Details

analyze2.0s (16.2%)

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)

sample89.0ms (0.7%)

Algorithm

1×

intervals

Results

43.0ms	64×	body	1024	valid
17.0ms	143×	body	128	valid
15.0ms	34×	body	512	valid
4.0ms	15×	body	256	valid

Compiler

Compiled 49 to 48 computations (2% saved)

simplify248.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4871	37
1	4871	37

prune3.0ms (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

Merged error: 20.4b

Counts

2 → 1

Compiler

Compiled 48 to 44 computations (8.3% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.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)
8.5b	(.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))))
10.6b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite51.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-exp-log_binary64_1123`
20×	`pow1_binary64_1146`
18×	`add-cbrt-cube_binary64_1121`
15×	`*-un-lft-identity_binary64_1088`
12×	`add-sqr-sqrt_binary64_1109` `prod-exp_binary64_1134`
11×	`add-cube-cbrt_binary64_1120`
10×	`associate-r_binary64_1030`
9×	`cbrt-unprod_binary64_1118` `pow-prod-down_binary64_1156`
8×	`sqrt-prod_binary64_1103`
7×	`unpow-prod-down_binary64_1164`
4×	`pow-exp_binary64_1153` `sqrt-div_binary64_1104` `add-log-exp_binary64_1124`
3×	`times-frac_binary64_1094` `div-exp_binary64_1136` `pow-unpow_binary64_1162`
2×	`-commutative_binary64_1021` `associate-l_binary64_1031` `flip-+_binary64_1062` `flip3-+_binary64_1091` `distribute-lft-out_binary64_1041` `associate-r/_binary64_1032`
1×	`rem-sqrt-square_binary64_1101` `sqr-pow_binary64_1060` `pow-pow_binary64_1157` `pow-to-exp_binary64_1154` `unpow2_binary64_1150` `sqrt-pow1_binary64_1105` `div-inv_binary64_1085` `pow1/2_binary64_1165`

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

series854.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

318.0ms	(.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))))
270.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
199.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
66.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

simplify58.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5201	2385

prune193.0ms (1.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	90	8	98
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	90	9	99

Merged error: 15.1b

Counts

99 → 9

Compiler

Compiled 3185 to 2566 computations (19.4% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

8.5b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
8.5b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
10.6b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
10.6b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite47.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`sqrt-prod_binary64_1103`
18×	`*-un-lft-identity_binary64_1088`
16×	`add-sqr-sqrt_binary64_1109`
12×	`sqrt-div_binary64_1104`
10×	`pow1_binary64_1146` `sqrt-pow1_binary64_1105` `add-cube-cbrt_binary64_1120`
6×	`rem-sqrt-square_binary64_1101` `pow1/2_binary64_1165`
4×	`add-cbrt-cube_binary64_1121` `add-exp-log_binary64_1123` `flip-+_binary64_1062` `add-log-exp_binary64_1124` `flip3-+_binary64_1091` `distribute-lft-out_binary64_1041`

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))))
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)))

series1.5s (12.2%)

Counts

4 → 12

Calls

4 calls:

497.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
490.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
278.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
261.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify66.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4952	2368
1	4952	2368

prune266.0ms (2.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	88	9	97

Merged error: 15.1b

Counts

97 → 9

Compiler

Compiled 4623 to 3788 computations (18.1% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

8.5b	(sqrt.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) (sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))))
10.6b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
17.4b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
17.4b	(cbrt.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

13×	`*-un-lft-identity_binary64_1088`
8×	`add-sqr-sqrt_binary64_1109` `cbrt-prod_binary64_1116` `pow1_binary64_1146`
7×	`add-cube-cbrt_binary64_1120`
6×	`cbrt-div_binary64_1117` `sqrt-div_binary64_1104`
5×	`sqrt-prod_binary64_1103`
4×	`add-cbrt-cube_binary64_1121` `add-exp-log_binary64_1123` `flip-+_binary64_1062` `add-log-exp_binary64_1124` `flip3-+_binary64_1091`
3×	`distribute-lft-out_binary64_1041` `sqrt-pow1_binary64_1105`
2×	`pow1/3_binary64_1167` `associate-*r/_binary64_1032` `pow1/2_binary64_1165`
1×	`rem-sqrt-square_binary64_1101` `pow-prod-down_binary64_1156`

Counts

4 → 57

Calls

4 calls:

12.0ms	(sqrt.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) (sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))))
9.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
9.0ms	(cbrt.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)))

series2.1s (17%)

Counts

4 → 12

Calls

4 calls:

823.0ms	(sqrt.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) (sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))))
524.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
515.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
262.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify83.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4910	2421
1	4910	2421

prune285.0ms (2.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	69	9	78

Merged error: 15.1b

Counts

78 → 9

Compiler

Compiled 4988 to 4078 computations (18.2% saved)

localize21.0ms (0.2%)

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)))
8.5b	(.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))))
10.6b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite51.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64_1146`
29×	`add-exp-log_binary64_1123`
20×	`add-cbrt-cube_binary64_1121`
19×	`cbrt-unprod_binary64_1118` `pow-prod-down_binary64_1156` `prod-exp_binary64_1134`
13×	`*-un-lft-identity_binary64_1088`
10×	`add-sqr-sqrt_binary64_1109`
9×	`add-cube-cbrt_binary64_1120`
8×	`sqrt-prod_binary64_1103`
7×	`associate-r_binary64_1030`
6×	`cbrt-prod_binary64_1116`
4×	`sqrt-div_binary64_1104` `add-log-exp_binary64_1124`
2×	`flip-+_binary64_1062` `pow1/3_binary64_1167` `flip3-+_binary64_1091` `distribute-lft-out_binary64_1041` `associate-*r/_binary64_1032`
1×	`-commutative_binary64_1021` `rem-sqrt-square_binary64_1101` `associate-l*_binary64_1031` `sqrt-pow1_binary64_1105` `pow1/2_binary64_1165`

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))))
11.0ms	(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)))

series841.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

324.0ms	(.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))))
271.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
131.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
115.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

simplify57.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4927	2205
1	4927	2205

prune184.0ms (1.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	0	6	6
Picked	1	0	1
Done	0	2	2
Total	85	10	95

Merged error: 15.1b

Counts

95 → 10

Compiler

Compiled 3214 to 2616 computations (18.6% saved)

regimes205.0ms (1.6%)

Compiler: Compiled 2216 to 1992 computations (10.1% 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%)

sample3.1s (24.9%)

Algorithm

1×

intervals

Results

1.3s	1992×	body	1024	valid
541.0ms	4476×	body	128	valid
439.0ms	1022×	body	512	valid
146.0ms	509×	body	256	valid
1.0ms	1×	body	2048	valid
0.0ms	1×	body	512	invalid
0.0ms	2×	body	128	invalid

Compiler

Compiled 481 to 425 computations (11.6% saved)

Details

analyze2.0s (16.2%)

sample89.0ms (0.7%)

simplify248.0ms (2%)

prune3.0ms (0%)

localize16.0ms (0.1%)

rewrite51.0ms (0.4%)

series854.0ms (6.8%)

simplify58.0ms (0.5%)

prune193.0ms (1.5%)

localize19.0ms (0.1%)

rewrite47.0ms (0.4%)

series1.5s (12.2%)

simplify66.0ms (0.5%)

prune266.0ms (2.1%)

localize29.0ms (0.2%)

rewrite49.0ms (0.4%)

series2.1s (17%)

simplify83.0ms (0.7%)

prune285.0ms (2.3%)

localize21.0ms (0.2%)

rewrite51.0ms (0.4%)

series841.0ms (6.7%)

simplify57.0ms (0.5%)

prune184.0ms (1.5%)

regimes205.0ms (1.6%)

bsearch2.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.1s (24.9%)

Profiling