Details

analyze536.0ms (5%)

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)

sample78.0ms (0.7%)

Algorithm

1×

intervals

Results

21.0ms	47×	body	1024	nan
19.0ms	256×	body	128	valid
10.0ms	77×	body	128	overflowed
6.0ms	20×	body	512	nan
2.0ms	38×	body	128	nan
2.0ms	10×	body	256	nan
1.0ms	10×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify53.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4933	22
1	4933	22

prune4.0ms (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)

rewrite217.0ms (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:

11.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
9.0ms	(.f64 (.f64 2 PI.f64) n)
7.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))

Compiler

Compiled 2834 to 1916 computations (32.4% saved)

series422.0ms (4%)

Error

0.2b

Counts

3 → 18

Calls

3 calls:

193.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
176.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
30.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 1100 to 864 computations (21.5% saved)

simplify93.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4969	3385
1	4969	3385

prune182.0ms (1.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	124	9	133
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	126	9	135

Error

0.0b

Counts

135 → 9

Compiler

Compiled 3079 to 1939 computations (37% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(sqrt.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)))

rewrite177.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

53×	`add-sqr-sqrt_binary64_782`
37×	`sqrt-prod_binary64_776`
28×	`*-un-lft-identity_binary64_760`
26×	`times-frac_binary64_766`
24×	`add-cube-cbrt_binary64_795`
19×	`associate-r_binary64_700`
15×	`associate-l_binary64_701`
14×	`pow1_binary64_821`
13×	`unswap-sqr_binary64_728`
11×	`add-exp-log_binary64_798`
8×	`add-cbrt-cube_binary64_796` `unpow-prod-down_binary64_839`
6×	`sqrt-pow1_binary64_778`
5×	`sqr-pow_binary64_732`
4×	`add-log-exp_binary64_799` `pow-prod-down_binary64_831` `prod-exp_binary64_809` `unpow-prod-up_binary64_838`
3×	`sqrt-div_binary64_777` `cancel-sign-sub-inv_binary64_726` `rem-sqrt-square_binary64_773`
2×	`pow1/2_binary64_840` `cbrt-unprod_binary64_793` `*-commutative_binary64_691` `pow-sub_binary64_836` `div-inv_binary64_757`
1×	`pow-to-exp_binary64_829` `pow-exp_binary64_828` `frac-times_binary64_770` `associate-l/_binary64_703` `associate-r/_binary64_702` `sub-neg_binary64_753` `inv-pow_binary64_845` `pow-flip_binary64_834`

Counts

4 → 113

Calls

4 calls:

16.0ms	(.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n PI.f64))) (-.f64 1 k)) (sqrt.f64 (/.f64 1 k)))
4.0ms	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))
4.0ms	(*.f64 n PI.f64)
3.0ms	(sqrt.f64 (/.f64 1 k))

Compiler

Compiled 2685 to 1842 computations (31.4% saved)

series201.0ms (1.9%)

Error

0.0b

Counts

4 → 15

Calls

4 calls:

133.0ms	(.f64 (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n PI.f64))) (-.f64 1 k)) (sqrt.f64 (/.f64 1 k)))
23.0ms	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))
20.0ms	(*.f64 n PI.f64)
13.0ms	(sqrt.f64 (/.f64 1 k))

Compiler

Compiled 958 to 774 computations (19.2% saved)

simplify75.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5060	2458

prune157.0ms (1.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	129	8	137

Error

0.0b

Counts

137 → 8

Compiler

Compiled 2897 to 1984 computations (31.5% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite254.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

72×	`times-frac_binary64_766`
61×	`add-sqr-sqrt_binary64_782`
59×	`*-un-lft-identity_binary64_760`
56×	`add-cube-cbrt_binary64_795`
48×	`sqrt-prod_binary64_776`
32×	`unpow-prod-down_binary64_839` `unpow-prod-up_binary64_838`
24×	`cancel-sign-sub-inv_binary64_726`
19×	`pow1_binary64_821`
12×	`add-exp-log_binary64_798` `associate-/r*_binary64_704`
8×	`add-cbrt-cube_binary64_796` `sub-neg_binary64_753` `sqr-pow_binary64_732`
7×	`pow-prod-down_binary64_831`
6×	`sqrt-pow1_binary64_778` `associate-/l*_binary64_705` `pow-unpow_binary64_837`
5×	`pow-pow_binary64_832`
4×	`add-log-exp_binary64_799`
3×	`associate-l_binary64_701` `associate-r_binary64_700` `div-exp_binary64_811`
2×	`pow1/2_binary64_840` `pow-to-exp_binary64_829` `pow-exp_binary64_828` `pow-sub_binary64_836` `difference-of-squares_binary64_729`
1×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793` `unswap-sqr_binary64_728` `*-commutative_binary64_691` `cbrt-undiv_binary64_794` `frac-2neg_binary64_771` `clear-num_binary64_759` `div-inv_binary64_757` `associate-/r/_binary64_706` `distribute-lft-out--_binary64_712` `sqrt-pow2_binary64_779`

Counts

4 → 166

Calls

4 calls:

10.0ms	(/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (-.f64 1 k)))
9.0ms	(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 4431 to 2589 computations (41.6% saved)

series333.0ms (3.1%)

Error

0.0b

Counts

4 → 21

Calls

4 calls:

141.0ms	(/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (-.f64 1 k)))
124.0ms	(pow.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (-.f64 1 k))
25.0ms	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))
21.0ms	(*.f64 n PI.f64)

Compiler

Compiled 1615 to 1232 computations (23.7% saved)

simplify110.0ms (1%)

Algorithm

1×	egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4975	5206
1	4975	5206

prune229.0ms (2.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	187	0	187
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	187	8	195

Error

0.0b

Counts

195 → 8

Compiler

Compiled 4639 to 2756 computations (40.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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)
0.4b	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))

rewrite485.0ms (4.5%)

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×	`sqrt-pow1_binary64_778` `pow-exp_binary64_828` `cbrt-undiv_binary64_794`
2×	`cbrt-unprod_binary64_793` `unswap-sqr_binary64_728` `*-commutative_binary64_691`
1×	`pow1/2_binary64_840` `pow-to-exp_binary64_829` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l/_binary64_707`

Counts

4 → 241

Calls

4 calls:

18.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (pow.f64 (.f64 2 (.f64 n PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
4.0ms	(*.f64 n PI.f64)
4.0ms	(*.f64 n PI.f64)
4.0ms	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))

Compiler

Compiled 8806 to 4891 computations (44.5% saved)

series228.0ms (2.1%)

Error

0.0b

Counts

4 → 15

Calls

4 calls:

146.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (pow.f64 (.f64 2 (.f64 n PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
26.0ms	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))
22.0ms	(*.f64 n PI.f64)
21.0ms	(*.f64 n PI.f64)

Compiler

Compiled 1094 to 837 computations (23.5% saved)

simplify142.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5004	11439

prune466.0ms (4.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	255	1	256
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	256	8	264

Error

Counts

264 → 8

Compiler

Compiled 8549 to 5236 computations (38.8% saved)

regimes1.0s (9.7%)

Accuracy

Total 0.5b remaining (99.8%)

Threshold costs 0.5b (99.8%)

Compiler

Compiled 13787 to 11134 computations (19.2% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	22
1	27	22

end0.0ms (0%)

sample5.1s (48.2%)

Algorithm

1×

intervals

Results

634.0ms	8000×	body	128	valid
589.0ms	1271×	body	1024	nan
317.0ms	2228×	body	128	overflowed
212.0ms	646×	body	512	nan
59.0ms	326×	body	256	nan
56.0ms	1018×	body	128	nan
19.0ms	212×	body	128	invalid

Compiler

Compiled 3197 to 2579 computations (19.3% saved)

Details

analyze536.0ms (5%)

sample78.0ms (0.7%)

simplify53.0ms (0.5%)

prune4.0ms (0%)

localize10.0ms (0.1%)

rewrite217.0ms (2%)

series422.0ms (4%)

simplify93.0ms (0.9%)

prune182.0ms (1.7%)

localize11.0ms (0.1%)

rewrite177.0ms (1.7%)

series201.0ms (1.9%)

simplify75.0ms (0.7%)

prune157.0ms (1.5%)

localize15.0ms (0.1%)

rewrite254.0ms (2.4%)

series333.0ms (3.1%)

simplify110.0ms (1%)

prune229.0ms (2.1%)

localize13.0ms (0.1%)

rewrite485.0ms (4.5%)

series228.0ms (2.1%)

simplify142.0ms (1.3%)

prune466.0ms (4.4%)

regimes1.0s (9.7%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.1s (48.2%)

Profiling