Details

analyze2.0s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	81.1%	18.9%	7
0%	68.6%	31.4%	8
0%	59.2%	40.8%	9
0%	59.2%	40.8%	10
0%	59.2%	40.8%	11
0.4%	49.5%	50.1%	12
0.8%	44.4%	54.8%	13
1.4%	39.9%	58.7%	14

sample212.0ms

Algorithm

intervals

Results

68.0ms	256×	body	80	valid
56.0ms	263×	body	80	nan
48.0ms	182×	body	80	invalid

simplify23.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5401	35

prune9.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 23.8b

Counts

2 → 1

localize28.0ms

Local error

Found 4 expressions with local error:

6.6b	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1.0 2.0)) (pow.f64 (/.f64 d l) (/.f64 1.0 2.0))) (-.f64 1.0 (.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))))
10.1b	(pow.f64 (/.f64 d h) (/.f64 1.0 2.0))
10.4b	(pow.f64 (/.f64 d l) (/.f64 1.0 2.0))
12.6b	(.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

205×	`add-exp-log_binary64`
107×	`prod-exp_binary64`
55×	`div-exp_binary64`
45×	`times-frac_binary64`
40×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `pow-exp_binary64`
30×	`add-cbrt-cube_binary64`
26×	`pow-unpow_binary64` `unpow-prod-down_binary64`
16×	`associate-r_binary64`
14×	`pow-to-exp_binary64`
13×	`cbrt-unprod_binary64`
10×	`pow1_binary64`
5×	`cbrt-undiv_binary64` `div-inv_binary64`
4×	`add-log-exp_binary64`
3×	`associate-r/_binary64` `associate-l/_binary64`
2×	`pow-prod-down_binary64` `sub-neg_binary64` `pow-pow_binary64` `sqr-pow_binary64` `associate-l_binary64` `*-commutative_binary64`
1×	`flip3--_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `flip--_binary64` `frac-times_binary64`

Counts

4 → 174

Calls

4 calls:

17.0ms	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1.0 2.0)) (pow.f64 (/.f64 d l) (/.f64 1.0 2.0))) (-.f64 1.0 (.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))))
6.0ms	(pow.f64 (/.f64 d h) (/.f64 1.0 2.0))
8.0ms	(pow.f64 (/.f64 d l) (/.f64 1.0 2.0))
13.0ms	(.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))

series586.0ms

Counts

4 → 12

Calls

4 calls:

312.0ms	(.f64 (.f64 (pow.f64 (/.f64 d h) (/.f64 1.0 2.0)) (pow.f64 (/.f64 d l) (/.f64 1.0 2.0))) (-.f64 1.0 (.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))))
14.0ms	(pow.f64 (/.f64 d h) (/.f64 1.0 2.0))
14.0ms	(pow.f64 (/.f64 d l) (/.f64 1.0 2.0))
246.0ms	(.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))

simplify55.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5226	3512

prune384.0ms

Filtered

109 candidates to 186 candidates (-70.6%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	165	21	186
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	166	21	187

Merged error: 10.0b

Counts

187 → 21

localize38.0ms

Local error

Found 4 expressions with local error:

3.2b	(pow.f64 (/.f64 (cbrt.f64 d) h) (/.f64 1.0 2.0))
6.6b	(.f64 (.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (/.f64 1.0 2.0)) (pow.f64 (/.f64 (cbrt.f64 d) h) (/.f64 1.0 2.0))) (pow.f64 (/.f64 d l) (/.f64 1.0 2.0))) (-.f64 1.0 (.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))))
10.4b	(pow.f64 (/.f64 d l) (/.f64 1.0 2.0))
12.6b	(.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

425×	`add-exp-log_binary64`
291×	`prod-exp_binary64`
122×	`pow-exp_binary64`
80×	`div-exp_binary64`
55×	`pow-to-exp_binary64`
54×	`times-frac_binary64`
46×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
35×	`unpow-prod-down_binary64`
34×	`add-cbrt-cube_binary64`
26×	`pow-unpow_binary64`
16×	`cbrt-unprod_binary64` `associate-r_binary64`
10×	`pow1_binary64`
9×	`cbrt-prod_binary64`
5×	`cbrt-undiv_binary64` `div-inv_binary64`
4×	`add-log-exp_binary64`
3×	`associate-r/_binary64` `associate-l/_binary64`
2×	`pow-prod-down_binary64` `sub-neg_binary64` `pow-pow_binary64` `sqr-pow_binary64` `associate-l_binary64` `*-commutative_binary64`
1×	`flip3--_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `flip--_binary64` `frac-times_binary64`

Counts

4 → 236

Calls

4 calls:

7.0ms	(pow.f64 (/.f64 (cbrt.f64 d) h) (/.f64 1.0 2.0))
28.0ms	(.f64 (.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (/.f64 1.0 2.0)) (pow.f64 (/.f64 (cbrt.f64 d) h) (/.f64 1.0 2.0))) (pow.f64 (/.f64 d l) (/.f64 1.0 2.0))) (-.f64 1.0 (.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))))
6.0ms	(pow.f64 (/.f64 d l) (/.f64 1.0 2.0))
13.0ms	(.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))

series683.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(pow.f64 (/.f64 (cbrt.f64 d) h) (/.f64 1.0 2.0))
380.0ms	(.f64 (.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (/.f64 1.0 2.0)) (pow.f64 (/.f64 (cbrt.f64 d) h) (/.f64 1.0 2.0))) (pow.f64 (/.f64 d l) (/.f64 1.0 2.0))) (-.f64 1.0 (.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))))
14.0ms	(pow.f64 (/.f64 d l) (/.f64 1.0 2.0))
250.0ms	(.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))

simplify69.0ms

Algorithm

egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	6185	6153

prune405.0ms

Filtered

116 candidates to 248 candidates (-113.8%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	241	7	248
Fresh	2	18	20
Picked	1	0	1
Done	0	0	0
Total	244	25	269

Merged error: 9.9b

Counts

269 → 25

localize49.0ms

Local error

Found 4 expressions with local error:

3.2b	(pow.f64 (/.f64 (cbrt.f64 d) h) (/.f64 1.0 2.0))
3.3b	(pow.f64 (/.f64 d (cbrt.f64 l)) (/.f64 1.0 2.0))
6.6b	(.f64 (.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (/.f64 1.0 2.0)) (pow.f64 (/.f64 (cbrt.f64 d) h) (/.f64 1.0 2.0))) (.f64 (pow.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 1.0 2.0)) (pow.f64 (/.f64 d (cbrt.f64 l)) (/.f64 1.0 2.0)))) (-.f64 1.0 (.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))))
12.6b	(.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

3520×	`add-exp-log_binary64`
2889×	`prod-exp_binary64`
1398×	`pow-exp_binary64`
620×	`div-exp_binary64`
523×	`pow-to-exp_binary64`
136×	`1-exp_binary64` `rec-exp_binary64`
63×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
44×	`unpow-prod-down_binary64`
43×	`add-cbrt-cube_binary64`
26×	`pow-unpow_binary64`
23×	`cbrt-unprod_binary64`
18×	`cbrt-prod_binary64`
16×	`associate-r_binary64`
13×	`pow1_binary64`
5×	`cbrt-undiv_binary64` `div-inv_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64`
3×	`associate-r/_binary64` `associate-l/_binary64`
2×	`sub-neg_binary64` `pow-pow_binary64` `sqr-pow_binary64` `associate-l_binary64` `*-commutative_binary64`
1×	`flip3--_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `flip--_binary64` `frac-times_binary64`

Counts

4 → 809

Calls

4 calls:

7.0ms	(pow.f64 (/.f64 (cbrt.f64 d) h) (/.f64 1.0 2.0))
7.0ms	(pow.f64 (/.f64 d (cbrt.f64 l)) (/.f64 1.0 2.0))
58.0ms	(.f64 (.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (/.f64 1.0 2.0)) (pow.f64 (/.f64 (cbrt.f64 d) h) (/.f64 1.0 2.0))) (.f64 (pow.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 1.0 2.0)) (pow.f64 (/.f64 d (cbrt.f64 l)) (/.f64 1.0 2.0)))) (-.f64 1.0 (.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))))
13.0ms	(.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))

series666.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(pow.f64 (/.f64 (cbrt.f64 d) h) (/.f64 1.0 2.0))
46.0ms	(pow.f64 (/.f64 d (cbrt.f64 l)) (/.f64 1.0 2.0))
325.0ms	(.f64 (.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (/.f64 1.0 2.0)) (pow.f64 (/.f64 (cbrt.f64 d) h) (/.f64 1.0 2.0))) (.f64 (pow.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 1.0 2.0)) (pow.f64 (/.f64 d (cbrt.f64 l)) (/.f64 1.0 2.0)))) (-.f64 1.0 (.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))))
256.0ms	(.f64 (.f64 (/.f64 1.0 2.0) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 h l))

simplify215.0ms

Algorithm

egg-herbie

Counts

821 → 821

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5070	33692

prune579.0ms

Filtered

126 candidates to 821 candidates (-551.6%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	815	6	821
Fresh	4	20	24
Picked	1	0	1
Done	0	0	0
Total	820	26	846

Merged error: 8.2b

Counts

846 → 26

localize51.0ms

Local error

Found 4 expressions with local error:

3.3b	(pow.f64 (/.f64 d (cbrt.f64 l)) (/.f64 1.0 2.0))
5.0b	(/.f64 (.f64 h (.f64 1.0 (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0))) (*.f64 2.0 l))
6.6b	(.f64 (.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (/.f64 1.0 2.0)) (pow.f64 (/.f64 (cbrt.f64 d) h) (/.f64 1.0 2.0))) (.f64 (pow.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 1.0 2.0)) (pow.f64 (/.f64 d (cbrt.f64 l)) (/.f64 1.0 2.0)))) (-.f64 1.0 (/.f64 (.f64 h (.f64 1.0 (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0))) (*.f64 2.0 l))))
7.0b	(.f64 h (.f64 1.0 (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)))

rewrite199.0ms

Algorithm

rewrite-expression-head

Rules

3491×	`add-exp-log_binary64`
2881×	`prod-exp_binary64`
1391×	`pow-exp_binary64`
604×	`div-exp_binary64`
521×	`pow-to-exp_binary64`
136×	`1-exp_binary64` `rec-exp_binary64`
48×	`add-cbrt-cube_binary64`
28×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64` `times-frac_binary64`
26×	`add-cube-cbrt_binary64`
25×	`cbrt-unprod_binary64`
22×	`unpow-prod-down_binary64`
13×	`pow-unpow_binary64`
12×	`pow1_binary64`
9×	`cbrt-prod_binary64`
6×	`associate-r_binary64` `cbrt-undiv_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `associate-l_binary64`
3×	`div-inv_binary64`
2×	`sub-neg_binary64` `associate-r/_binary64` `-commutative_binary64`
1×	`associate-/r_binary64` `flip3--_binary64` `pow-pow_binary64` `sqr-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `associate-/l_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

4 → 762

Calls

4 calls:

7.0ms	(pow.f64 (/.f64 d (cbrt.f64 l)) (/.f64 1.0 2.0))
11.0ms	(/.f64 (.f64 h (.f64 1.0 (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0))) (*.f64 2.0 l))
59.0ms	(.f64 (.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (/.f64 1.0 2.0)) (pow.f64 (/.f64 (cbrt.f64 d) h) (/.f64 1.0 2.0))) (.f64 (pow.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 1.0 2.0)) (pow.f64 (/.f64 d (cbrt.f64 l)) (/.f64 1.0 2.0)))) (-.f64 1.0 (/.f64 (.f64 h (.f64 1.0 (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0))) (*.f64 2.0 l))))
8.0ms	(.f64 h (.f64 1.0 (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)))

series710.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(pow.f64 (/.f64 d (cbrt.f64 l)) (/.f64 1.0 2.0))
215.0ms	(/.f64 (.f64 h (.f64 1.0 (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0))) (*.f64 2.0 l))
325.0ms	(.f64 (.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (/.f64 1.0 2.0)) (pow.f64 (/.f64 (cbrt.f64 d) h) (/.f64 1.0 2.0))) (.f64 (pow.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 1.0 2.0)) (pow.f64 (/.f64 d (cbrt.f64 l)) (/.f64 1.0 2.0)))) (-.f64 1.0 (/.f64 (.f64 h (.f64 1.0 (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0))) (*.f64 2.0 l))))
124.0ms	(.f64 h (.f64 1.0 (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)))

simplify208.0ms

Algorithm

egg-herbie

Counts

774 → 774

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5046	33703

prune257.0ms

Filtered

87 candidates to 774 candidates (-789.7%)

Pruning

30 alts after pruning (30 fresh and 0 done)

	Pruned	Kept	Total
New	767	7	774
Fresh	2	23	25
Picked	1	0	1
Done	0	0	0
Total	770	30	800

Merged error: 8.0b

Counts

800 → 30

regimes1.4s

Accuracy

10.6% (6.5b remaining)

Error of 15.0b against oracle of 8.5b and baseline of 15.8b

bsearch502.0ms

Steps

Iters	Range		Point
8	5.1223268688161886e+123	3.827998108312392e+127	6.009050044890221e+124
5	2.310090923512182e+33	7.842364856305733e+33	2.3451948097595518e+33
10	-9.258688367867694e-54	-4.676280766776147e-72	-9.103863212509198e-54
3	-1.2486150746478509e+30	-1.0576687913663744e+30	-1.0934712194816513e+30

simplify6.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	332	290
1	332	290

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	8000×	body	80	valid
1.2s	8455×	body	80	nan
884.0ms	4900×	body	80	invalid

Details

analyze2.0s

sample212.0ms

simplify23.0ms

prune9.0ms

localize28.0ms

rewrite53.0ms

series586.0ms

simplify55.0ms

prune384.0ms

localize38.0ms

rewrite69.0ms

series683.0ms

simplify69.0ms

prune405.0ms

localize49.0ms

rewrite203.0ms

series666.0ms

simplify215.0ms

prune579.0ms

localize51.0ms

rewrite199.0ms

series710.0ms

simplify208.0ms

prune257.0ms

regimes1.4s

bsearch502.0ms

simplify6.0ms

end0.0ms

sample4.2s

Profiling