Details

analyze1.9s (10.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
15.6%	84.3%	0.1%	8
15.6%	84.3%	0.1%	9
15.6%	84.3%	0.1%	10
30.4%	69.4%	0.1%	11
30.4%	69.4%	0.1%	12
30.4%	69.4%	0.1%	13
39.6%	60.3%	0.1%	14

Compiler

Compiled 25 to 23 computations (8% saved)

sample86.0ms (0.5%)

Algorithm

1×

intervals

Results

36.0ms	64×	body	1024	valid
20.0ms	141×	body	128	valid
10.0ms	27×	body	512	valid
6.0ms	24×	body	256	valid

Compiler

Compiled 49 to 48 computations (2% saved)

simplify182.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4871	37
1	4871	37

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

17.1b

Counts

2 → 1

Compiler

Compiled 48 to 44 computations (8.3% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
0.3b	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
5.3b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
10.8b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite239.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

17.1b

Rules

28×	`add-exp-log_binary64_798`
20×	`pow1_binary64_821`
18×	`add-cbrt-cube_binary64_796`
15×	`*-un-lft-identity_binary64_760`
12×	`add-sqr-sqrt_binary64_782` `prod-exp_binary64_809`
11×	`add-cube-cbrt_binary64_795`
10×	`associate-r_binary64_700`
9×	`pow-prod-down_binary64_831` `cbrt-unprod_binary64_793`
8×	`sqrt-prod_binary64_776`
7×	`unpow-prod-down_binary64_839`
4×	`add-log-exp_binary64_799` `sqrt-div_binary64_777` `pow-exp_binary64_828`
3×	`times-frac_binary64_766` `pow-unpow_binary64_837` `div-exp_binary64_811`
2×	`flip3-+_binary64_763` `flip-+_binary64_734` `distribute-lft-out_binary64_711` `associate-r/_binary64_702` `associate-l_binary64_701` `-commutative_binary64_691`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `div-inv_binary64_757` `pow-pow_binary64_832` `pow-to-exp_binary64_829` `unpow2_binary64_825` `sqr-pow_binary64_732`

Counts

4 → 86

Calls

4 calls:

16.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
13.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
7.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
6.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

Compiler

Compiled 3141 to 2524 computations (19.6% saved)

series1.8s (10.1%)

Error

0.1b

Counts

4 → 61

Calls

4 calls:

816.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
496.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
306.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
122.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

Compiler

Compiled 4427 to 3788 computations (14.4% saved)

simplify64.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4999	4018
1	4999	4018

prune270.0ms (1.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	142	5	147
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	142	6	148

Error

0.0b

Counts

148 → 6

Compiler

Compiled 4426 to 3416 computations (22.8% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
5.3b	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
10.8b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite278.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

30×	`pow1_binary64_821`
29×	`add-exp-log_binary64_798`
20×	`add-cbrt-cube_binary64_796`
19×	`pow-prod-down_binary64_831` `prod-exp_binary64_809` `cbrt-unprod_binary64_793`
13×	`*-un-lft-identity_binary64_760`
10×	`add-sqr-sqrt_binary64_782`
9×	`add-cube-cbrt_binary64_795`
8×	`sqrt-prod_binary64_776`
7×	`associate-r_binary64_700`
6×	`cbrt-prod_binary64_791`
4×	`add-log-exp_binary64_799` `sqrt-div_binary64_777`
2×	`flip3-+_binary64_763` `flip-+_binary64_734` `distribute-lft-out_binary64_711` `associate-*r/_binary64_702` `pow1/3_binary64_842`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `associate-l_binary64_701` `*-commutative_binary64_691`

Counts

4 → 74

Calls

4 calls:

26.0ms	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
1.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
1.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

Compiler

Compiled 3902 to 3195 computations (18.1% saved)

series1.6s (9%)

Error

0.0b

Counts

4 → 55

Calls

4 calls:

820.0ms	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
527.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
100.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
99.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

Compiler

Compiled 4835 to 4112 computations (15% saved)

simplify64.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5255	3685

prune306.0ms (1.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	129	6	135

Error

0.0b

Counts

135 → 6

Compiler

Compiled 4905 to 3886 computations (20.8% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
0.4b	(cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))
5.3b	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
10.8b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite500.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

58×	`pow1_binary64_821`
57×	`add-exp-log_binary64_798`
42×	`pow-prod-down_binary64_831` `prod-exp_binary64_809` `cbrt-unprod_binary64_793`
39×	`add-cbrt-cube_binary64_796`
14×	`*-un-lft-identity_binary64_760`
12×	`cbrt-prod_binary64_791`
11×	`add-sqr-sqrt_binary64_782`
10×	`add-cube-cbrt_binary64_795`
8×	`sqrt-prod_binary64_776`
7×	`associate-r_binary64_700`
4×	`add-log-exp_binary64_799` `sqrt-div_binary64_777`
2×	`flip3-+_binary64_763` `flip-+_binary64_734` `distribute-lft-out_binary64_711` `associate-*r/_binary64_702` `pow1/3_binary64_842`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `associate-l_binary64_701` `*-commutative_binary64_691`

Counts

4 → 92

Calls

4 calls:

31.0ms	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
2.0ms	(cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))
1.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

Compiler

Compiled 6501 to 5379 computations (17.3% saved)

series1.7s (9.2%)

Error

0.0b

Counts

4 → 55

Calls

4 calls:

827.0ms	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
537.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
94.0ms	(cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))
91.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

Compiler

Compiled 5899 to 5022 computations (14.9% saved)

simplify126.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	5134	4344

prune442.0ms (2.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	146	7	153

Error

0.0b

Counts

153 → 7

Compiler

Compiled 6514 to 5245 computations (19.5% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))
0.3b	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
4.1b	(.f64 (.f64 (.f64 (.f64 J -2) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
10.8b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite287.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

33×	`add-exp-log_binary64_798`
25×	`pow1_binary64_821`
23×	`add-cbrt-cube_binary64_796`
16×	`prod-exp_binary64_809`
15×	`*-un-lft-identity_binary64_760`
13×	`pow-prod-down_binary64_831` `cbrt-unprod_binary64_793`
12×	`add-sqr-sqrt_binary64_782`
11×	`add-cube-cbrt_binary64_795`
10×	`associate-r_binary64_700`
8×	`sqrt-prod_binary64_776`
7×	`unpow-prod-down_binary64_839`
4×	`add-log-exp_binary64_799` `sqrt-div_binary64_777` `pow-exp_binary64_828`
3×	`times-frac_binary64_766` `pow-unpow_binary64_837` `div-exp_binary64_811`
2×	`flip3-+_binary64_763` `flip-+_binary64_734` `distribute-lft-out_binary64_711` `associate-r/_binary64_702` `associate-l_binary64_701` `-commutative_binary64_691`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `div-inv_binary64_757` `pow-pow_binary64_832` `pow-to-exp_binary64_829` `unpow2_binary64_825` `sqr-pow_binary64_732`

Counts

4 → 89

Calls

4 calls:

20.0ms	(.f64 (.f64 (.f64 (.f64 J -2) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
9.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
6.0ms	(.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))

Compiler

Compiled 3986 to 3242 computations (18.7% saved)

series1.9s (10.3%)

Error

0.0b

Counts

4 → 60

Calls

4 calls:

807.0ms	(.f64 (.f64 (.f64 (.f64 J -2) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
519.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
325.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
124.0ms	(.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))

Compiler

Compiled 5070 to 4343 computations (14.3% saved)

simplify74.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5216	4108

prune326.0ms (1.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	149	7	156

Error

0.0b

Counts

156 → 7

Compiler

Compiled 5065 to 3956 computations (21.9% saved)

regimes1.4s (7.7%)

Accuracy

Total 9.2b remaining (99.8%)

Threshold costs 0b (0%)

Compiler

Compiled 13693 to 12016 computations (12.2% saved)

bsearch5.0ms (0%)

Compiler: Compiled 24 to 22 computations (8.3% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	126
1	42	126

end0.0ms (0%)

sample4.7s (25.5%)

Algorithm

1×

intervals

Results

1.2s	2016×	body	1024	valid
497.0ms	4414×	body	128	valid
420.0ms	1045×	body	512	valid
146.0ms	525×	body	256	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 2331 to 2043 computations (12.4% saved)

Details

analyze1.9s (10.1%)

sample86.0ms (0.5%)

simplify182.0ms (1%)

prune4.0ms (0%)

localize15.0ms (0.1%)

rewrite239.0ms (1.3%)

series1.8s (10.1%)

simplify64.0ms (0.4%)

prune270.0ms (1.5%)

localize22.0ms (0.1%)

rewrite278.0ms (1.5%)

series1.6s (9%)

simplify64.0ms (0.3%)

prune306.0ms (1.7%)

localize23.0ms (0.1%)

rewrite500.0ms (2.7%)

series1.7s (9.2%)

simplify126.0ms (0.7%)

prune442.0ms (2.4%)

localize18.0ms (0.1%)

rewrite287.0ms (1.6%)

series1.9s (10.3%)

simplify74.0ms (0.4%)

prune326.0ms (1.8%)

regimes1.4s (7.7%)

bsearch5.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample4.7s (25.5%)

Profiling