Details

analyze441.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
23.4%	51.5%	25.1%	7
24.2%	50.7%	25.1%	8
24.6%	50.3%	25.1%	9
36.9%	25.5%	37.6%	10
37.2%	25.3%	37.6%	11
37.3%	25.1%	37.6%	12
43.5%	12.7%	43.8%	13
43.6%	12.6%	43.8%	14

sample43.0ms

Algorithm

intervals

Results

24.0ms	256×	body	80	valid
3.0ms	30×	body	80	nan

simplify127.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (118.0ms)

Iter	Nodes	Cost
0	5238	19

prune20.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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

Merged error: 33.0b

Counts

2 → 2

localize16.0ms

Local error

Found 2 expressions with local error:

0.4b	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
30.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac_binary64`
22×	`log-pow_binary64`
20×	`pow1_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`pow1/2_binary64` `sqrt-pow1_binary64` `associate-/l*_binary64`
4×	`associate-/r*_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`sqrt-prod_binary64`
2×	`flip3-+_binary64` `add-log-exp_binary64` `div-sub_binary64` `log-div_binary64` `flip-+_binary64`
1×	`cbrt-undiv_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

2 → 63

Calls

2 calls:

8.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series122.0ms

Counts

2 → 6

Calls

2 calls:

95.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
27.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify79.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4976	1640
1	4976	1640

prune226.0ms

Filtered

45 candidates to 69 candidates (-53.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	59	10	69
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	60	11	71

Merged error: 7.7b

Counts

71 → 11

localize17.0ms

Local error

Found 3 expressions with local error:

0.3b	(/.f64 1 (log.f64 base))
0.4b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (/.f64 1 (log.f64 base)))
30.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
26×	`times-frac_binary64`
23×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
16×	`pow1_binary64` `associate-r_binary64`
13×	`add-exp-log_binary64`
10×	`log-pow_binary64` `add-cbrt-cube_binary64`
6×	`associate-l_binary64`
4×	`associate-/r*_binary64`
3×	`add-log-exp_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l*_binary64` `sqrt-prod_binary64`
2×	`pow1/2_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rec-exp_binary64` `div-inv_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-r/_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `pow-flip_binary64` `flip-+_binary64` `-commutative_binary64`

Counts

3 → 90

Calls

3 calls:

3.0ms	(/.f64 1 (log.f64 base))
10.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (/.f64 1 (log.f64 base)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series196.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(/.f64 1 (log.f64 base))
97.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (/.f64 1 (log.f64 base)))
27.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify91.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4932	1561
1	4932	1561

prune275.0ms

Filtered

60 candidates to 99 candidates (-65.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	92	7	99
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	96	14	110

Merged error: 7.7b

Counts

110 → 14

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
0.4b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
0.6b	(*.f64 (log.f64 base) (log.f64 base))
30.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
23×	`pow1_binary64` `add-cube-cbrt_binary64`
12×	`log-prod_binary64`
10×	`log-pow_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
9×	`times-frac_binary64`
8×	`associate-r_binary64`
6×	`swap-sqr_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`add-log-exp_binary64`
3×	`flip3-+_binary64` `associate-/r_binary64` `associate-/l_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sqrt-div_binary64` `*-commutative_binary64`
1×	`pow-prod-up_binary64` `cbrt-undiv_binary64` `pow-plus_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `pow-sqr_binary64` `pow2_binary64`

Counts

4 → 110

Calls

4 calls:

11.0ms	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
6.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
5.0ms	(*.f64 (log.f64 base) (log.f64 base))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series274.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
80.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
66.0ms	(*.f64 (log.f64 base) (log.f64 base))
26.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify72.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5000	2524

prune400.0ms

Filtered

84 candidates to 122 candidates (-45.2%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	117	5	122
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	117	19	136

Merged error: 7.7b

Counts

136 → 19

localize39.0ms

Local error

Found 4 expressions with local error:

0.4b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
0.6b	(cbrt.f64 base)
0.6b	(cbrt.f64 base)
30.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`pow1_binary64`
6×	`log-prod_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64` `cbrt-prod_binary64`
4×	`add-log-exp_binary64` `associate-r_binary64` `log-pow_binary64`
3×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-prod_binary64`
2×	`pow1/2_binary64` `pow1/3_binary64` `sqrt-pow1_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

4 → 65

Calls

4 calls:

7.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
1.0ms	(cbrt.f64 base)
1.0ms	(cbrt.f64 base)
8.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
84.0ms	(cbrt.f64 base)
88.0ms	(cbrt.f64 base)
27.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify77.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4900	1153
1	4900	1153

prune226.0ms

Filtered

60 candidates to 77 candidates (-28.3%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	1	16	17
Picked	1	0	1
Done	0	1	1
Total	77	19	96

Merged error: 7.6b

Counts

96 → 19

regimes968.0ms

Accuracy

55.8% (10.8b remaining)

Error of 18.1b against oracle of 7.3b and baseline of 31.6b

bsearch185.0ms

Steps

Iters	Range		Point
2	11564828128829714386035245900141059637248	13925002093196445070716999465128666595328	1.1859849874375555e+40
9	3218145231422383/27967679607885704301190218685229334463595448410322902860782665724913148442727445468110629165844363647880233895721679414135153184333079469434028345743715409785657103816385949318619923106913065211176796883038813718238213431256579671499373815533666304	7262552707715741/106688230926077668385277628651540124754316133157054530566340124988224595805082113144342915213944868651886878569494931847134220826465909841285813696837293280737522521272224232935409252574589024395663440258174185631707051968599623380658622038016	1.2029630995824736e-228
11	-5151048578563713/7914572847139345089936080672628710081124203171238778877250017794972711203409019749450124833959777439667125485632516458859243681097816038718961476963260581373331416708758372352	-2533852854382877/9343878384890255807777119448474196633381331982845050737826186276657715542443371287564109437577976626746659450006721346172290467269376897020421450382791094657540085093089822617769726345721044533248	-1.5366008112942153e-167
5	-24652733754771875499572286734810933146532365166054399036021526924099904705430664778583010665562112	-10810056581737976848893553054432641225054322036914390266381570055766623748101509938810301779542016	-1.3796695805914547e+97

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	126
1	49	126

end0.0ms

sample1.1s

Algorithm

intervals

Results

769.0ms	8000×	body	80	valid
87.0ms	994×	body	80	nan

Details

analyze441.0ms

sample43.0ms

simplify127.0ms

prune20.0ms

localize16.0ms

rewrite15.0ms

series122.0ms

simplify79.0ms

prune226.0ms

localize17.0ms

rewrite20.0ms

series196.0ms

simplify91.0ms

prune275.0ms

localize28.0ms

rewrite30.0ms

series274.0ms

simplify72.0ms

prune400.0ms

localize39.0ms

rewrite19.0ms

series275.0ms

simplify77.0ms

prune226.0ms

regimes968.0ms

bsearch185.0ms

simplify4.0ms

end0.0ms

sample1.1s

Profiling