Details

analyze556.0ms (5.2%)

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)

sample77.0ms (0.7%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	128	valid
16.0ms	36×	body	1024	nan
10.0ms	76×	body	128	overflowed
6.0ms	21×	body	512	nan
2.0ms	32×	body	128	nan
1.0ms	6×	body	256	nan
1.0ms	9×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify49.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (43.0ms)

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

0.4b

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

rewrite238.0ms (2.2%)

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×	`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:

13.0ms	(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)

series616.0ms (5.7%)

Error

0.2b

Counts

3 → 18

Calls

3 calls:

292.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
266.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
32.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 1100 to 864 computations (21.5% saved)

simplify91.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4969	3385
1	4969	3385

prune204.0ms (1.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	123	10	133
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	125	10	135

Error

0.0b

Counts

135 → 10

Compiler

Compiled 3115 to 2119 computations (32% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite571.0ms (5.3%)

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×	`pow-prod-down_binary64_831` `prod-exp_binary64_809`
8×	`div-inv_binary64_757`
6×	`cbrt-unprod_binary64_793` `associate-l_binary64_701` `associate-/r*_binary64_704`
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)

series346.0ms (3.2%)

Error

0.0b

Counts

4 → 15

Calls

4 calls:

213.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
43.0ms	(.f64 n (.f64 2 PI.f64))
42.0ms	(.f64 n (.f64 2 PI.f64))
32.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))

Compiler

Compiled 1094 to 858 computations (21.6% saved)

simplify139.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5070	11529

prune547.0ms (5.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	253	3	256
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	255	11	266

Error

Counts

266 → 11

Compiler

Compiled 8791 to 5109 computations (41.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite124.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

30×	`add-exp-log_binary64_798`
17×	`pow1_binary64_821`
16×	`add-cbrt-cube_binary64_796`
12×	`prod-exp_binary64_809`
11×	`add-sqr-sqrt_binary64_782`
9×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
7×	`pow-prod-down_binary64_831`
6×	`associate-l_binary64_701` `div-exp_binary64_811`
5×	`cbrt-unprod_binary64_793`
4×	`add-log-exp_binary64_799` `associate-r_binary64_700` `times-frac_binary64_766` `associate-/l*_binary64_705`
3×	`pow-exp_binary64_828` `sqrt-prod_binary64_776` `sqrt-pow1_binary64_778`
2×	`*-commutative_binary64_691` `cbrt-undiv_binary64_794`
1×	`unswap-sqr_binary64_728` `pow-to-exp_binary64_829` `frac-2neg_binary64_771` `clear-num_binary64_759` `div-inv_binary64_757` `associate-/r*_binary64_704` `pow1/2_binary64_840`

Counts

4 → 75

Calls

4 calls:

10.0ms	(/.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))
5.0ms	(.f64 n (.f64 2 PI.f64))
4.0ms	(*.f64 n PI.f64)
3.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))

Compiler

Compiled 1947 to 1180 computations (39.4% saved)

series328.0ms (3%)

Error

Counts

4 → 15

Calls

4 calls:

209.0ms	(/.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))
41.0ms	(.f64 n (.f64 2 PI.f64))
32.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))
30.0ms	(*.f64 n PI.f64)

Compiler

Compiled 1094 to 846 computations (22.7% saved)

simplify97.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4974	1593
1	4974	1593

prune119.0ms (1.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	90	11	101

Error

Counts

101 → 11

Compiler

Compiled 2261 to 1372 computations (39.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite232.0ms (2.2%)

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`
18×	`pow1_binary64_821`
17×	`associate-r_binary64_700`
15×	`add-exp-log_binary64_798` `associate-l_binary64_701`
12×	`unpow-prod-down_binary64_839` `unswap-sqr_binary64_728`
11×	`add-cbrt-cube_binary64_796`
8×	`unpow-prod-up_binary64_838`
6×	`pow-prod-down_binary64_831` `prod-exp_binary64_809` `sqr-pow_binary64_732` `cancel-sign-sub-inv_binary64_726` `pow-unpow_binary64_837` `sqrt-pow1_binary64_778`
5×	`pow-pow_binary64_832`
4×	`add-log-exp_binary64_799` `cbrt-unprod_binary64_793`
3×	`sqrt-div_binary64_777` `pow-sub_binary64_836` `rem-sqrt-square_binary64_773`
2×	`*-commutative_binary64_691` `pow-to-exp_binary64_829` `pow-exp_binary64_828` `sub-neg_binary64_753` `div-inv_binary64_757` `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:

17.0ms	(.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))
3.0ms	(sqrt.f64 (/.f64 1 k))

Compiler

Compiled 3155 to 2339 computations (25.9% saved)

series437.0ms (4.1%)

Error

Counts

4 → 21

Calls

4 calls:

178.0ms	(pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k))
172.0ms	(.f64 (pow.f64 (sqrt.f64 (.f64 n (*.f64 2 PI.f64))) (-.f64 1 k)) (sqrt.f64 (/.f64 1 k)))
40.0ms	(.f64 n (.f64 2 PI.f64))
18.0ms	(sqrt.f64 (/.f64 1 k))

Compiler

Compiled 1565 to 1200 computations (23.3% saved)

simplify84.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4951	3278
1	4951	3278

prune199.0ms (1.9%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	2	6	8
Picked	0	1	1
Done	0	2	2
Total	154	10	164

Error

Counts

164 → 10

Compiler

Compiled 3286 to 2271 computations (30.9% saved)

regimes876.0ms (8.2%)

Accuracy

Total 0.4b remaining (99.1%)

Threshold costs 0.4b (99.1%)

Compiler

Compiled 9952 to 8386 computations (15.7% 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%)

sample4.8s (44.3%)

Algorithm

1×

intervals

Results

622.0ms	1336×	body	1024	nan
601.0ms	8000×	body	128	valid
341.0ms	2406×	body	128	overflowed
215.0ms	655×	body	512	nan
62.0ms	353×	body	256	nan
57.0ms	956×	body	128	nan
22.0ms	249×	body	128	invalid

Compiler

Compiled 2317 to 1953 computations (15.7% saved)

Details

analyze556.0ms (5.2%)

sample77.0ms (0.7%)

simplify49.0ms (0.5%)

prune5.0ms (0%)

localize11.0ms (0.1%)

rewrite238.0ms (2.2%)

series616.0ms (5.7%)

simplify91.0ms (0.8%)

prune204.0ms (1.9%)

localize14.0ms (0.1%)

rewrite571.0ms (5.3%)

series346.0ms (3.2%)

simplify139.0ms (1.3%)

prune547.0ms (5.1%)

localize13.0ms (0.1%)

rewrite124.0ms (1.2%)

series328.0ms (3%)

simplify97.0ms (0.9%)

prune119.0ms (1.1%)

localize11.0ms (0.1%)

rewrite232.0ms (2.2%)

series437.0ms (4.1%)

simplify84.0ms (0.8%)

prune199.0ms (1.9%)

regimes876.0ms (8.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample4.8s (44.3%)

Profiling