Details

analyze544.0ms (6.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
49.9%	49.9%	0.2%	2
49.9%	49.9%	0.2%	3
49.9%	49.9%	0.2%	4
49.9%	49.9%	0.2%	5
49.9%	49.9%	0.2%	6
49.9%	49.9%	0.2%	7
53%	46.8%	0.2%	8
57.7%	42.1%	0.2%	9
61.6%	38.2%	0.2%	10
63.5%	30%	6.4%	11
63.5%	30%	6.4%	12
67.6%	25.9%	6.4%	13
68.9%	24.7%	6.4%	14

Compiler

Compiled 20 to 15 computations (25% saved)

sample101.0ms (1.2%)

Algorithm

1×

intervals

Results

23.0ms	55×	body	1024	valid
18.0ms	71×	body	1024	invalid
9.0ms	134×	body	128	valid
8.0ms	124×	body	128	invalid
7.0ms	29×	body	512	valid
5.0ms	35×	body	256	valid
4.0ms	22×	body	512	invalid
2.0ms	3×	body	2048	valid
2.0ms	14×	body	256	invalid

Compiler

Compiled 43 to 33 computations (23.3% saved)

simplify106.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

720×	`div-sub_binary64`
424×	`times-frac_binary64`
411×	`associate-/l*_binary64`
370×	`cancel-sign-sub-inv_binary64`
355×	`distribute-neg-frac_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	28	24
2	50	24
3	96	24
4	205	24
5	441	24
6	997	24
7	1569	24
8	2735	24
9	3755	24
10	4991	24
11	4999	24
12	4815	24

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

18.5b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	18.5b	(+.f64 (.f64 (.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2))) U)

Compiler

Compiled 38 to 28 computations (26.3% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
0.0b	(.f64 (.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)))
6.6b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

rewrite75.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

15×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
10×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-cube-cbrt_binary64` `cancel-sign-sub-inv_binary64` `associate-r_binary64`
5×	`add-log-exp_binary64`

Counts

3 → 68

Calls

3 calls:

9.0ms	(.f64 (.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)))
8.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
5.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

Compiler

Compiled 1510 to 558 computations (63% saved)

series102.0ms (1.2%)

Error

0.1b

Counts

3 → 21

Calls

3 calls:

49.0ms	(.f64 (.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)))
22.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
8.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

Compiler

Compiled 1051 to 740 computations (29.6% saved)

simplify108.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

469×	`neg-mul-1_binary64`
356×	`*-commutative_binary64`
269×	`distribute-rgt-neg-out_binary64`
267×	`distribute-lft-neg-out_binary64`
228×	`distribute-rgt-in_binary64`

Counts

89 → 66

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	138	1736
1	320	1492
2	998	1464
3	2187	1464
4	4447	1461
5	5098	1461

prune47.0ms (0.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	2	67

Error

0.0b

Counts

67 → 2

Alt Table

Status	Error	Program
	0.1b	(+.f64 (.f64 2 (.f64 l (.f64 (cos.f64 (.f64 1/2 K)) J))) U)
▶	0.1b	(+.f64 (.f64 (.f64 J (+.f64 (+.f64 l l) (*.f64 1/3 (pow.f64 l 3)))) (cos.f64 (/.f64 K 2))) U)

Compiler

Compiled 922 to 449 computations (51.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 J (+.f64 (+.f64 l l) (.f64 1/3 (pow.f64 l 3))))
0.0b	(+.f64 (.f64 (.f64 J (+.f64 (+.f64 l l) (*.f64 1/3 (pow.f64 l 3)))) (cos.f64 (/.f64 K 2))) U)
0.1b	(*.f64 1/3 (pow.f64 l 3))
0.2b	(.f64 (.f64 J (+.f64 (+.f64 l l) (*.f64 1/3 (pow.f64 l 3)))) (cos.f64 (/.f64 K 2)))

rewrite219.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

20×	`add-sqr-sqrt_binary64`
18×	`associate-r_binary64`
16×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
11×	`pow1_binary64` `add-cube-cbrt_binary64` `*-un-lft-identity_binary64`

Counts

4 → 84

Calls

4 calls:

12.0ms	(+.f64 (.f64 (.f64 J (+.f64 (+.f64 l l) (*.f64 1/3 (pow.f64 l 3)))) (cos.f64 (/.f64 K 2))) U)
12.0ms	(.f64 (.f64 J (+.f64 (+.f64 l l) (*.f64 1/3 (pow.f64 l 3)))) (cos.f64 (/.f64 K 2)))
10.0ms	(.f64 J (+.f64 (+.f64 l l) (.f64 1/3 (pow.f64 l 3))))
7.0ms	(*.f64 1/3 (pow.f64 l 3))

Compiler

Compiled 2179 to 1399 computations (35.8% saved)

series301.0ms (3.6%)

Error

0.0b

Counts

4 → 50

Calls

4 calls:

151.0ms	(+.f64 (.f64 (.f64 J (+.f64 (+.f64 l l) (*.f64 1/3 (pow.f64 l 3)))) (cos.f64 (/.f64 K 2))) U)
78.0ms	(.f64 (.f64 J (+.f64 (+.f64 l l) (*.f64 1/3 (pow.f64 l 3)))) (cos.f64 (/.f64 K 2)))
38.0ms	(.f64 J (+.f64 (+.f64 l l) (.f64 1/3 (pow.f64 l 3))))
14.0ms	(*.f64 1/3 (pow.f64 l 3))

Compiler

Compiled 2359 to 1758 computations (25.5% saved)

simplify181.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

440×	`unswap-sqr_binary64`
386×	`distribute-rgt-neg-in_binary64`
282×	`associate-l_binary64`
273×	`cancel-sign-sub-inv_binary64`
265×	`associate-r_binary64`

Counts

134 → 110

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	181	3087
1	471	2698
2	1754	2650
3	3202	2650
4	4733	2620
5	4823	2620
6	4944	2620

prune121.0ms (1.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	103	7	110
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	104	8	112

Error

Counts

112 → 8

Alt Table

Status	Error	Program
	0.4b	(+.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 J (+.f64 (.f64 1/3 (pow.f64 l 3)) (+.f64 l l)))) (cbrt.f64 (.f64 J (+.f64 (.f64 1/3 (pow.f64 l 3)) (+.f64 l l))))) (cbrt.f64 (.f64 J (+.f64 (*.f64 1/3 (pow.f64 l 3)) (+.f64 l l))))) (cos.f64 (/.f64 K 2))) U)
	0.1b	(+.f64 (.f64 2 (.f64 l (.f64 (cos.f64 (.f64 1/2 K)) J))) U)
	0.1b	(+.f64 (.f64 J (.f64 (+.f64 (*.f64 1/3 (pow.f64 l 3)) (+.f64 l l)) (cos.f64 (/.f64 K 2)))) U)
▶	0.1b	(+.f64 (.f64 (+.f64 (.f64 2 (.f64 l J)) (.f64 1/3 (*.f64 (pow.f64 l 3) J))) (cos.f64 (/.f64 K 2))) U)
	24.9b	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 J (+.f64 (.f64 1/3 (pow.f64 l 3)) (+.f64 l l))) (cos.f64 (/.f64 K 2)))) (sqrt.f64 (.f64 (.f64 J (+.f64 (*.f64 1/3 (pow.f64 l 3)) (+.f64 l l))) (cos.f64 (/.f64 K 2))))) U)
	0.4b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 J (+.f64 (.f64 1/3 (pow.f64 l 3)) (+.f64 l l))) (cos.f64 (/.f64 K 2)))) (cbrt.f64 (.f64 (.f64 J (+.f64 (.f64 1/3 (pow.f64 l 3)) (+.f64 l l))) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (.f64 J (+.f64 (*.f64 1/3 (pow.f64 l 3)) (+.f64 l l))) (cos.f64 (/.f64 K 2))))) U)
	5.4b	(+.f64 (.f64 (/.f64 (.f64 J (+.f64 (.f64 l (.f64 l 4)) (.f64 (pow.f64 l 6) -1/9))) (-.f64 (+.f64 l l) (.f64 1/3 (pow.f64 l 3)))) (cos.f64 (/.f64 K 2))) U)
	5.4b	(+.f64 (/.f64 (.f64 (cos.f64 (/.f64 K 2)) (.f64 J (+.f64 (.f64 l (.f64 l 4)) (.f64 (pow.f64 l 6) -1/9)))) (-.f64 (+.f64 l l) (.f64 1/3 (pow.f64 l 3)))) U)

Compiler

Compiled 2043 to 1349 computations (34% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 2 (.f64 l J))
0.1b	(.f64 1/3 (.f64 (pow.f64 l 3) J))
0.2b	(.f64 (+.f64 (.f64 2 (.f64 l J)) (.f64 1/3 (*.f64 (pow.f64 l 3) J))) (cos.f64 (/.f64 K 2)))
5.1b	(*.f64 (pow.f64 l 3) J)

rewrite228.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

26×	`add-exp-log_binary64`
21×	`add-sqr-sqrt_binary64` `associate-l_binary64`
18×	`add-cbrt-cube_binary64`
14×	`prod-exp_binary64`
13×	`pow1_binary64`

Counts

4 → 88

Calls

4 calls:

9.0ms	(.f64 (+.f64 (.f64 2 (.f64 l J)) (.f64 1/3 (*.f64 (pow.f64 l 3) J))) (cos.f64 (/.f64 K 2)))
6.0ms	(*.f64 (pow.f64 l 3) J)
6.0ms	(.f64 1/3 (.f64 (pow.f64 l 3) J))
5.0ms	(.f64 2 (.f64 l J))

Compiler

Compiled 2155 to 1446 computations (32.9% saved)

series169.0ms (2%)

Error

Counts

4 → 31

Calls

4 calls:

84.0ms	(.f64 (+.f64 (.f64 2 (.f64 l J)) (.f64 1/3 (*.f64 (pow.f64 l 3) J))) (cos.f64 (/.f64 K 2)))
23.0ms	(.f64 1/3 (.f64 (pow.f64 l 3) J))
21.0ms	(*.f64 (pow.f64 l 3) J)
19.0ms	(.f64 2 (.f64 l J))

Compiler

Compiled 1659 to 1231 computations (25.8% saved)

simplify154.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

362×	`associate-r_binary64`
330×	`associate-l_binary64`
270×	`distribute-rgt-in_binary64` `distribute-lft-in_binary64`
245×	`log-prod_binary64`
244×	`exp-prod_binary64`

Counts

119 → 98

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	173	1910
1	405	1706
2	1749	1684
3	4032	1660
4	4809	1660
5	4989	1660
6	4946	1660

prune165.0ms (2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	99	7	106

Error

Counts

106 → 7

Alt Table

Status	Error	Program
	0.1b	(+.f64 (.f64 2 (.f64 l (.f64 (cos.f64 (.f64 1/2 K)) J))) U)
	0.3b	(+.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) (.f64 (.f64 J l) (sqrt.f64 2))) (.f64 1/3 (.f64 (pow.f64 l 3) J))) (cos.f64 (/.f64 K 2))) U)
▶	0.1b	(+.f64 (.f64 J (.f64 (+.f64 (*.f64 1/3 (pow.f64 l 3)) (+.f64 l l)) (cos.f64 (/.f64 K 2)))) U)
✓	0.1b	(+.f64 (.f64 (+.f64 (.f64 2 (.f64 l J)) (.f64 1/3 (*.f64 (pow.f64 l 3) J))) (cos.f64 (/.f64 K 2))) U)
	24.9b	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 J (+.f64 (.f64 1/3 (pow.f64 l 3)) (+.f64 l l))) (cos.f64 (/.f64 K 2)))) (sqrt.f64 (.f64 (.f64 J (+.f64 (*.f64 1/3 (pow.f64 l 3)) (+.f64 l l))) (cos.f64 (/.f64 K 2))))) U)
	5.4b	(+.f64 (/.f64 (.f64 (cos.f64 (/.f64 K 2)) (.f64 J (+.f64 (.f64 l (.f64 l 4)) (.f64 (pow.f64 l 6) -1/9)))) (-.f64 (+.f64 l l) (.f64 1/3 (pow.f64 l 3)))) U)
	0.4b	(+.f64 (.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 J (.f64 l 2))) (cbrt.f64 (.f64 J (.f64 l 2)))) (cbrt.f64 (.f64 J (.f64 l 2)))) (.f64 1/3 (*.f64 (pow.f64 l 3) J))) (cos.f64 (/.f64 K 2))) U)

Compiler

Compiled 1882 to 1335 computations (29.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 J (.f64 (+.f64 (*.f64 1/3 (pow.f64 l 3)) (+.f64 l l)) (cos.f64 (/.f64 K 2)))) U)
0.1b	(.f64 J (.f64 (+.f64 (*.f64 1/3 (pow.f64 l 3)) (+.f64 l l)) (cos.f64 (/.f64 K 2))))
0.1b	(*.f64 1/3 (pow.f64 l 3))
0.1b	(.f64 (+.f64 (.f64 1/3 (pow.f64 l 3)) (+.f64 l l)) (cos.f64 (/.f64 K 2)))

rewrite205.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

20×	`add-sqr-sqrt_binary64`
16×	`add-exp-log_binary64` `associate-r_binary64`
13×	`add-cbrt-cube_binary64`
11×	`pow1_binary64` `add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
9×	`associate-l_binary64`

Counts

4 → 82

Calls

4 calls:

16.0ms	(+.f64 (.f64 J (.f64 (+.f64 (*.f64 1/3 (pow.f64 l 3)) (+.f64 l l)) (cos.f64 (/.f64 K 2)))) U)
12.0ms	(.f64 J (.f64 (+.f64 (*.f64 1/3 (pow.f64 l 3)) (+.f64 l l)) (cos.f64 (/.f64 K 2))))
11.0ms	(.f64 (+.f64 (.f64 1/3 (pow.f64 l 3)) (+.f64 l l)) (cos.f64 (/.f64 K 2)))
7.0ms	(*.f64 1/3 (pow.f64 l 3))

Compiler

Compiled 2143 to 1388 computations (35.2% saved)

series329.0ms (4%)

Error

Counts

4 → 51

Calls

4 calls:

154.0ms	(+.f64 (.f64 J (.f64 (+.f64 (*.f64 1/3 (pow.f64 l 3)) (+.f64 l l)) (cos.f64 (/.f64 K 2)))) U)
82.0ms	(.f64 J (.f64 (+.f64 (*.f64 1/3 (pow.f64 l 3)) (+.f64 l l)) (cos.f64 (/.f64 K 2))))
52.0ms	(.f64 (+.f64 (.f64 1/3 (pow.f64 l 3)) (+.f64 l l)) (cos.f64 (/.f64 K 2)))
9.0ms	(*.f64 1/3 (pow.f64 l 3))

Compiler

Compiled 2472 to 1851 computations (25.1% saved)

simplify186.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

537×	`unswap-sqr_binary64`
347×	`distribute-rgt-neg-in_binary64`
330×	`cancel-sign-sub-inv_binary64`
328×	`sub-neg_binary64`
249×	`associate-r_binary64`

Counts

133 → 91

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	182	3288
1	471	2839
2	1655	2785
3	3134	2785
4	4588	2755
5	4745	2755
6	5030	2755

prune94.0ms (1.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	91	7	98

Error

Counts

98 → 7

Alt Table

Status	Error	Program
	0.1b	(+.f64 (.f64 2 (.f64 l (.f64 (cos.f64 (.f64 1/2 K)) J))) U)
	0.3b	(+.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) (.f64 (.f64 J l) (sqrt.f64 2))) (.f64 1/3 (.f64 (pow.f64 l 3) J))) (cos.f64 (/.f64 K 2))) U)
	0.1b	(+.f64 (.f64 J (.f64 (+.f64 (*.f64 1/3 (pow.f64 l 3)) (+.f64 l l)) (cos.f64 (/.f64 K 2)))) U)
	0.1b	(+.f64 (.f64 (+.f64 (.f64 2 (.f64 l J)) (.f64 1/3 (*.f64 (pow.f64 l 3) J))) (cos.f64 (/.f64 K 2))) U)
	24.9b	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 J (+.f64 (.f64 1/3 (pow.f64 l 3)) (+.f64 l l))) (cos.f64 (/.f64 K 2)))) (sqrt.f64 (.f64 (.f64 J (+.f64 (*.f64 1/3 (pow.f64 l 3)) (+.f64 l l))) (cos.f64 (/.f64 K 2))))) U)
	5.4b	(+.f64 (/.f64 (.f64 (cos.f64 (/.f64 K 2)) (.f64 J (+.f64 (.f64 l (.f64 l 4)) (.f64 (pow.f64 l 6) -1/9)))) (-.f64 (+.f64 l l) (.f64 1/3 (pow.f64 l 3)))) U)
	0.4b	(+.f64 (.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 J (.f64 l 2))) (cbrt.f64 (.f64 J (.f64 l 2)))) (cbrt.f64 (.f64 J (.f64 l 2)))) (.f64 1/3 (*.f64 (pow.f64 l 3) J))) (cos.f64 (/.f64 K 2))) U)

Compiler

Compiled 1308 to 852 computations (34.9% saved)

regimes1.5s (18.6%)

Accuracy

Total 0.1b remaining (10.2%)

Threshold costs 0.1b (10.2%)

Compiler

Compiled 29776 to 21686 computations (27.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	30
1	25	30
2	25	30

end1.0ms (0%)

Compiler: Compiled 24 to 18 computations (25% saved)

sample3.2s (39.1%)

Algorithm

1×

intervals

Results

715.0ms	1726×	body	1024	valid
508.0ms	1907×	body	1024	invalid
289.0ms	4360×	body	128	valid
268.0ms	1184×	body	512	valid
225.0ms	3390×	body	128	invalid
188.0ms	924×	body	512	invalid
94.0ms	673×	body	256	valid
65.0ms	502×	body	256	invalid
35.0ms	57×	body	2048	valid

Compiler

Compiled 252 to 188 computations (25.4% saved)

Details

analyze544.0ms (6.6%)

sample101.0ms (1.2%)

simplify106.0ms (1.3%)

prune2.0ms (0%)

localize12.0ms (0.1%)

rewrite75.0ms (0.9%)

series102.0ms (1.2%)

simplify108.0ms (1.3%)

prune47.0ms (0.6%)

localize12.0ms (0.2%)

rewrite219.0ms (2.7%)

series301.0ms (3.6%)

simplify181.0ms (2.2%)

prune121.0ms (1.5%)

localize15.0ms (0.2%)

rewrite228.0ms (2.8%)

series169.0ms (2%)

simplify154.0ms (1.9%)

prune165.0ms (2%)

localize14.0ms (0.2%)

rewrite205.0ms (2.5%)

series329.0ms (4%)

simplify186.0ms (2.3%)

prune94.0ms (1.1%)

regimes1.5s (18.6%)

simplify3.0ms (0%)

end1.0ms (0%)

sample3.2s (39.1%)

Profiling