Details

analyze961.0ms (5.1%)

Algorithm

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

Compiler

Compiled 34 to 32 computations (5.9% saved)

sample3.5s (18.4%)

Algorithm

2×

intervals

Results

151.0ms	1755×	body	128	nan
45.0ms	97×	body	1024	nan
38.0ms	512×	body	128	valid
24.0ms	165×	body	128	overflowed
14.0ms	147×	body	128	invalid
13.0ms	39×	body	512	nan
4.0ms	21×	body	256	nan

Compiler

Compiled 24819 to 26277 computations (-5.9% saved)

simplify49.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4933	22
1	4933	22

prune5.0ms (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

0.3b

Counts

2 → 2

Compiler

Compiled 44 to 41 computations (6.8% saved)

localize10.0ms (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)

rewrite232.0ms (1.2%)

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 2834 to 1916 computations (32.4% saved)

series635.0ms (3.4%)

Error

0.1b

Counts

3 → 18

Calls

3 calls:

306.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
263.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
42.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 1100 to 864 computations (21.5% saved)

simplify89.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4969	3385
1	4969	3385

prune204.0ms (1.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	126	7	133
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	128	7	135

Error

0.0b

Counts

135 → 7

Compiler

Compiled 3021 to 1891 computations (37.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(pow.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (-.f64 1 k))
0.2b	(.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n PI.f64))) (-.f64 1 k)) (sqrt.f64 (/.f64 1 k)))
0.3b	(*.f64 n PI.f64)
0.4b	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))

rewrite206.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

48×	`add-sqr-sqrt_binary64_782`
26×	`*-un-lft-identity_binary64_760`
25×	`sqrt-prod_binary64_776`
20×	`add-cube-cbrt_binary64_795`
19×	`pow1_binary64_821` `associate-r_binary64_700`
15×	`associate-l_binary64_701` `times-frac_binary64_766`
13×	`unswap-sqr_binary64_728`
12×	`add-exp-log_binary64_798` `unpow-prod-down_binary64_839`
8×	`add-cbrt-cube_binary64_796` `unpow-prod-up_binary64_838`
7×	`pow-prod-down_binary64_831`
6×	`sqrt-pow1_binary64_778` `sqr-pow_binary64_732` `cancel-sign-sub-inv_binary64_726` `pow-unpow_binary64_837`
5×	`pow-pow_binary64_832`
4×	`add-log-exp_binary64_799` `prod-exp_binary64_809`
3×	`pow-sub_binary64_836`
2×	`pow1/2_binary64_840` `cbrt-unprod_binary64_793` `*-commutative_binary64_691` `pow-to-exp_binary64_829` `pow-exp_binary64_828` `sqrt-div_binary64_777` `sub-neg_binary64_753` `difference-of-squares_binary64_729`
1×	`frac-times_binary64_770` `associate-l/_binary64_703` `associate-r/_binary64_702` `div-inv_binary64_757` `distribute-lft-out--_binary64_712` `sqrt-pow2_binary64_779`

Counts

4 → 116

Calls

4 calls:

14.0ms	(.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n PI.f64))) (-.f64 1 k)) (sqrt.f64 (/.f64 1 k)))
8.0ms	(pow.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (-.f64 1 k))
4.0ms	(*.f64 n PI.f64)
4.0ms	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))

Compiler

Compiled 2800 to 1904 computations (32% saved)

series453.0ms (2.4%)

Error

0.0b

Counts

4 → 21

Calls

4 calls:

182.0ms	(pow.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (-.f64 1 k))
178.0ms	(.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n PI.f64))) (-.f64 1 k)) (sqrt.f64 (/.f64 1 k)))
34.0ms	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))
32.0ms	(*.f64 n PI.f64)

Compiler

Compiled 1589 to 1224 computations (23% saved)

simplify94.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4929	3096
1	4929	3096

prune196.0ms (1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	135	2	137
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	138	6	144

Error

Counts

144 → 6

Compiler

Compiled 3171 to 2143 computations (32.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (-.f64 1 k)))
0.2b	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (-.f64 1 k))))
0.3b	(*.f64 n PI.f64)
0.4b	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))

rewrite1.2s (6.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

591×	`times-frac_binary64_766`
305×	`add-sqr-sqrt_binary64_782`
303×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
215×	`sqrt-prod_binary64_776`
124×	`unpow-prod-down_binary64_839` `unpow-prod-up_binary64_838`
93×	`cancel-sign-sub-inv_binary64_726`
89×	`associate-/r*_binary64_704`
33×	`add-exp-log_binary64_798`
31×	`sub-neg_binary64_753` `sqr-pow_binary64_732`
20×	`div-exp_binary64_811`
13×	`pow1_binary64_821` `add-cbrt-cube_binary64_796`
9×	`associate-/l*_binary64_705`
6×	`div-inv_binary64_757` `associate-/r/_binary64_706`
5×	`pow-sub_binary64_836`
4×	`add-log-exp_binary64_799` `pow-prod-down_binary64_831` `pow-to-exp_binary64_829` `1-exp_binary64_804` `pow-exp_binary64_828` `rec-exp_binary64_810` `cbrt-undiv_binary64_794`
3×	`sqrt-pow1_binary64_778` `associate-l_binary64_701` `associate-r_binary64_700`
2×	`frac-2neg_binary64_771` `clear-num_binary64_759`
1×	`pow1/2_binary64_840` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `unswap-sqr_binary64_728` `*-commutative_binary64_691` `inv-pow_binary64_845` `pow-flip_binary64_834`

Counts

4 → 473

Calls

4 calls:

23.0ms	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (-.f64 1 k))))
8.0ms	(/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (-.f64 1 k)))
4.0ms	(*.f64 n PI.f64)
4.0ms	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))

Compiler

Compiled 15265 to 9060 computations (40.6% saved)

series477.0ms (2.5%)

Error

Counts

4 → 18

Calls

4 calls:

213.0ms	(/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (-.f64 1 k)))
183.0ms	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (-.f64 1 k))))
33.0ms	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))
31.0ms	(*.f64 n PI.f64)

Compiler

Compiled 1331 to 1050 computations (21.1% saved)

simplify213.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

491 → 491

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4949	17685
1	4949	17685

prune1.0s (5.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	491	0	491
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	491	6	497

Error

Counts

497 → 6

Compiler

Compiled 13376 to 7563 computations (43.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 n PI.f64)
0.3b	(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (.f64 2 (*.f64 n PI.f64))))
0.4b	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))
0.4b	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))

rewrite158.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

29×	`pow1_binary64_821`
26×	`add-sqr-sqrt_binary64_782`
19×	`sqrt-prod_binary64_776` `associate-l_binary64_701`
16×	`*-un-lft-identity_binary64_760`
15×	`add-cube-cbrt_binary64_795` `pow-prod-down_binary64_831`
12×	`sqrt-pow1_binary64_778`
11×	`times-frac_binary64_766`
8×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
7×	`associate-r_binary64_700`
5×	`unswap-sqr_binary64_728`
4×	`pow1/2_binary64_840` `add-log-exp_binary64_799`
2×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793` `*-commutative_binary64_691`
1×	`sqrt-unprod_binary64_780` `sqrt-div_binary64_777` `associate-*l/_binary64_703` `div-inv_binary64_757`

Counts

4 → 83

Calls

4 calls:

13.0ms	(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (.f64 2 (*.f64 n PI.f64))))
4.0ms	(*.f64 n PI.f64)
4.0ms	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))
4.0ms	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))

Compiler

Compiled 2201 to 1388 computations (36.9% saved)

series223.0ms (1.2%)

Error

Counts

4 → 15

Calls

4 calls:

102.0ms	(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (.f64 2 (*.f64 n PI.f64))))
36.0ms	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))
35.0ms	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))
34.0ms	(*.f64 n PI.f64)

Compiler

Compiled 1044 to 805 computations (22.9% saved)

simplify69.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5186	1383

prune136.0ms (0.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	98	6	104

Error

Counts

104 → 6

Compiler

Compiled 2373 to 1477 computations (37.8% saved)

regimes934.0ms (5%)

Accuracy

Total 0.4b remaining (99.7%)

Threshold costs 0.4b (99.7%)

Compiler

Compiled 10769 to 8854 computations (17.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	21
1	25	21

end0.0ms (0%)

sample7.7s (40.8%)

Algorithm

1×

intervals

Results

2.1s	27534×	body	128	nan
628.0ms	1357×	body	1024	nan
622.0ms	8000×	body	128	valid
356.0ms	2451×	body	128	overflowed
239.0ms	2717×	body	128	invalid
221.0ms	713×	body	512	nan
61.0ms	325×	body	256	nan

Compiler

Compiled 2480 to 2040 computations (17.7% saved)

Details

analyze961.0ms (5.1%)

sample3.5s (18.4%)

simplify49.0ms (0.3%)

prune5.0ms (0%)

localize10.0ms (0.1%)

rewrite232.0ms (1.2%)

series635.0ms (3.4%)

simplify89.0ms (0.5%)

prune204.0ms (1.1%)

localize10.0ms (0.1%)

rewrite206.0ms (1.1%)

series453.0ms (2.4%)

simplify94.0ms (0.5%)

prune196.0ms (1%)

localize10.0ms (0.1%)

rewrite1.2s (6.6%)

series477.0ms (2.5%)

simplify213.0ms (1.1%)

prune1.0s (5.5%)

localize11.0ms (0.1%)

rewrite158.0ms (0.8%)

series223.0ms (1.2%)

simplify69.0ms (0.4%)

prune136.0ms (0.7%)

regimes934.0ms (5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample7.7s (40.8%)

Profiling