Details

analyze382.0ms (3.4%)

Algorithm

1×

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 (0.7%)

Algorithm

1×

intervals

Results

24.0ms	256×	body	128	valid
17.0ms	39×	body	1024	nan
10.0ms	74×	body	128	overflowed
8.0ms	26×	body	512	nan
2.0ms	13×	body	256	nan
2.0ms	33×	body	128	nan
1.0ms	6×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify137.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

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

0.6b

Counts

2 → 2

Compiler

Compiled 44 to 41 computations (6.8% saved)

localize11.0ms (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	(.f64 (.f64 2 PI.f64) n)
0.5b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))

rewrite202.0ms (1.8%)

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×	`difference-of-squares_binary64_729` `pow-prod-down_binary64_831` `pow-exp_binary64_828` `associate-/r*_binary64_704`
5×	`div-exp_binary64_811` `associate-/l*_binary64_705`
3×	`distribute-lft-out--_binary64_712` `pow-pow_binary64_832` `add-log-exp_binary64_799` `cbrt-unprod_binary64_793` `associate-r_binary64_700`
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)

series438.0ms (3.9%)

Error

0.2b

Counts

3 → 18

Calls

3 calls:

204.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
182.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
27.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 1100 to 864 computations (21.5% saved)

simplify97.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4969	3385
1	4969	3385

prune181.0ms (1.6%)

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 3081 to 2093 computations (32.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite124.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

26×	`pow1_binary64_821`
20×	`add-exp-log_binary64_798`
14×	`add-cbrt-cube_binary64_796`
13×	`add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782` `*-un-lft-identity_binary64_760` `pow-unpow_binary64_837`
12×	`pow-prod-down_binary64_831`
9×	`times-frac_binary64_766` `prod-exp_binary64_809`
6×	`cbrt-unprod_binary64_793` `associate-l_binary64_701`
4×	`add-log-exp_binary64_799`
3×	`sqrt-pow1_binary64_778` `pow-pow_binary64_832` `pow-exp_binary64_828`
2×	`associate-r_binary64_700` `*-commutative_binary64_691`
1×	`pow1/2_binary64_840` `sqrt-prod_binary64_776` `unpow-prod-down_binary64_839` `div-inv_binary64_757` `pow-to-exp_binary64_829` `sqr-pow_binary64_732`

Counts

4 → 77

Calls

4 calls:

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

Compiler

Compiled 1909 to 1250 computations (34.5% saved)

series258.0ms (2.3%)

Error

0.0b

Counts

4 → 18

Calls

4 calls:

158.0ms	(pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))
30.0ms	(.f64 n (.f64 2 PI.f64))
28.0ms	(.f64 n (.f64 2 PI.f64))
23.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))

Compiler

Compiled 1128 to 877 computations (22.3% saved)

simplify86.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5013	1194

prune121.0ms (1.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	95	9	104

Error

0.0b

Counts

104 → 9

Compiler

Compiled 2370 to 1592 computations (32.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite197.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

45×	`add-sqr-sqrt_binary64_782`
25×	`sqrt-prod_binary64_776` `*-un-lft-identity_binary64_760`
22×	`pow1_binary64_821`
19×	`add-cube-cbrt_binary64_795`
17×	`associate-r_binary64_700`
15×	`add-exp-log_binary64_798` `times-frac_binary64_766` `associate-l_binary64_701`
12×	`unpow-prod-down_binary64_839` `unswap-sqr_binary64_728`
11×	`add-cbrt-cube_binary64_796`
9×	`pow-prod-down_binary64_831`
8×	`unpow-prod-up_binary64_838`
6×	`sqrt-pow1_binary64_778` `prod-exp_binary64_809` `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` `cbrt-unprod_binary64_793`
3×	`pow-sub_binary64_836`
2×	`pow1/2_binary64_840` `pow-to-exp_binary64_829` `pow-exp_binary64_828` `sqrt-div_binary64_777` `sub-neg_binary64_753` `*-commutative_binary64_691` `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 n (*.f64 2 PI.f64))) (-.f64 1 k)) (sqrt.f64 (/.f64 1 k)))
8.0ms	(pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k))
5.0ms	(.f64 n (.f64 2 PI.f64))
4.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))

Compiler

Compiled 2812 to 2087 computations (25.8% saved)

series315.0ms (2.8%)

Error

0.0b

Counts

4 → 21

Calls

4 calls:

123.0ms	(pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k))
123.0ms	(.f64 (pow.f64 (sqrt.f64 (.f64 n (*.f64 2 PI.f64))) (-.f64 1 k)) (sqrt.f64 (/.f64 1 k)))
25.0ms	(.f64 n (.f64 2 PI.f64))
23.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))

Compiler

Compiled 1589 to 1224 computations (23% saved)

simplify108.0ms (1%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4939	3141
1	4939	3141

prune176.0ms (1.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	138	8	146

Error

0.0b

Counts

146 → 8

Compiler

Compiled 3147 to 2183 computations (30.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite1.2s (10.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

591×	`times-frac_binary64_766`
302×	`add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782` `*-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`
36×	`add-exp-log_binary64_798`
31×	`sub-neg_binary64_753` `sqr-pow_binary64_732`
20×	`div-exp_binary64_811`
16×	`pow1_binary64_821` `add-cbrt-cube_binary64_796`
9×	`associate-/l*_binary64_705`
6×	`pow-prod-down_binary64_831` `div-inv_binary64_757` `associate-/r/_binary64_706`
5×	`pow-sub_binary64_836`
4×	`add-log-exp_binary64_799` `pow-to-exp_binary64_829` `pow-exp_binary64_828` `cbrt-undiv_binary64_794` `1-exp_binary64_804` `rec-exp_binary64_810`
3×	`sqrt-pow1_binary64_778` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `associate-l_binary64_701`
2×	`frac-2neg_binary64_771` `clear-num_binary64_759`
1×	`pow1/2_binary64_840` `associate-r_binary64_700` `*-commutative_binary64_691` `inv-pow_binary64_845` `pow-flip_binary64_834`

Counts

4 → 473

Calls

4 calls:

20.0ms	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k))))
8.0ms	(/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k)))
5.0ms	(.f64 n (.f64 2 PI.f64))
4.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))

Compiler

Compiled 15277 to 9928 computations (35% saved)

series322.0ms (2.9%)

Error

0.0b

Counts

4 → 18

Calls

4 calls:

135.0ms	(/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k)))
125.0ms	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k))))
26.0ms	(.f64 n (.f64 2 PI.f64))
23.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))

Compiler

Compiled 1331 to 1050 computations (21.1% saved)

simplify254.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

491 → 491

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	4949	17730
1	4949	17730

prune991.0ms (8.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	490	1	491
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	490	9	499

Error

0.0b

Counts

499 → 9

Compiler

Compiled 13194 to 7571 computations (42.6% saved)

regimes826.0ms (7.3%)

Accuracy

Total 0.4b remaining (99.6%)

Threshold costs 0.4b (99.6%)

Compiler

Compiled 10950 to 9138 computations (16.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	32
1	18	32

end0.0ms (0%)

sample4.7s (42.1%)

Algorithm

1×

intervals

Results

619.0ms	1375×	body	1024	nan
611.0ms	8000×	body	128	valid
315.0ms	2327×	body	128	overflowed
230.0ms	689×	body	512	nan
66.0ms	1047×	body	128	nan
60.0ms	348×	body	256	nan
21.0ms	232×	body	128	invalid

Compiler

Compiled 2763 to 2307 computations (16.5% saved)

Details

analyze382.0ms (3.4%)

sample80.0ms (0.7%)

simplify137.0ms (1.2%)

prune4.0ms (0%)

localize11.0ms (0.1%)

rewrite202.0ms (1.8%)

series438.0ms (3.9%)

simplify97.0ms (0.9%)

prune181.0ms (1.6%)

localize11.0ms (0.1%)

rewrite124.0ms (1.1%)

series258.0ms (2.3%)

simplify86.0ms (0.8%)

prune121.0ms (1.1%)

localize13.0ms (0.1%)

rewrite197.0ms (1.7%)

series315.0ms (2.8%)

simplify108.0ms (1%)

prune176.0ms (1.6%)

localize10.0ms (0.1%)

rewrite1.2s (10.6%)

series322.0ms (2.9%)

simplify254.0ms (2.2%)

prune991.0ms (8.8%)

regimes826.0ms (7.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample4.7s (42.1%)

Profiling