Details

analyze416.0ms (5.6%)

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)

sample85.0ms (1.1%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	128	valid
20.0ms	42×	body	1024	nan
11.0ms	71×	body	128	overflowed
11.0ms	20×	body	512	nan
2.0ms	37×	body	128	nan
2.0ms	11×	body	256	nan
1.0ms	8×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify209.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4908	22
1	4908	22

prune6.0ms (0.1%)

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

Merged error: 0.4b

Counts

2 → 2

Compiler

Compiled 74 to 69 computations (6.8% saved)

localize13.0ms (0.2%)

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

rewrite36.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`times-frac_binary64_773`
42×	`add-sqr-sqrt_binary64_789` `*-un-lft-identity_binary64_767`
33×	`add-cube-cbrt_binary64_802`
26×	`add-exp-log_binary64_805`
22×	`pow-unpow_binary64_844`
18×	`sqrt-prod_binary64_783`
14×	`pow1_binary64_828`
10×	`add-cbrt-cube_binary64_803`
9×	`prod-exp_binary64_816`
8×	`sqr-pow_binary64_739` `unpow-prod-down_binary64_846`
6×	`associate-/r*_binary64_711` `pow-exp_binary64_835` `pow-prod-down_binary64_838` `difference-of-squares_binary64_736`
5×	`associate-/l*_binary64_712` `div-exp_binary64_818`
3×	`associate-r_binary64_707` `cbrt-unprod_binary64_800` `add-log-exp_binary64_806` `distribute-lft-out--_binary64_719` `pow-pow_binary64_839`
2×	`pow-to-exp_binary64_836` `div-sub_binary64_772` `pow-sub_binary64_843` `div-inv_binary64_764`
1×	`associate-l_binary64_708` `frac-2neg_binary64_778` `associate-/l/_binary64_714` `cbrt-undiv_binary64_801` `*-commutative_binary64_698` `clear-num_binary64_766`

Counts

3 → 115

Calls

3 calls:

11.0ms	(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))
6.0ms	(.f64 (.f64 2 PI.f64) n)

series489.0ms (6.6%)

Counts

3 → 9

Calls

3 calls:

307.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
145.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
36.0ms	(.f64 (.f64 2 PI.f64) n)

simplify63.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5400	3540

prune695.0ms (9.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	114	10	124
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	116	10	126

Merged error: 0.0b

Counts

126 → 10

Compiler

Compiled 12417 to 9951 computations (19.9% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite43.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

127×	`add-exp-log_binary64_805`
67×	`prod-exp_binary64_816`
36×	`pow-exp_binary64_835`
30×	`div-exp_binary64_818`
20×	`pow1_binary64_828`
19×	`add-cbrt-cube_binary64_803`
15×	`add-sqr-sqrt_binary64_789` `*-un-lft-identity_binary64_767` `add-cube-cbrt_binary64_802`
14×	`times-frac_binary64_773`
13×	`pow-unpow_binary64_844`
12×	`pow-to-exp_binary64_836`
9×	`pow-prod-down_binary64_838`
7×	`cbrt-unprod_binary64_800`
6×	`associate-r_binary64_707`
5×	`associate-/l*_binary64_712`
4×	`add-log-exp_binary64_806`
3×	`sqr-pow_binary64_739` `unpow-prod-down_binary64_846` `pow-pow_binary64_839`
2×	`associate-l_binary64_708` `cbrt-undiv_binary64_801` `*-commutative_binary64_698` `div-inv_binary64_764`
1×	`frac-2neg_binary64_778` `associate-/r*_binary64_711` `clear-num_binary64_766`

Counts

4 → 118

Calls

4 calls:

11.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
7.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
6.0ms	(.f64 (.f64 2 PI.f64) n)
6.0ms	(.f64 (.f64 2 PI.f64) n)

series696.0ms (9.4%)

Counts

4 → 12

Calls

4 calls:

416.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
204.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
39.0ms	(.f64 (.f64 2 PI.f64) n)
37.0ms	(.f64 (.f64 2 PI.f64) n)

simplify58.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5603	2652

prune312.0ms (4.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	126	4	130
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	129	11	140

Merged error: 0b

Counts

140 → 11

Compiler

Compiled 5942 to 4418 computations (25.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite36.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`times-frac_binary64_773`
23×	`add-sqr-sqrt_binary64_789` `*-un-lft-identity_binary64_767` `sqrt-prod_binary64_783` `add-cube-cbrt_binary64_802`
20×	`pow1_binary64_828`
16×	`add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
9×	`pow-prod-down_binary64_838`
6×	`associate-r_binary64_707` `associate-/r*_binary64_711` `cbrt-unprod_binary64_800` `prod-exp_binary64_816`
4×	`add-log-exp_binary64_806` `associate-/l*_binary64_712`
3×	`sqrt-pow1_binary64_785`
2×	`associate-l_binary64_708` `*-commutative_binary64_698`
1×	`frac-2neg_binary64_778` `cbrt-undiv_binary64_801` `pow1/2_binary64_847` `div-exp_binary64_818` `clear-num_binary64_766` `sqrt-undiv_binary64_788` `div-inv_binary64_764`

Counts

4 → 95

Calls

4 calls:

8.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (sqrt.f64 k))
8.0ms	(.f64 (.f64 2 PI.f64) n)
6.0ms	(.f64 (.f64 2 PI.f64) n)
4.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))

series283.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

150.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (sqrt.f64 k))
47.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
47.0ms	(.f64 (.f64 2 PI.f64) n)
39.0ms	(.f64 (.f64 2 PI.f64) n)

simplify70.0ms (1%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4957	1953
1	4957	1953

prune206.0ms (2.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	104	3	107
Fresh	6	4	10
Picked	0	1	1
Done	0	0	0
Total	110	8	118

Merged error: 0b

Counts

118 → 8

Compiler

Compiled 4005 to 2793 computations (30.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite46.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`sqrt-prod_binary64_783`
42×	`times-frac_binary64_773`
37×	`add-sqr-sqrt_binary64_789` `*-un-lft-identity_binary64_767` `add-cube-cbrt_binary64_802`
21×	`add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
19×	`pow1_binary64_828`
9×	`associate-r_binary64_707` `cbrt-unprod_binary64_800` `prod-exp_binary64_816` `pow-prod-down_binary64_838`
7×	`associate-/l*_binary64_712`
6×	`associate-/r*_binary64_711`
4×	`add-log-exp_binary64_806`
3×	`associate-l_binary64_708` `*-commutative_binary64_698`
1×	`frac-2neg_binary64_778` `cbrt-undiv_binary64_801` `div-exp_binary64_818` `clear-num_binary64_766` `sqrt-undiv_binary64_788` `div-inv_binary64_764`

Counts

4 → 122

Calls

4 calls:

13.0ms	(/.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n))) (sqrt.f64 k))
6.0ms	(.f64 (.f64 2 PI.f64) n)
6.0ms	(.f64 (.f64 2 PI.f64) n)
6.0ms	(.f64 (.f64 2 PI.f64) n)

series314.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

203.0ms	(/.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n))) (sqrt.f64 k))
39.0ms	(.f64 (.f64 2 PI.f64) n)
37.0ms	(.f64 (.f64 2 PI.f64) n)
35.0ms	(.f64 (.f64 2 PI.f64) n)

simplify212.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5493	2757

prune252.0ms (3.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	134	8	142

Merged error: 0b

Counts

142 → 8

Compiler

Compiled 4842 to 3283 computations (32.2% saved)

regimes61.0ms (0.8%)

Compiler: Compiled 539 to 455 computations (15.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	31
1	15	31

end0.0ms (0%)

sample2.8s (37.2%)

Algorithm

1×

intervals

Results

807.0ms	8000×	body	128	valid
691.0ms	1344×	body	1024	nan
369.0ms	2381×	body	128	overflowed
224.0ms	648×	body	512	nan
63.0ms	961×	body	128	nan
62.0ms	308×	body	256	nan
27.0ms	230×	body	128	invalid

Compiler

Compiled 211 to 179 computations (15.2% saved)

Details

analyze416.0ms (5.6%)

sample85.0ms (1.1%)

simplify209.0ms (2.8%)

prune6.0ms (0.1%)

localize13.0ms (0.2%)

rewrite36.0ms (0.5%)

series489.0ms (6.6%)

simplify63.0ms (0.8%)

prune695.0ms (9.4%)

localize18.0ms (0.2%)

rewrite43.0ms (0.6%)

series696.0ms (9.4%)

simplify58.0ms (0.8%)

prune312.0ms (4.2%)

localize12.0ms (0.2%)

rewrite36.0ms (0.5%)

series283.0ms (3.8%)

simplify70.0ms (1%)

prune206.0ms (2.8%)

localize15.0ms (0.2%)

rewrite46.0ms (0.6%)

series314.0ms (4.2%)

simplify212.0ms (2.9%)

prune252.0ms (3.4%)

regimes61.0ms (0.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.8s (37.2%)

Profiling