Details

analyze582.0ms (3.8%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4942	44
1	4942	44
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
12.5%	37.5%	50%	5
15.6%	31.2%	53.2%	6
17.2%	26.5%	56.3%	7
18%	22.6%	59.4%	8
18.3%	19.9%	61.8%	9
18.5%	17.8%	63.7%	10
18.6%	16.3%	65.1%	11
18.7%	15.2%	66.1%	12
18.7%	14.4%	66.9%	13
18.7%	13.8%	67.4%	14

Compiler

Compiled 17 to 16 computations (5.9% saved)

sample80.0ms (0.5%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
18.0ms	40×	body	1024	nan
13.0ms	97×	body	128	overflowed
6.0ms	21×	body	512	nan
3.0ms	16×	body	256	nan
2.0ms	40×	body	128	nan
0.0ms	5×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify52.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4933	22
1	4933	22

prune6.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.4b

Counts

2 → 2

Compiler

Compiled 44 to 41 computations (6.8% saved)

localize16.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.2b	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
0.2b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
0.3b	(.f64 (.f64 2 PI.f64) n)

rewrite263.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

48×	`times-frac_binary64_766`
42×	`add-sqr-sqrt_binary64_782` `*-un-lft-identity_binary64_760`
33×	`add-cube-cbrt_binary64_795`
26×	`add-exp-log_binary64_798`
22×	`pow-unpow_binary64_837`
18×	`sqrt-prod_binary64_776`
14×	`pow1_binary64_821`
10×	`add-cbrt-cube_binary64_796`
9×	`prod-exp_binary64_809`
8×	`unpow-prod-down_binary64_839` `sqr-pow_binary64_732`
6×	`pow-prod-down_binary64_831` `difference-of-squares_binary64_729` `pow-exp_binary64_828` `associate-/r*_binary64_704`
5×	`div-exp_binary64_811` `associate-/l*_binary64_705`
3×	`add-log-exp_binary64_799` `cbrt-unprod_binary64_793` `associate-r_binary64_700` `distribute-lft-out--_binary64_712` `pow-pow_binary64_832`
2×	`div-inv_binary64_757` `div-sub_binary64_765` `pow-sub_binary64_836` `pow-to-exp_binary64_829`
1×	`associate-l_binary64_701` `*-commutative_binary64_691` `cbrt-undiv_binary64_794` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l/_binary64_707`

Counts

3 → 115

Calls

3 calls:

10.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
7.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
5.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 2465 to 1670 computations (32.3% saved)

series697.0ms (4.6%)

Error

0.2b

Counts

3 → 18

Calls

3 calls:

349.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
280.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
40.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 1015 to 812 computations (20% saved)

simplify96.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4969	3385
1	4969	3385

prune209.0ms (1.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	125	8	133
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	127	8	135

Error

0.0b

Counts

135 → 8

Compiler

Compiled 2248 to 1437 computations (36.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))
0.2b	(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (pow.f64 (.f64 2 (.f64 n PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
0.3b	(*.f64 n PI.f64)
0.3b	(*.f64 n PI.f64)

rewrite691.0ms (4.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

284×	`times-frac_binary64_766`
132×	`add-sqr-sqrt_binary64_782`
128×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
111×	`sqrt-prod_binary64_776`
28×	`unpow-prod-down_binary64_839` `sqr-pow_binary64_732`
27×	`add-exp-log_binary64_798`
24×	`associate-/l*_binary64_705`
14×	`pow1_binary64_821`
13×	`add-cbrt-cube_binary64_796`
11×	`div-exp_binary64_811`
8×	`div-inv_binary64_757`
6×	`associate-l_binary64_701` `associate-r_binary64_700` `associate-/r*_binary64_704`
5×	`pow-prod-down_binary64_831` `prod-exp_binary64_809`
4×	`add-log-exp_binary64_799`
3×	`pow-exp_binary64_828` `cbrt-undiv_binary64_794` `sqrt-pow1_binary64_778`
2×	`cbrt-unprod_binary64_793` `unswap-sqr_binary64_728` `*-commutative_binary64_691`
1×	`pow-to-exp_binary64_829` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l/_binary64_707` `pow1/2_binary64_840`

Counts

4 → 241

Calls

4 calls:

16.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (pow.f64 (.f64 2 (.f64 n PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
6.0ms	(*.f64 n PI.f64)
4.0ms	(*.f64 n PI.f64)
4.0ms	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))

Compiler

Compiled 7609 to 4231 computations (44.4% saved)

series336.0ms (2.2%)

Error

0.0b

Counts

4 → 15

Calls

4 calls:

239.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (pow.f64 (.f64 2 (.f64 n PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
33.0ms	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))
31.0ms	(*.f64 n PI.f64)
29.0ms	(*.f64 n PI.f64)

Compiler

Compiled 823 to 674 computations (18.1% saved)

simplify143.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5004	11439

prune731.0ms (4.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	252	4	256
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	257	7	264

Error

Counts

264 → 7

Compiler

Compiled 5999 to 3674 computations (38.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))
0.2b	(/.f64 (/.f64 (.f64 1 (sqrt.f64 (.f64 2 (.f64 n PI.f64)))) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
0.3b	(*.f64 n PI.f64)
0.3b	(*.f64 n PI.f64)

rewrite404.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

89×	`times-frac_binary64_766`
66×	`add-exp-log_binary64_798`
46×	`add-sqr-sqrt_binary64_782`
42×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
31×	`div-exp_binary64_811` `sqrt-prod_binary64_776`
21×	`prod-exp_binary64_809`
17×	`add-cbrt-cube_binary64_796`
14×	`pow1_binary64_821`
9×	`pow-exp_binary64_828` `associate-/l*_binary64_705`
8×	`div-inv_binary64_757`
7×	`unpow-prod-down_binary64_839` `sqr-pow_binary64_732`
6×	`associate-l_binary64_701` `associate-r_binary64_700` `associate-/r*_binary64_704`
5×	`pow-prod-down_binary64_831` `1-exp_binary64_804` `cbrt-undiv_binary64_794`
4×	`add-log-exp_binary64_799`
3×	`cbrt-unprod_binary64_793` `pow-to-exp_binary64_829` `sqrt-pow1_binary64_778`
2×	`unswap-sqr_binary64_728` `*-commutative_binary64_691`
1×	`frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l/_binary64_707` `pow1/2_binary64_840`

Counts

4 → 147

Calls

4 calls:

14.0ms	(/.f64 (/.f64 (.f64 1 (sqrt.f64 (.f64 2 (.f64 n PI.f64)))) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
4.0ms	(*.f64 n PI.f64)
4.0ms	(*.f64 n PI.f64)
4.0ms	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))

Compiler

Compiled 4200 to 2408 computations (42.7% saved)

series338.0ms (2.2%)

Error

Counts

4 → 15

Calls

4 calls:

238.0ms	(/.f64 (/.f64 (.f64 1 (sqrt.f64 (.f64 2 (.f64 n PI.f64)))) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
35.0ms	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))
32.0ms	(*.f64 n PI.f64)
30.0ms	(*.f64 n PI.f64)

Compiler

Compiled 861 to 712 computations (17.3% saved)

simplify107.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4988	5195
1	4988	5195

prune261.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	161	1	162
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	162	7	169

Error

Counts

169 → 7

Compiler

Compiled 2936 to 1815 computations (38.2% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n PI.f64)))
0.3b	(*.f64 n PI.f64)
0.3b	(*.f64 n PI.f64)
0.3b	(.f64 n (.f64 PI.f64 2))

rewrite334.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

30×	`add-sqr-sqrt_binary64_782`
26×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
24×	`times-frac_binary64_766`
22×	`sqrt-prod_binary64_776`
15×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
13×	`pow1_binary64_821`
9×	`associate-l_binary64_701`
7×	`associate-r_binary64_700`
6×	`associate-/l*_binary64_705`
5×	`pow-prod-down_binary64_831` `prod-exp_binary64_809` `cbrt-unprod_binary64_793`
4×	`add-log-exp_binary64_799` `associate-/r*_binary64_704`
3×	`*-commutative_binary64_691`
2×	`unswap-sqr_binary64_728`
1×	`div-exp_binary64_811` `cbrt-undiv_binary64_794` `sqrt-undiv_binary64_781` `frac-2neg_binary64_771` `clear-num_binary64_759` `div-inv_binary64_757`

Counts

4 → 101

Calls

4 calls:

6.0ms	(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n PI.f64)))
5.0ms	(.f64 n (.f64 PI.f64 2))
4.0ms	(*.f64 n PI.f64)
4.0ms	(*.f64 n PI.f64)

Compiler

Compiled 3410 to 1860 computations (45.5% saved)

series207.0ms (1.4%)

Error

Counts

4 → 15

Calls

4 calls:

82.0ms	(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n PI.f64)))
45.0ms	(.f64 n (.f64 PI.f64 2))
36.0ms	(*.f64 n PI.f64)
36.0ms	(*.f64 n PI.f64)

Compiler

Compiled 1100 to 849 computations (22.8% saved)

simplify93.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5057	1557

prune244.0ms (1.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	116	7	123

Error

Counts

123 → 7

Compiler

Compiled 2790 to 1522 computations (45.4% saved)

regimes6.6s (43.8%)

Accuracy

Total 0.4b remaining (94.1%)

Threshold costs 0.4b (94.1%)

Compiler

Compiled 72309 to 56100 computations (22.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	31
1	19	31

end2.0ms (0%)

Compiler: Compiled 19 to 15 computations (21.1% saved)

sample2.6s (17.1%)

Algorithm

1×

intervals

Results

638.0ms	1339×	body	1024	nan
610.0ms	8000×	body	128	valid
334.0ms	2377×	body	128	overflowed
199.0ms	642×	body	512	nan
63.0ms	342×	body	256	nan
61.0ms	973×	body	128	nan
23.0ms	253×	body	128	invalid

Compiler

Compiled 205 to 179 computations (12.7% saved)

Details

analyze582.0ms (3.8%)

sample80.0ms (0.5%)

simplify52.0ms (0.3%)

prune6.0ms (0%)

localize16.0ms (0.1%)

rewrite263.0ms (1.7%)

series697.0ms (4.6%)

simplify96.0ms (0.6%)

prune209.0ms (1.4%)

localize11.0ms (0.1%)

rewrite691.0ms (4.6%)

series336.0ms (2.2%)

simplify143.0ms (0.9%)

prune731.0ms (4.8%)

localize13.0ms (0.1%)

rewrite404.0ms (2.7%)

series338.0ms (2.2%)

simplify107.0ms (0.7%)

prune261.0ms (1.7%)

localize23.0ms (0.2%)

rewrite334.0ms (2.2%)

series207.0ms (1.4%)

simplify93.0ms (0.6%)

prune244.0ms (1.6%)

regimes6.6s (43.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end2.0ms (0%)

sample2.6s (17.1%)

Profiling