Details

analyze539.0ms (6%)

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)

sample84.0ms (0.9%)

Algorithm

1×

intervals

Results

24.0ms	51×	body	1024	nan
21.0ms	256×	body	128	valid
12.0ms	79×	body	128	overflowed
7.0ms	22×	body	512	nan
2.0ms	30×	body	128	nan
1.0ms	4×	body	256	nan
0.0ms	4×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify57.0ms (0.6%)

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)

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

rewrite205.0ms (2.3%)

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)

series422.0ms (4.7%)

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))
167.0ms	(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)

simplify91.0ms (1%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4969	3385
1	4969	3385

prune180.0ms (2%)

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 3076 to 1939 computations (37% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite210.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

124×	`add-exp-log_binary64_798`
65×	`prod-exp_binary64_809`
36×	`pow-exp_binary64_828`
30×	`div-exp_binary64_811`
18×	`add-sqr-sqrt_binary64_782`
17×	`pow1_binary64_821`
16×	`add-cbrt-cube_binary64_796` `add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
14×	`times-frac_binary64_766`
13×	`pow-unpow_binary64_837`
12×	`pow-to-exp_binary64_829`
7×	`pow-prod-down_binary64_831`
6×	`associate-r_binary64_700`
5×	`cbrt-unprod_binary64_793` `associate-/l*_binary64_705`
4×	`add-log-exp_binary64_799` `associate-l_binary64_701`
3×	`unpow-prod-down_binary64_839` `sqr-pow_binary64_732` `pow-pow_binary64_832`
2×	`*-commutative_binary64_691` `cbrt-undiv_binary64_794` `div-inv_binary64_757`
1×	`unswap-sqr_binary64_728` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/r*_binary64_704`

Counts

4 → 118

Calls

4 calls:

10.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))
7.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
5.0ms	(.f64 (.f64 2 PI.f64) n)
4.0ms	(*.f64 n PI.f64)

Compiler

Compiled 3457 to 2289 computations (33.8% saved)

series299.0ms (3.3%)

Error

0.0b

Counts

4 → 15

Calls

4 calls:

137.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))
95.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
30.0ms	(.f64 (.f64 2 PI.f64) n)
22.0ms	(*.f64 n PI.f64)

Compiler

Compiled 1100 to 849 computations (22.8% saved)

simplify76.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4999	2500
1	4999	2500

prune170.0ms (1.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	129	4	133
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	132	10	142

Error

Counts

142 → 10

Compiler

Compiled 3310 to 2075 computations (37.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite229.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

59×	`sqrt-prod_binary64_776`
46×	`add-sqr-sqrt_binary64_782`
42×	`times-frac_binary64_766`
40×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
12×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
10×	`pow1_binary64_821`
9×	`associate-l_binary64_701` `associate-r_binary64_700`
7×	`associate-/l*_binary64_705`
6×	`associate-/r*_binary64_704`
4×	`add-log-exp_binary64_799`
3×	`pow-prod-down_binary64_831` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `unswap-sqr_binary64_728` `*-commutative_binary64_691`
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 → 122

Calls

4 calls:

9.0ms	(/.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64)))) (sqrt.f64 k))
4.0ms	(*.f64 n PI.f64)
4.0ms	(*.f64 n PI.f64)
4.0ms	(*.f64 n PI.f64)

Compiler

Compiled 4466 to 2481 computations (44.4% saved)

series235.0ms (2.6%)

Error

Counts

4 → 15

Calls

4 calls:

146.0ms	(/.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64)))) (sqrt.f64 k))
26.0ms	(*.f64 n PI.f64)
25.0ms	(*.f64 n PI.f64)
21.0ms	(*.f64 n PI.f64)

Compiler

Compiled 1360 to 976 computations (28.2% saved)

simplify96.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5197	2558

prune222.0ms (2.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	137	10	147

Error

Counts

147 → 10

Compiler

Compiled 4904 to 2809 computations (42.7% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (.f64 (sqrt.f64 (.f64 2 PI.f64)) (sqrt.f64 n)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))
0.3b	(*.f64 n PI.f64)
0.5b	(.f64 (sqrt.f64 (.f64 2 PI.f64)) (sqrt.f64 n))
1.0b	(sqrt.f64 (*.f64 2 PI.f64))

rewrite139.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

52×	`add-exp-log_binary64_798`
24×	`prod-exp_binary64_809`
20×	`add-cbrt-cube_binary64_796`
16×	`pow1_binary64_821`
15×	`add-sqr-sqrt_binary64_782`
12×	`div-exp_binary64_811`
9×	`add-cube-cbrt_binary64_795` `-un-lft-identity_binary64_760` `associate-r*_binary64_700`
7×	`pow-prod-down_binary64_831` `associate-l_binary64_701`
6×	`sqrt-pow1_binary64_778` `sqrt-prod_binary64_776` `cbrt-unprod_binary64_793` `pow-exp_binary64_828`
4×	`add-log-exp_binary64_799` `cbrt-undiv_binary64_794`
3×	`pow1/2_binary64_840` `unswap-sqr_binary64_728`
2×	`*-commutative_binary64_691` `pow-to-exp_binary64_829`
1×	`sqrt-unprod_binary64_780` `frac-2neg_binary64_771` `times-frac_binary64_766` `clear-num_binary64_759` `div-inv_binary64_757` `associate-/l_binary64_705` `associate-/r_binary64_704`

Counts

4 → 85

Calls

4 calls:

12.0ms	(/.f64 (.f64 (sqrt.f64 (.f64 2 PI.f64)) (sqrt.f64 n)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))
7.0ms	(.f64 (sqrt.f64 (.f64 2 PI.f64)) (sqrt.f64 n))
4.0ms	(*.f64 n PI.f64)
2.0ms	(sqrt.f64 (*.f64 2 PI.f64))

Compiler

Compiled 2342 to 1351 computations (42.3% saved)

series213.0ms (2.4%)

Error

Counts

4 → 12

Calls

4 calls:

149.0ms	(/.f64 (.f64 (sqrt.f64 (.f64 2 PI.f64)) (sqrt.f64 n)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))
31.0ms	(.f64 (sqrt.f64 (.f64 2 PI.f64)) (sqrt.f64 n))
22.0ms	(*.f64 n PI.f64)
0.0ms	(sqrt.f64 (*.f64 2 PI.f64))

Compiler

Compiled 948 to 747 computations (21.2% saved)

simplify62.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5185	1839

prune105.0ms (1.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	97	10	107

Error

Counts

107 → 10

Compiler

Compiled 2268 to 1355 computations (40.3% saved)

regimes725.0ms (8.1%)

Accuracy

Total 0.4b remaining (99.4%)

Threshold costs 0.4b (99.4%)

Compiler

Compiled 9250 to 7654 computations (17.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	22
1	25	22

end0.0ms (0%)

sample4.5s (50.4%)

Algorithm

1×

intervals

Results

642.0ms	8000×	body	128	valid
632.0ms	1355×	body	1024	nan
328.0ms	2311×	body	128	overflowed
239.0ms	732×	body	512	nan
64.0ms	359×	body	256	nan
56.0ms	998×	body	128	nan
21.0ms	240×	body	128	invalid

Compiler

Compiled 2332 to 1932 computations (17.2% saved)

Details

analyze539.0ms (6%)

sample84.0ms (0.9%)

simplify57.0ms (0.6%)

prune4.0ms (0%)

localize11.0ms (0.1%)

rewrite205.0ms (2.3%)

series422.0ms (4.7%)

simplify91.0ms (1%)

prune180.0ms (2%)

localize18.0ms (0.2%)

rewrite210.0ms (2.4%)

series299.0ms (3.3%)

simplify76.0ms (0.9%)

prune170.0ms (1.9%)

localize14.0ms (0.2%)

rewrite229.0ms (2.6%)

series235.0ms (2.6%)

simplify96.0ms (1.1%)

prune222.0ms (2.5%)

localize15.0ms (0.2%)

rewrite139.0ms (1.6%)

series213.0ms (2.4%)

simplify62.0ms (0.7%)

prune105.0ms (1.2%)

regimes725.0ms (8.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample4.5s (50.4%)

Profiling