Details

analyze2.2s (19.7%)

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)

sample78.0ms (0.7%)

Algorithm

1×

intervals

Results

32.0ms	51×	body	1024	valid
16.0ms	150×	body	128	valid
12.0ms	31×	body	512	valid
6.0ms	24×	body	256	valid

Compiler

Compiled 49 to 48 computations (2% saved)

simplify93.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (86.0ms)

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

16.7b

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)))
0.2b	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
6.2b	(.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))))
9.4b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite48.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-exp-log_binary64_457`
20×	`pow1_binary64_480`
18×	`add-cbrt-cube_binary64_455`
15×	`*-un-lft-identity_binary64_419`
12×	`prod-exp_binary64_468` `add-sqr-sqrt_binary64_441`
11×	`add-cube-cbrt_binary64_454`
10×	`associate-r_binary64_359`
9×	`pow-prod-down_binary64_490` `cbrt-unprod_binary64_452`
8×	`sqrt-prod_binary64_435`
7×	`unpow-prod-down_binary64_498`
4×	`sqrt-div_binary64_436` `add-log-exp_binary64_458` `pow-exp_binary64_487`
3×	`times-frac_binary64_425` `pow-unpow_binary64_496` `div-exp_binary64_470`
2×	`flip3-+_binary64_422` `distribute-lft-out_binary64_370` `associate-r/_binary64_361` `-commutative_binary64_350` `associate-l_binary64_360` `flip-+_binary64_393`
1×	`pow1/2_binary64_499` `div-inv_binary64_416` `sqr-pow_binary64_391` `pow-to-exp_binary64_488` `pow-pow_binary64_491` `sqrt-pow1_binary64_437` `unpow2_binary64_484` `rem-sqrt-square_binary64_432`

Counts

4 → 86

Calls

4 calls:

17.0ms	(.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	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
5.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

series482.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

177.0ms	(.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))))
155.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
114.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
36.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

simplify66.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5257	2394

prune192.0ms (1.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	88	10	98
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	88	11	99

Error

12.4b

Counts

99 → 11

Compiler

Compiled 3282 to 2647 computations (19.3% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
0.3b	(.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
6.0b	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
9.4b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite55.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-exp-log_binary64_457`
20×	`pow1_binary64_480`
18×	`add-cbrt-cube_binary64_455`
16×	`add-sqr-sqrt_binary64_441`
15×	`*-un-lft-identity_binary64_419`
12×	`prod-exp_binary64_468`
11×	`add-cube-cbrt_binary64_454`
9×	`pow-prod-down_binary64_490` `cbrt-unprod_binary64_452` `sqrt-prod_binary64_435`
8×	`associate-r_binary64_359`
7×	`unpow-prod-down_binary64_498`
6×	`sqrt-div_binary64_436` `associate-*r/_binary64_361`
4×	`add-log-exp_binary64_458` `pow-exp_binary64_487` `associate-l_binary64_360`
3×	`flip3-+_binary64_422` `times-frac_binary64_425` `flip-+_binary64_393` `pow-unpow_binary64_496` `div-exp_binary64_470`
2×	`unswap-sqr_binary64_387` `distribute-lft-out_binary64_370` `*-commutative_binary64_350`
1×	`pow1/2_binary64_499` `div-inv_binary64_416` `sqr-pow_binary64_391` `pow-to-exp_binary64_488` `pow-pow_binary64_491` `sqrt-pow1_binary64_437` `unpow2_binary64_484` `rem-sqrt-square_binary64_432`

Counts

4 → 90

Calls

4 calls:

16.0ms	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
14.0ms	(.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)

series689.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

244.0ms	(.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
175.0ms	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
160.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
110.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)

simplify70.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5251	2895

prune203.0ms (1.8%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	97	5	102
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	97	16	113

Error

12.4b

Counts

113 → 16

Compiler

Compiled 3593 to 2907 computations (19.1% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

6.2b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
6.2b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
9.4b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
9.4b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite50.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`sqrt-prod_binary64_435`
18×	`*-un-lft-identity_binary64_419`
16×	`add-sqr-sqrt_binary64_441`
12×	`sqrt-div_binary64_436`
10×	`add-cube-cbrt_binary64_454` `sqrt-pow1_binary64_437` `pow1_binary64_480`
6×	`pow1/2_binary64_499` `rem-sqrt-square_binary64_432`
4×	`flip3-+_binary64_422` `add-log-exp_binary64_458` `distribute-lft-out_binary64_370` `flip-+_binary64_393` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`

Counts

4 → 76

Calls

4 calls:

12.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
10.0ms	(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)))

series878.0ms (8%)

Counts

4 → 12

Calls

4 calls:

292.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
289.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
150.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
146.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify76.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5157	2368

prune261.0ms (2.4%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	1	12	13
Picked	1	0	1
Done	0	2	2
Total	89	15	104

Error

12.4b

Counts

104 → 15

Compiler

Compiled 4786 to 3934 computations (17.8% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

6.2b	(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))))))
9.4b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
14.8b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
14.8b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite48.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64_419`
8×	`cbrt-prod_binary64_450` `add-sqr-sqrt_binary64_441` `pow1_binary64_480`
7×	`add-cube-cbrt_binary64_454`
6×	`sqrt-div_binary64_436` `cbrt-div_binary64_451`
5×	`sqrt-prod_binary64_435`
4×	`flip3-+_binary64_422` `add-log-exp_binary64_458` `flip-+_binary64_393` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
3×	`distribute-lft-out_binary64_370` `sqrt-pow1_binary64_437`
2×	`pow1/3_binary64_501` `pow1/2_binary64_499` `associate-*r/_binary64_361`
1×	`pow-prod-down_binary64_490` `rem-sqrt-square_binary64_432`

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)))

series1.2s (11%)

Counts

4 → 12

Calls

4 calls:

488.0ms	(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))))))
293.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
286.0ms	(cbrt.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)))

simplify108.0ms (1%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4900	2421
1	4900	2421

prune267.0ms (2.4%)

Pruning

16 alts after pruning (13 fresh and 3 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	0	12	12
Picked	0	1	1
Done	0	2	2
Total	68	16	84

Error

12.4b

Counts

84 → 16

Compiler

Compiled 4751 to 3868 computations (18.6% saved)

regimes488.0ms (4.4%)

Accuracy

Total 0.6b remaining (4.5%)

Threshold costs 0.6b (4.5%)

Compiler

Compiled 6218 to 5526 computations (11.1% saved)

bsearch3.0ms (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	48	163
1	48	163

end0.0ms (0%)

sample3.4s (30.9%)

Algorithm

1×

intervals

Results

1.1s	1956×	body	1024	valid
515.0ms	4543×	body	128	valid
413.0ms	1024×	body	512	valid
118.0ms	475×	body	256	valid
2.0ms	2×	body	2048	valid

Compiler

Compiled 1156 to 1019 computations (11.9% saved)

Details

analyze2.2s (19.7%)

sample78.0ms (0.7%)

simplify93.0ms (0.8%)

prune4.0ms (0%)

localize15.0ms (0.1%)

rewrite48.0ms (0.4%)

series482.0ms (4.4%)

simplify66.0ms (0.6%)

prune192.0ms (1.7%)

localize18.0ms (0.2%)

rewrite55.0ms (0.5%)

series689.0ms (6.2%)

simplify70.0ms (0.6%)

prune203.0ms (1.8%)

localize18.0ms (0.2%)

rewrite50.0ms (0.5%)

series878.0ms (8%)

simplify76.0ms (0.7%)

prune261.0ms (2.4%)

localize26.0ms (0.2%)

rewrite48.0ms (0.4%)

series1.2s (11%)

simplify108.0ms (1%)

prune267.0ms (2.4%)

regimes488.0ms (4.4%)

bsearch3.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.4s (30.9%)

Profiling