Details

analyze1.8s (21.7%)

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)

sample104.0ms (1.2%)

Algorithm

1×

intervals

Results

41.0ms	50×	body	1280	valid
27.0ms	49×	body	640	valid
14.0ms	126×	body	80	valid
7.0ms	19×	body	320	valid
3.0ms	12×	body	160	valid
0.0ms	1×	body	80	invalid

Compiler

Compiled 49 to 48 computations (2% saved)

simplify120.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (107.0ms)

Iter	Nodes	Cost
0	4872	37
1	4872	37

prune5.0ms (0.1%)

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: 16.7b

Counts

2 → 1

Compiler

Compiled 48 to 44 computations (8.3% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.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)
7.5b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.0b	(.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))))

rewrite40.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-exp-log_binary64`
20×	`pow1_binary64`
18×	`add-cbrt-cube_binary64`
15×	`*-un-lft-identity_binary64`
12×	`prod-exp_binary64` `add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
10×	`associate-r_binary64`
9×	`pow-prod-down_binary64` `cbrt-unprod_binary64`
8×	`sqrt-prod_binary64`
7×	`unpow-prod-down_binary64`
4×	`add-log-exp_binary64` `pow-exp_binary64` `sqrt-div_binary64`
3×	`pow-unpow_binary64` `times-frac_binary64` `div-exp_binary64`
2×	`flip3-+_binary64` `distribute-lft-out_binary64` `associate-r/_binary64` `associate-l_binary64` `flip-+_binary64` `-commutative_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64`

Counts

4 → 86

Calls

4 calls:

15.0ms	(.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))))
8.0ms	(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)))

series117.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

47.0ms	(.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))))
37.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
25.0ms	(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)))

simplify103.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5168	2394

prune158.0ms (1.9%)

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: 12.0b

Counts

99 → 9

Compiler

Compiled 3230 to 2599 computations (19.5% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))
0.3b	(pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)
7.5b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)))
8.1b	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2)))))

rewrite39.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-exp-log_binary64`
23×	`pow1_binary64`
21×	`add-cbrt-cube_binary64`
14×	`prod-exp_binary64`
11×	`pow-prod-down_binary64` `*-un-lft-identity_binary64` `cbrt-unprod_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
7×	`unpow-prod-down_binary64`
4×	`add-log-exp_binary64` `associate-r/_binary64` `associate-l*_binary64` `sqrt-prod_binary64` `pow-exp_binary64` `sqrt-div_binary64`
3×	`pow-unpow_binary64` `times-frac_binary64` `div-exp_binary64`
2×	`flip3-+_binary64` `associate-r_binary64` `flip-+_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `distribute-lft-out_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64`

Counts

4 → 83

Calls

4 calls:

15.0ms	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2)))))
8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)))
8.0ms	(pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)
6.0ms	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))

series119.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

47.0ms	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2)))))
35.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)))
26.0ms	(pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)
11.0ms	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))

simplify72.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5037	2337

prune143.0ms (1.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	93	11	104

Merged error: 12.0b

Counts

104 → 11

Compiler

Compiled 3120 to 2502 computations (19.8% saved)

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.2b	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
2.3b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2)))))
13.5b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)))
13.5b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite36.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
14×	`pow1_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `cbrt-prod_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
7×	`sqrt-prod_binary64`
6×	`cbrt-div_binary64` `pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64`
3×	`flip3-+_binary64` `distribute-lft-out_binary64` `associate-r_binary64` `pow1/3_binary64` `flip-+_binary64`
2×	`sqrt-pow1_binary64` `rem-sqrt-square_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate-l_binary64` `*-commutative_binary64`

Counts

4 → 70

Calls

4 calls:

11.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
8.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)))
7.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2)))))

series260.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

77.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)))
71.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
69.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
42.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2)))))

simplify117.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	5143	2723

prune189.0ms (2.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	1	7	8
Picked	1	0	1
Done	0	2	2
Total	82	11	93

Merged error: 12.0b

Counts

93 → 11

Compiler

Compiled 4460 to 3635 computations (18.5% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.3b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2)))))
7.5b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.3b	(cbrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
13.5b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)))

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
14×	`pow1_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`cbrt-prod_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
8×	`sqrt-prod_binary64`
6×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`cbrt-div_binary64` `add-log-exp_binary64` `sqrt-div_binary64`
3×	`flip3-+_binary64` `distribute-lft-out_binary64` `associate-r_binary64` `flip-+_binary64`
2×	`pow1/3_binary64`
1×	`pow1/2_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `*-commutative_binary64`

Counts

4 → 68

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))))
8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)))
7.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2)))))

series230.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

78.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))) 2)))
70.0ms	(cbrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
42.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))) 2)))))
39.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify96.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4936	2731
1	4936	2731

prune175.0ms (2.1%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	80	11	91

Merged error: 12.0b

Counts

91 → 11

Compiler

Compiled 4104 to 3351 computations (18.3% saved)

regimes372.0ms (4.4%)

Compiler: Compiled 2504 to 2220 computations (11.3% saved)

bsearch1.0ms (0%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	179
1	48	179

end0.0ms (0%)

sample4.0s (47.5%)

Algorithm

1×

intervals

Results

1.3s	1486×	body	1280	valid
732.0ms	1284×	body	640	valid
491.0ms	4310×	body	80	valid
249.0ms	622×	body	320	valid
78.0ms	298×	body	160	valid
1.0ms	1×	body	640	invalid
0.0ms	2×	body	80	invalid

Compiler

Compiled 547 to 476 computations (13% saved)

Details

analyze1.8s (21.7%)

sample104.0ms (1.2%)

simplify120.0ms (1.4%)

prune5.0ms (0.1%)

localize16.0ms (0.2%)

rewrite40.0ms (0.5%)

series117.0ms (1.4%)

simplify103.0ms (1.2%)

prune158.0ms (1.9%)

localize15.0ms (0.2%)

rewrite39.0ms (0.5%)

series119.0ms (1.4%)

simplify72.0ms (0.8%)

prune143.0ms (1.7%)

localize26.0ms (0.3%)

rewrite36.0ms (0.4%)

series260.0ms (3.1%)

simplify117.0ms (1.4%)

prune189.0ms (2.2%)

localize29.0ms (0.3%)

rewrite34.0ms (0.4%)

series230.0ms (2.7%)

simplify96.0ms (1.1%)

prune175.0ms (2.1%)

regimes372.0ms (4.4%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample4.0s (47.5%)

Profiling