Details

analyze2.1s (19.3%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5366	148
0	3	3
1	3	3

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)

sample94.0ms (0.9%)

Algorithm

1×

intervals

Results

48.0ms	74×	body	1024	valid
16.0ms	135×	body	128	valid
13.0ms	31×	body	512	valid
4.0ms	15×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 49 to 48 computations (2% saved)

simplify92.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (87.0ms)

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

17.7b

Counts

2 → 1

Compiler

Compiled 48 to 44 computations (8.3% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2))))
0.2b	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
7.4b	(.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))))
9.2b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite49.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-exp-log_binary64_1139`
22×	`add-cbrt-cube_binary64_1137`
16×	`*-un-lft-identity_binary64_1101`
15×	`pow1_binary64_1162`
13×	`add-sqr-sqrt_binary64_1123`
12×	`prod-exp_binary64_1150` `add-cube-cbrt_binary64_1136`
9×	`cbrt-unprod_binary64_1134`
8×	`sqrt-prod_binary64_1117`
7×	`unpow-prod-down_binary64_1180` `associate-r_binary64_1041`
6×	`times-frac_binary64_1107` `pow-prod-down_binary64_1172` `div-exp_binary64_1152`
4×	`pow-exp_binary64_1169` `add-log-exp_binary64_1140` `sqrt-div_binary64_1118`
3×	`pow-unpow_binary64_1178` `associate-/l*_binary64_1046` `cbrt-undiv_binary64_1135`
2×	`distribute-lft-out_binary64_1052` `flip3-+_binary64_1104` `associate-*r/_binary64_1043` `div-inv_binary64_1098` `flip-+_binary64_1075`
1×	`-commutative_binary64_1032` `rem-sqrt-square_binary64_1114` `pow-pow_binary64_1173` `frac-2neg_binary64_1112` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `associate-l_binary64_1042` `sqr-pow_binary64_1073` `pow-to-exp_binary64_1170` `associate-/r_binary64_1045` `unpow2_binary64_1166` `pow1/2_binary64_1181`

Counts

4 → 91

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))))
9.0ms	(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)
7.0ms	(/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2))))

series492.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

166.0ms	(.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))))
144.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
107.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
73.0ms	(/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2))))

simplify69.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4989	2554
1	4989	2554

prune392.0ms (3.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	97	6	103
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	97	7	104

Error

13.4b

Counts

104 → 7

Compiler

Compiled 3270 to 2604 computations (20.4% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.4b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
7.4b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
9.2b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
9.2b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite45.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`sqrt-prod_binary64_1117`
18×	`*-un-lft-identity_binary64_1101`
16×	`add-sqr-sqrt_binary64_1123`
12×	`sqrt-div_binary64_1118`
10×	`pow1_binary64_1162` `sqrt-pow1_binary64_1119` `add-cube-cbrt_binary64_1136`
6×	`rem-sqrt-square_binary64_1114` `pow1/2_binary64_1181`
4×	`add-log-exp_binary64_1140` `distribute-lft-out_binary64_1052` `add-exp-log_binary64_1139` `flip3-+_binary64_1104` `add-cbrt-cube_binary64_1137` `flip-+_binary64_1075`

Counts

4 → 76

Calls

4 calls:

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

series878.0ms (8%)

Counts

4 → 12

Calls

4 calls:

288.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
284.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
157.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
148.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify69.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5157	2368

prune269.0ms (2.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	87	8	95

Error

13.4b

Counts

95 → 8

Compiler

Compiled 4569 to 3739 computations (18.2% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.6b	(cbrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
9.2b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
9.2b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
9.2b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite49.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64_1101`
16×	`sqrt-prod_binary64_1117`
12×	`add-sqr-sqrt_binary64_1123`
9×	`add-cube-cbrt_binary64_1136`
8×	`sqrt-div_binary64_1118`
7×	`pow1_binary64_1162` `cbrt-prod_binary64_1132`
4×	`add-log-exp_binary64_1140` `distribute-lft-out_binary64_1052` `add-exp-log_binary64_1139` `flip3-+_binary64_1104` `add-cbrt-cube_binary64_1137` `flip-+_binary64_1075`
3×	`rem-sqrt-square_binary64_1114` `sqrt-pow1_binary64_1119` `pow1/2_binary64_1181`
2×	`cbrt-div_binary64_1133`
1×	`pow1/3_binary64_1183`

Counts

4 → 65

Calls

4 calls:

9.0ms	(cbrt.f64 (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)))
9.0ms	(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)))

series735.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

291.0ms	(cbrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
151.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
148.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
145.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify68.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5106	2083

prune333.0ms (3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	77	8	85

Error

13.4b

Counts

85 → 8

Compiler

Compiled 5392 to 4444 computations (17.6% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.4b	(.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2)))
9.2b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
9.2b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
9.2b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite62.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64_1101`
16×	`pow1_binary64_1162` `sqrt-prod_binary64_1117`
13×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
12×	`add-sqr-sqrt_binary64_1123`
9×	`add-cube-cbrt_binary64_1136`
8×	`sqrt-div_binary64_1118`
7×	`associate-l_binary64_1042`
6×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `pow-prod-down_binary64_1172`
4×	`add-log-exp_binary64_1140` `distribute-lft-out_binary64_1052` `flip3-+_binary64_1104` `flip-+_binary64_1075`
3×	`rem-sqrt-square_binary64_1114` `sqrt-pow1_binary64_1119` `pow1/2_binary64_1181`
2×	`associate-*l/_binary64_1044`
1×	`-commutative_binary64_1032` `associate-r*_binary64_1041`

Counts

4 → 75

Calls

4 calls:

18.0ms	(.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2)))
11.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
10.0ms	(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)))

series619.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

197.0ms	(.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))) (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2)))
147.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
140.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
135.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify50.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5028	2542

prune466.0ms (4.2%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	85	10	95

Error

13.4b

Counts

95 → 10

Compiler

Compiled 7313 to 5910 computations (19.2% saved)

regimes458.0ms (4.2%)

Accuracy

Total 0.7b remaining (5.2%)

Threshold costs 0.7b (5.2%)

Compiler

Compiled 5864 to 5107 computations (12.9% saved)

bsearch2.0ms (0%)

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

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	46	152
1	46	152

end0.0ms (0%)

sample3.5s (31.7%)

Algorithm

1×

intervals

Results

1.2s	2025×	body	1024	valid
543.0ms	4463×	body	128	valid
422.0ms	971×	body	512	valid
148.0ms	536×	body	256	valid
4.0ms	5×	body	2048	valid
1.0ms	6×	body	128	invalid
1.0ms	1×	body	1024	invalid
0.0ms	1×	body	256	invalid

Compiler

Compiled 967 to 838 computations (13.3% saved)

Details

analyze2.1s (19.3%)

sample94.0ms (0.9%)

simplify92.0ms (0.8%)

prune4.0ms (0%)

localize17.0ms (0.2%)

rewrite49.0ms (0.4%)

series492.0ms (4.5%)

simplify69.0ms (0.6%)

prune392.0ms (3.6%)

localize23.0ms (0.2%)

rewrite45.0ms (0.4%)

series878.0ms (8%)

simplify69.0ms (0.6%)

prune269.0ms (2.4%)

localize27.0ms (0.2%)

rewrite49.0ms (0.4%)

series735.0ms (6.7%)

simplify68.0ms (0.6%)

prune333.0ms (3%)

localize24.0ms (0.2%)

rewrite62.0ms (0.6%)

series619.0ms (5.6%)

simplify50.0ms (0.5%)

prune466.0ms (4.2%)

regimes458.0ms (4.2%)

bsearch2.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.5s (31.7%)

Profiling