (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 2/945 (pow.f64 x 5))) (*.f64 1/4725 (pow.f64 x 7))))
	38.4b	(+.f64 (cbrt.f64 (pow.f64 (.f64 1/3 x) 3)) (+.f64 (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 2/945 (pow.f64 x 5))) (.f64 1/4725 (pow.f64 x 7))))
	1.5b	(+.f64 (.f64 (.f64 1/3 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x)) (+.f64 (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 2/945 (pow.f64 x 5))) (*.f64 1/4725 (pow.f64 x 7))))
✓	0.4b	(+.f64 (.f64 1/3 x) (+.f64 (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 2/945 (pow.f64 x 5))) (.f64 1/4725 (pow.f64 x 7))))
	1.5b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 x 1/3)) (cbrt.f64 (.f64 x 1/3))) (cbrt.f64 (.f64 x 1/3))) (+.f64 (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 2/945 (pow.f64 x 5))) (.f64 1/4725 (pow.f64 x 7))))
▶	0.5b	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2))) (+.f64 (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 2/945 (pow.f64 x 5))) (*.f64 1/4725 (pow.f64 x 7))))
	31.9b	(+.f64 (.f64 (sqrt.f64 (.f64 x 1/3)) (sqrt.f64 (.f64 x 1/3))) (+.f64 (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 2/945 (pow.f64 x 5))) (.f64 1/4725 (pow.f64 x 7))))
	32.0b	(+.f64 (.f64 (sqrt.f64 1/3) (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 1/3) (sqrt.f64 x)))) (+.f64 (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 2/945 (pow.f64 x 5))) (.f64 1/4725 (pow.f64 x 7))))

Compiler

Compiled 1600 to 1319 computations (17.6% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 2/945 (pow.f64 x 5))
0.1b	(*.f64 1/45 (pow.f64 x 3))
0.3b	(.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))

rewrite221.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

37×	`add-sqr-sqrt_binary64`
30×	`associate-r_binary64`
29×	`add-exp-log_binary64`
18×	`add-cube-cbrt_binary64` `-un-lft-identity_binary64` `associate-l*_binary64`
16×	`prod-exp_binary64` `unpow-prod-down_binary64`

Counts

4 → 110

Calls

4 calls:

10.0ms	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)))
7.0ms	(*.f64 x (pow.f64 (sqrt.f64 1/3) 3/2))
6.0ms	(*.f64 1/45 (pow.f64 x 3))
5.0ms	(*.f64 2/945 (pow.f64 x 5))

Compiler

Compiled 3266 to 2800 computations (14.3% saved)

series61.0ms (0.6%)

Error

0.2b

Counts

4 → 12

Calls

4 calls:

18.0ms	(*.f64 x (pow.f64 (sqrt.f64 1/3) 3/2))
13.0ms	(*.f64 1/45 (pow.f64 x 3))
13.0ms	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)))
12.0ms	(*.f64 2/945 (pow.f64 x 5))

Compiler

Compiled 760 to 652 computations (14.2% saved)

simplify117.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

558×	`*-commutative_binary64`
379×	`sqr-pow_binary64`
333×	`log-prod_binary64`
332×	`exp-prod_binary64`
288×	`associate-/l/_binary64`

Counts

122 → 88

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	182	1546
1	360	1389
2	1074	1369
3	1849	1201
4	2963	1142
5	4622	1124
6	4911	1124

prune105.0ms (1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	83	5	88
Fresh	2	4	6
Picked	1	0	1
Done	0	2	2
Total	86	11	97

Error

0.0b

Counts

97 → 11

Alt Table

Status	Error	Program
	31.9b	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (sqrt.f64 x) (.f64 (pow.f64 (sqrt.f64 1/3) 3/2) (sqrt.f64 x)))) (+.f64 (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 2/945 (pow.f64 x 5))) (.f64 1/4725 (pow.f64 x 7))))
	1.6b	(+.f64 (.f64 (sqrt.f64 1/3) (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (sqrt.f64 1/3) (cbrt.f64 x)))) (+.f64 (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 2/945 (pow.f64 x 5))) (*.f64 1/4725 (pow.f64 x 7))))
	0.7b	(+.f64 (.f64 (sqrt.f64 1/3) (.f64 x (sqrt.f64 1/3))) (+.f64 (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 2/945 (pow.f64 x 5))) (*.f64 1/4725 (pow.f64 x 7))))
	1.5b	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (pow.f64 (sqrt.f64 1/3) 3/2) (cbrt.f64 x)))) (+.f64 (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 2/945 (pow.f64 x 5))) (*.f64 1/4725 (pow.f64 x 7))))
	0.5b	(+.f64 (.f64 (.f64 x (sqrt.f64 (sqrt.f64 1/3))) (pow.f64 (sqrt.f64 1/3) 3/2)) (+.f64 (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 2/945 (pow.f64 x 5))) (*.f64 1/4725 (pow.f64 x 7))))
	0.4b	(+.f64 (.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))) (+.f64 (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 2/945 (pow.f64 x 5))) (.f64 1/4725 (pow.f64 x 7))))
	1.5b	(+.f64 (.f64 (.f64 1/3 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x)) (+.f64 (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 2/945 (pow.f64 x 5))) (*.f64 1/4725 (pow.f64 x 7))))
	0.4b	(+.f64 (.f64 1/3 x) (+.f64 (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 2/945 (pow.f64 x 5))) (.f64 1/4725 (pow.f64 x 7))))
	1.5b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 x 1/3)) (cbrt.f64 (.f64 x 1/3))) (cbrt.f64 (.f64 x 1/3))) (+.f64 (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 2/945 (pow.f64 x 5))) (.f64 1/4725 (pow.f64 x 7))))
	0.5b	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 (cbrt.f64 1/3) (cbrt.f64 1/3)))) (.f64 (pow.f64 (sqrt.f64 1/3) 3/2) (.f64 x (sqrt.f64 (sqrt.f64 (cbrt.f64 1/3)))))) (+.f64 (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 2/945 (pow.f64 x 5))) (*.f64 1/4725 (pow.f64 x 7))))
	31.9b	(+.f64 (.f64 (sqrt.f64 (.f64 x 1/3)) (sqrt.f64 (.f64 x 1/3))) (+.f64 (+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 2/945 (pow.f64 x 5))) (.f64 1/4725 (pow.f64 x 7))))

Compiler

Compiled 1840 to 1553 computations (15.6% saved)

regimes746.0ms (7.4%)

Accuracy

Total 0.3b remaining (91%)

Threshold costs 0.3b (91%)

Compiler

Compiled 9251 to 7697 computations (16.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
3×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	31
1	26	31
2	26	31

end1.0ms (0%)

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

sample7.3s (73%)

Algorithm

1×

intervals

Results

5.5s	4040×	body	2048	valid
667.0ms	2021×	body	1024	valid
142.0ms	8000×	pre	128	true
127.0ms	942×	body	512	valid
112.0ms	205×	body	4096	valid
48.0ms	546×	body	256	valid
11.0ms	246×	body	128	valid

Compiler

Compiled 380 to 313 computations (17.6% saved)

Iter	Nodes	Cost
0	7	12
1	11	12
2	17	12
3	24	12
4	31	12
5	47	12
6	69	12
7	78	12
8	90	12
9	92	12
10	86	12
11	72	12

Iter	Nodes	Cost
0	7	12
1	11	12
2	17	12
3	24	12
4	31	12
5	47	12
6	69	12
7	78	12
8	90	12
9	92	12
10	86	12
11	72	12

Details

analyze27.0ms (0.3%)

sample214.0ms (2.1%)

simplify12.0ms (0.1%)

prune2.0ms (0%)

localize5.0ms (0%)

rewrite107.0ms (1.1%)

series46.0ms (0.5%)

simplify135.0ms (1.3%)

prune18.0ms (0.2%)

localize13.0ms (0.1%)

rewrite163.0ms (1.6%)

series42.0ms (0.4%)

simplify160.0ms (1.6%)

prune56.0ms (0.6%)

localize18.0ms (0.2%)

rewrite176.0ms (1.8%)

series50.0ms (0.5%)

simplify119.0ms (1.2%)

prune80.0ms (0.8%)

localize19.0ms (0.2%)

rewrite221.0ms (2.2%)

series61.0ms (0.6%)

simplify117.0ms (1.2%)

prune105.0ms (1%)

regimes746.0ms (7.4%)

simplify3.0ms (0%)

end1.0ms (0%)

sample7.3s (73%)

Profiling

Iter	Nodes	Cost
0	7	12
1	11	12
2	17	12
3	24	12
4	31	12
5	47	12
6	69	12
7	78	12
8	90	12
9	92	12
10	86	12
11	72	12