Details

analyze530.0ms (4.4%)

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)

sample73.0ms (0.6%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	128	valid
15.0ms	72×	body	128	overflowed
13.0ms	30×	body	1024	nan
5.0ms	16×	body	512	nan
2.0ms	10×	body	256	nan
1.0ms	25×	body	128	nan
1.0ms	9×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify56.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (50.0ms)

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)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite215.0ms (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×	`pow-exp_binary64_828` `associate-/r*_binary64_704` `pow-prod-down_binary64_831` `difference-of-squares_binary64_729`
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×	`pow-to-exp_binary64_829` `div-inv_binary64_757` `div-sub_binary64_765` `pow-sub_binary64_836`
1×	`cbrt-undiv_binary64_794` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l/_binary64_707` `associate-l_binary64_701` `*-commutative_binary64_691`

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)

series448.0ms (3.7%)

Error

0.2b

Counts

3 → 18

Calls

3 calls:

212.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
186.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
28.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 1100 to 864 computations (21.5% saved)

simplify98.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4969	3385
1	4969	3385

prune186.0ms (1.5%)

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 3041 to 2057 computations (32.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite615.0ms (5.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

284×	`times-frac_binary64_766`
126×	`add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782` `*-un-lft-identity_binary64_760`
111×	`sqrt-prod_binary64_776`
33×	`add-exp-log_binary64_798`
28×	`unpow-prod-down_binary64_839` `sqr-pow_binary64_732`
24×	`associate-/l*_binary64_705`
20×	`pow1_binary64_821`
19×	`add-cbrt-cube_binary64_796`
11×	`div-exp_binary64_811`
9×	`prod-exp_binary64_809` `pow-prod-down_binary64_831`
8×	`div-inv_binary64_757`
6×	`associate-/r_binary64_704` `cbrt-unprod_binary64_793` `associate-l*_binary64_701`
4×	`add-log-exp_binary64_799`
3×	`pow-exp_binary64_828` `cbrt-undiv_binary64_794` `sqrt-pow1_binary64_778`
2×	`associate-r_binary64_700` `*-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 n (.f64 2 PI.f64))) (pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
5.0ms	(.f64 n (.f64 2 PI.f64))
5.0ms	(.f64 n (.f64 2 PI.f64))
3.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))

Compiler

Compiled 8830 to 5718 computations (35.2% saved)

series233.0ms (1.9%)

Error

0.0b

Counts

4 → 15

Calls

4 calls:

139.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
29.0ms	(.f64 n (.f64 2 PI.f64))
26.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))
25.0ms	(.f64 n (.f64 2 PI.f64))

Compiler

Compiled 1094 to 858 computations (21.6% saved)

simplify138.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5070	11529

prune490.0ms (4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	253	3	256
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	256	8	264

Error

Counts

264 → 8

Compiler

Compiled 8733 to 5643 computations (35.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite213.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

56×	`add-sqr-sqrt_binary64_782`
37×	`sqrt-prod_binary64_776`
33×	`*-un-lft-identity_binary64_760`
26×	`add-cube-cbrt_binary64_795` `times-frac_binary64_766`
19×	`associate-l_binary64_701`
18×	`pow1_binary64_821`
15×	`add-exp-log_binary64_798`
13×	`associate-r_binary64_700`
12×	`unpow-prod-down_binary64_839` `unswap-sqr_binary64_728`
11×	`add-cbrt-cube_binary64_796`
8×	`unpow-prod-up_binary64_838`
6×	`prod-exp_binary64_809` `sqr-pow_binary64_732` `cancel-sign-sub-inv_binary64_726` `pow-prod-down_binary64_831` `pow-unpow_binary64_837` `sqrt-pow1_binary64_778`
5×	`pow-pow_binary64_832`
4×	`add-log-exp_binary64_799` `cbrt-unprod_binary64_793`
3×	`pow-sub_binary64_836` `sqrt-div_binary64_777` `rem-sqrt-square_binary64_773`
2×	`pow-to-exp_binary64_829` `pow-exp_binary64_828` `div-inv_binary64_757` `sub-neg_binary64_753` `*-commutative_binary64_691` `difference-of-squares_binary64_729` `pow1/2_binary64_840`
1×	`frac-times_binary64_770` `associate-l/_binary64_703` `associate-r/_binary64_702` `distribute-lft-out--_binary64_712` `sqrt-pow2_binary64_779` `inv-pow_binary64_845` `pow-flip_binary64_834`

Counts

4 → 132

Calls

4 calls:

15.0ms	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (sqrt.f64 (.f64 n (*.f64 2 PI.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))
3.0ms	(sqrt.f64 (/.f64 1 k))

Compiler

Compiled 3155 to 2339 computations (25.9% saved)

series317.0ms (2.6%)

Error

Counts

4 → 21

Calls

4 calls:

129.0ms	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (sqrt.f64 (.f64 n (*.f64 2 PI.f64))) (-.f64 1 k)))
124.0ms	(pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k))
27.0ms	(.f64 n (.f64 2 PI.f64))
15.0ms	(sqrt.f64 (/.f64 1 k))

Compiler

Compiled 1565 to 1200 computations (23.3% saved)

simplify120.0ms (1%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4937	3270
1	4937	3270

prune205.0ms (1.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	1	5	6
Picked	1	0	1
Done	1	0	1
Total	155	6	161

Error

Counts

161 → 6

Compiler

Compiled 3481 to 2429 computations (30.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite167.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

38×	`add-sqr-sqrt_binary64_782`
30×	`sqrt-prod_binary64_776`
25×	`*-un-lft-identity_binary64_760`
24×	`pow1_binary64_821`
23×	`add-cube-cbrt_binary64_795`
22×	`times-frac_binary64_766` `associate-l_binary64_701`
13×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
12×	`pow-prod-down_binary64_831`
9×	`sqrt-pow1_binary64_778`
8×	`associate-r_binary64_700`
5×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793` `unswap-sqr_binary64_728`
4×	`add-log-exp_binary64_799`
3×	`pow1/2_binary64_840` `*-commutative_binary64_691` `rem-sqrt-square_binary64_773`
2×	`sqrt-div_binary64_777` `div-inv_binary64_757`
1×	`sqrt-unprod_binary64_780` `associate-*l/_binary64_703` `inv-pow_binary64_845` `pow-flip_binary64_834`

Counts

4 → 105

Calls

4 calls:

13.0ms	(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (.f64 (*.f64 n PI.f64) 2)))
5.0ms	(.f64 n (.f64 2 PI.f64))
4.0ms	(*.f64 n PI.f64)
3.0ms	(sqrt.f64 (/.f64 1 k))

Compiler

Compiled 2778 to 1852 computations (33.3% saved)

series148.0ms (1.2%)

Error

Counts

4 → 15

Calls

4 calls:

68.0ms	(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (.f64 (*.f64 n PI.f64) 2)))
34.0ms	(.f64 n (.f64 2 PI.f64))
21.0ms	(*.f64 n PI.f64)
13.0ms	(sqrt.f64 (/.f64 1 k))

Compiler

Compiled 985 to 761 computations (22.7% saved)

simplify71.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4955	1578
1	4955	1578

prune141.0ms (1.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	120	6	126

Error

Counts

126 → 6

Compiler

Compiled 2905 to 1901 computations (34.6% saved)

regimes1.4s (11.5%)

Accuracy

Total 0.4b remaining (99.9%)

Threshold costs 0.4b (99.9%)

Compiler

Compiled 19656 to 15666 computations (20.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	30
1	19	30

end0.0ms (0%)

sample6.2s (51.3%)

Algorithm

1×

intervals

Results

633.0ms	8000×	body	128	valid
604.0ms	1301×	body	1024	nan
330.0ms	2347×	body	128	overflowed
212.0ms	664×	body	512	nan
57.0ms	1012×	body	128	nan
55.0ms	316×	body	256	nan
22.0ms	236×	body	128	invalid

Compiler

Compiled 4674 to 3722 computations (20.4% saved)

Details

analyze530.0ms (4.4%)

sample73.0ms (0.6%)

simplify56.0ms (0.5%)

prune5.0ms (0%)

localize11.0ms (0.1%)

rewrite215.0ms (1.8%)

series448.0ms (3.7%)

simplify98.0ms (0.8%)

prune186.0ms (1.5%)

localize10.0ms (0.1%)

rewrite615.0ms (5.1%)

series233.0ms (1.9%)

simplify138.0ms (1.1%)

prune490.0ms (4%)

localize11.0ms (0.1%)

rewrite213.0ms (1.7%)

series317.0ms (2.6%)

simplify120.0ms (1%)

prune205.0ms (1.7%)

localize14.0ms (0.1%)

rewrite167.0ms (1.4%)

series148.0ms (1.2%)

simplify71.0ms (0.6%)

prune141.0ms (1.2%)

regimes1.4s (11.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample6.2s (51.3%)

Profiling