Details

analyze5.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
74.9%	25%	0.1%	3
87.4%	12.5%	0.1%	4
93.7%	6.2%	0.1%	5
96.8%	3.1%	0.1%	6
98.3%	1.6%	0.1%	7
99.1%	0.8%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

sample27.0ms

Algorithm

intervals

Results

15.0ms

256×

body

valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	12	19
1	12	19

prune5.0ms

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: 30.7b

Counts

2 → 1

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.6b	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 10))
28.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac_binary64`
22×	`log-pow_binary64`
21×	`pow1_binary64`
17×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`pow1/2_binary64` `sqrt-pow1_binary64` `associate-/l*_binary64`
5×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`associate-/r*_binary64` `sqrt-div_binary64`
3×	`flip3-+_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`div-sub_binary64` `log-div_binary64`
1×	`cbrt-undiv_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

3 → 74

Calls

3 calls:

5.0ms	(+.f64 (.f64 re re) (.f64 im im))
8.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 10))
6.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series142.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(+.f64 (.f64 re re) (.f64 im im))
77.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 10))
42.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify116.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4921	1833
1	4921	1833

prune277.0ms

Filtered

55 candidates to 83 candidates (-50.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	70	13	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	13	84

Merged error: 6.9b

Counts

84 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.3b	(.f64 (/.f64 1/2 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (sqrt.f64 (log.f64 10))))
0.5b	(/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (sqrt.f64 (log.f64 10)))
29.4b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

89×	`times-frac_binary64`
83×	`add-sqr-sqrt_binary64`
54×	`sqrt-prod_binary64`
53×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
34×	`pow1_binary64`
32×	`associate-r_binary64`
28×	`log-pow_binary64`
25×	`associate-l_binary64`
19×	`add-exp-log_binary64`
18×	`add-cbrt-cube_binary64`
9×	`unswap-sqr_binary64`
7×	`associate-/r*_binary64`
6×	`add-log-exp_binary64`
5×	`cbrt-undiv_binary64` `div-exp_binary64`
4×	`cbrt-unprod_binary64` `prod-exp_binary64` `associate-/l*_binary64` `log-div_binary64`
3×	`flip3-+_binary64` `log-prod_binary64` `div-inv_binary64` `flip-+_binary64`
2×	`div-sub_binary64`
1×	`pow-prod-down_binary64` `rem-log-exp_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `frac-times_binary64` `associate-l/_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 164

Calls

4 calls:

4.0ms	(+.f64 (.f64 re re) (.f64 im im))
30.0ms	(.f64 (/.f64 1/2 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (sqrt.f64 (log.f64 10))))
8.0ms	(/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (sqrt.f64 (log.f64 10)))
4.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

series223.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+.f64 (.f64 re re) (.f64 im im))
74.0ms	(.f64 (/.f64 1/2 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (sqrt.f64 (log.f64 10))))
96.0ms	(/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (sqrt.f64 (log.f64 10)))
32.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify140.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	5019	4821

prune471.0ms

Filtered

104 candidates to 176 candidates (-69.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	168	8	176
Fresh	7	5	12
Picked	1	0	1
Done	0	0	0
Total	176	13	189

Merged error: 6.7b

Counts

189 → 13

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.3b	(.f64 (/.f64 1/2 (sqrt.f64 (log.f64 10))) (.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (/.f64 1 (sqrt.f64 (log.f64 10)))))
0.3b	(.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (/.f64 1 (sqrt.f64 (log.f64 10))))
29.4b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64` `times-frac_binary64`
40×	`add-exp-log_binary64`
36×	`*-un-lft-identity_binary64`
34×	`add-cube-cbrt_binary64`
30×	`add-cbrt-cube_binary64`
29×	`associate-l_binary64`
26×	`associate-r_binary64` `sqrt-prod_binary64`
19×	`pow1_binary64`
17×	`prod-exp_binary64`
12×	`cbrt-unprod_binary64`
8×	`log-pow_binary64`
7×	`div-exp_binary64`
6×	`add-log-exp_binary64` `cbrt-undiv_binary64`
5×	`associate-*r/_binary64` `unswap-sqr_binary64`
4×	`pow-prod-down_binary64`
3×	`log-prod_binary64` `rec-exp_binary64` `un-div-inv_binary64`
2×	`flip3-+_binary64` `div-inv_binary64` `log-div_binary64` `flip-+_binary64` `frac-times_binary64` `*-commutative_binary64`
1×	`rem-log-exp_binary64` `+-commutative_binary64` `associate-*l/_binary64` `sum-log_binary64`

Counts

4 → 130

Calls

4 calls:

4.0ms	(+.f64 (.f64 re re) (.f64 im im))
15.0ms	(.f64 (/.f64 1/2 (sqrt.f64 (log.f64 10))) (.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (/.f64 1 (sqrt.f64 (log.f64 10)))))
12.0ms	(.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (/.f64 1 (sqrt.f64 (log.f64 10))))
4.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

series221.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+.f64 (.f64 re re) (.f64 im im))
79.0ms	(.f64 (/.f64 1/2 (sqrt.f64 (log.f64 10))) (.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (/.f64 1 (sqrt.f64 (log.f64 10)))))
86.0ms	(.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (/.f64 1 (sqrt.f64 (log.f64 10))))
36.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify105.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5065	3052

prune380.0ms

Filtered

82 candidates to 142 candidates (-73.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	141	1	142
Fresh	0	12	12
Picked	1	0	1
Done	0	0	0
Total	142	13	155

Merged error: 6.7b

Counts

155 → 13

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.3b	(.f64 (/.f64 1/2 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (+.f64 (.f64 re re) (*.f64 im im)) (/.f64 1 (sqrt.f64 (log.f64 10))))))
15.2b	(pow.f64 (+.f64 (.f64 re re) (.f64 im im)) (/.f64 1 (sqrt.f64 (log.f64 10))))
15.6b	(log.f64 (pow.f64 (+.f64 (.f64 re re) (.f64 im im)) (/.f64 1 (sqrt.f64 (log.f64 10)))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt_binary64`
44×	`times-frac_binary64`
40×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
25×	`pow-unpow_binary64` `associate-l_binary64` `sqrt-prod_binary64`
21×	`log-prod_binary64`
13×	`pow1_binary64`
12×	`add-exp-log_binary64` `unpow-prod-down_binary64`
9×	`add-cbrt-cube_binary64`
8×	`log-pow_binary64`
7×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
6×	`add-log-exp_binary64`
4×	`associate-r_binary64` `sqr-pow_binary64`
3×	`rem-log-exp_binary64` `unswap-sqr_binary64`
2×	`pow-to-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `div-inv_binary64` `pow-exp_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `div-exp_binary64` `+-commutative_binary64` `flip-+_binary64` `associate-l/_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 128

Calls

4 calls:

5.0ms	(+.f64 (.f64 re re) (.f64 im im))
14.0ms	(.f64 (/.f64 1/2 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (+.f64 (.f64 re re) (*.f64 im im)) (/.f64 1 (sqrt.f64 (log.f64 10))))))
8.0ms	(pow.f64 (+.f64 (.f64 re re) (.f64 im im)) (/.f64 1 (sqrt.f64 (log.f64 10))))
5.0ms	(log.f64 (pow.f64 (+.f64 (.f64 re re) (.f64 im im)) (/.f64 1 (sqrt.f64 (log.f64 10)))))

series470.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+.f64 (.f64 re re) (.f64 im im))
172.0ms	(.f64 (/.f64 1/2 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (+.f64 (.f64 re re) (*.f64 im im)) (/.f64 1 (sqrt.f64 (log.f64 10))))))
145.0ms	(pow.f64 (+.f64 (.f64 re re) (.f64 im im)) (/.f64 1 (sqrt.f64 (log.f64 10))))
133.0ms	(log.f64 (pow.f64 (+.f64 (.f64 re re) (.f64 im im)) (/.f64 1 (sqrt.f64 (log.f64 10)))))

simplify92.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5244	3565

prune344.0ms

Filtered

89 candidates to 140 candidates (-57.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	139	14	153

Merged error: 6.7b

Counts

153 → 14

regimes1.2s

Accuracy

52.9% (11.6b remaining)

Error of 19.0b against oracle of 7.4b and baseline of 32.1b

bsearch98.0ms

Steps

Iters	Range		Point
6	19004756534618838754254613744958371140300260927819038728891494899246253040007565198003079529934310782880217875611648	111052023399680033801727686773044388304023090741845300961548700951545777374288636554884133811949217195161640002125824	6.515608694411437e+115
8	-6675110420798417/8254602048994769474255309139320571976856989469314398783249386078541779727448825929287769623244643560854287421769642635607536680617229461519539671538483430889193541937484454440136429963694163141453503639190799818814812942074243152169349951543234944945149040326527156224	-4894925706639197/270486799941460606132397969877256502537649830930494219329515883021657038109043128050901635014480480202073290236547649883587761950465374995072275956973025063377093982207490603094390537050330337819148407249004128462923790485888799610285259212168722675962643753419641855148032	-1.9775890958403967e-256
7	-2831026060444805/10830740992659433045228180406808920716548582325686783496759685861775864483615725089999900023844295226942934417817982702456930304	-5710056608704447/5545339388241629719156828368286167406872874150751633150340959161229242615611251246079948812208279156194782421922807143657948315648	-1.0550493251927753e-114
8	-14319523412352969732746000804465132386635085888037299394887596438972251766784	-12717808897180064994222637875676788418069176984113378874451279832984584192	-1.3312363646484332e+76

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	58	169
1	58	169

end0.0ms

sample685.0ms

Algorithm

intervals

Results

499.0ms

8000×

body

valid

Details

analyze5.0ms

sample27.0ms

simplify12.0ms

prune5.0ms

localize16.0ms

rewrite22.0ms

series142.0ms

simplify116.0ms

prune277.0ms

localize19.0ms

rewrite55.0ms

series223.0ms

simplify140.0ms

prune471.0ms

localize21.0ms

rewrite41.0ms

series221.0ms

simplify105.0ms

prune380.0ms

localize26.0ms

rewrite41.0ms

series470.0ms

simplify92.0ms

prune344.0ms

regimes1.2s

bsearch98.0ms

simplify4.0ms

end0.0ms

sample685.0ms

Profiling