Details

analyze1.9s

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

sample136.0ms

Algorithm

intervals

Results

44.0ms	256×	body	80	valid
36.0ms	244×	body	80	nan
28.0ms	157×	body	80	invalid

simplify46.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5140	41

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 28.4b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

6.5b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
11.5b	(sqrt.f64 (/.f64 d h))
13.0b	(sqrt.f64 (/.f64 d l))
14.6b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-exp-log_binary64`
41×	`prod-exp_binary64`
32×	`add-sqr-sqrt_binary64`
29×	`times-frac_binary64`
26×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
21×	`add-cbrt-cube_binary64`
16×	`associate-r_binary64` `div-exp_binary64`
14×	`sqrt-div_binary64`
13×	`pow1_binary64`
10×	`pow-exp_binary64`
9×	`cbrt-unprod_binary64` `frac-times_binary64`
6×	`associate-r/_binary64` `associate-l/_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `flip3--_binary64` `rem-sqrt-square_binary64` `flip--_binary64`
3×	`div-inv_binary64`
2×	`pow-to-exp_binary64` `sub-neg_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `*-commutative_binary64`
1×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`

Counts

4 → 125

Calls

4 calls:

16.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
3.0ms	(sqrt.f64 (/.f64 d h))
3.0ms	(sqrt.f64 (/.f64 d l))
12.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

series501.0ms

Counts

4 → 12

Calls

4 calls:

312.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
41.0ms	(sqrt.f64 (/.f64 d h))
47.0ms	(sqrt.f64 (/.f64 d l))
101.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

simplify97.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5037	3491

prune222.0ms

Filtered

97 candidates to 137 candidates (-41.2%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	114	23	137
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	115	23	138

Merged error: 13.8b

Counts

138 → 23

localize24.0ms

Local error

Found 4 expressions with local error:

3.3b	(/.f64 (.f64 M D) (.f64 d 2))
6.5b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
13.0b	(sqrt.f64 (/.f64 d l))
14.6b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

93×	`add-exp-log_binary64`
48×	`prod-exp_binary64`
37×	`add-cbrt-cube_binary64`
22×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64` `div-exp_binary64`
19×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
16×	`pow1_binary64` `cbrt-unprod_binary64` `associate-r_binary64`
13×	`sqrt-prod_binary64` `sqrt-div_binary64`
12×	`associate-*r/_binary64`
10×	`pow-exp_binary64`
9×	`frac-times_binary64`
7×	`pow-prod-down_binary64`
6×	`cbrt-undiv_binary64` `associate-*l/_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `flip--_binary64`
3×	`div-inv_binary64`
2×	`pow-to-exp_binary64` `sub-neg_binary64` `associate-l_binary64` `rem-sqrt-square_binary64` `*-commutative_binary64`
1×	`associate-/r_binary64` `pow1/2_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64`

Counts

4 → 124

Calls

4 calls:

6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
20.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
3.0ms	(sqrt.f64 (/.f64 d l))
11.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

series1.2s

Counts

4 → 12

Calls

4 calls:

25.0ms	(/.f64 (.f64 M D) (.f64 d 2))
1.1s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
45.0ms	(sqrt.f64 (/.f64 d l))
93.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

simplify139.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4954	4331
1	4954	4331

prune196.0ms

Filtered

87 candidates to 136 candidates (-56.3%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	128	8	136
Fresh	4	18	22
Picked	1	0	1
Done	0	0	0
Total	133	26	159

Merged error: 12.3b

Counts

159 → 26

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 d)
3.3b	(/.f64 (.f64 M D) (.f64 d 2))
6.5b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
14.6b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

102×	`add-exp-log_binary64`
55×	`prod-exp_binary64`
46×	`add-cbrt-cube_binary64`
24×	`pow1_binary64`
23×	`cbrt-unprod_binary64`
20×	`div-exp_binary64`
18×	`associate-*r/_binary64`
16×	`associate-r_binary64`
14×	`pow-prod-down_binary64`
13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
12×	`sqrt-div_binary64`
10×	`times-frac_binary64` `pow-exp_binary64`
9×	`frac-times_binary64`
6×	`cbrt-undiv_binary64` `associate-*l/_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `flip--_binary64`
3×	`cbrt-prod_binary64`
2×	`pow-to-exp_binary64` `sub-neg_binary64` `associate-l_binary64` `div-inv_binary64` `*-commutative_binary64`
1×	`associate-/r_binary64` `pow1/3_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64`

Counts

4 → 116

Calls

4 calls:

1.0ms	(cbrt.f64 d)
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
26.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
11.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

series1.4s

Counts

4 → 12

Calls

4 calls:

84.0ms	(cbrt.f64 d)
26.0ms	(/.f64 (.f64 M D) (.f64 d 2))
1.2s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
97.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

simplify124.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4988	5016
1	4988	5016

prune191.0ms

Filtered

74 candidates to 128 candidates (-73.0%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	121	7	128
Fresh	4	21	25
Picked	1	0	1
Done	0	0	0
Total	126	28	154

Merged error: 8.6b

Counts

154 → 28

localize35.0ms

Local error

Found 4 expressions with local error:

3.3b	(/.f64 (.f64 M D) (.f64 d 2))
5.2b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (*.f64 (cbrt.f64 h) (cbrt.f64 h)))
5.5b	(.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
6.5b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

291×	`add-exp-log_binary64`
189×	`prod-exp_binary64`
70×	`add-cbrt-cube_binary64`
51×	`cbrt-unprod_binary64`
45×	`div-exp_binary64`
36×	`pow1_binary64`
30×	`pow-exp_binary64`
26×	`associate-r_binary64`
22×	`pow-prod-down_binary64`
19×	`times-frac_binary64`
18×	`-un-lft-identity_binary64` `associate-r/_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
12×	`sqrt-div_binary64`
9×	`cbrt-undiv_binary64` `frac-times_binary64` `cbrt-prod_binary64`
6×	`pow-to-exp_binary64` `associate-*l/_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `flip--_binary64`
3×	`associate-l_binary64` `*-commutative_binary64`
2×	`sub-neg_binary64` `div-inv_binary64`
1×	`associate-/r_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64`

Counts

4 → 172

Calls

4 calls:

6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
13.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (*.f64 (cbrt.f64 h) (cbrt.f64 h)))
20.0ms	(.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
31.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))

series1.6s

Counts

4 → 12

Calls

4 calls:

22.0ms	(/.f64 (.f64 M D) (.f64 d 2))
186.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (*.f64 (cbrt.f64 h) (cbrt.f64 h)))
106.0ms	(.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
1.2s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))

simplify128.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4990	6943
1	4990	6943

prune139.0ms

Filtered

81 candidates to 184 candidates (-127.2%)

Pruning

28 alts after pruning (27 fresh and 1 done)

	Pruned	Kept	Total
New	183	1	184
Fresh	1	26	27
Picked	0	1	1
Done	0	0	0
Total	184	28	212

Merged error: 8.1b

Counts

212 → 28

regimes503.0ms

Accuracy

6.6% (4.7b remaining)

Error of 14.5b against oracle of 9.8b and baseline of 14.8b

bsearch190.0ms

Steps

Iters	Range		Point
8	1.8215368600842543e+157	5.599041933329052e+160	1.6110136472930255e+160
7	1.0708266878166777e-93	2.1571706285488835e-92	1.2154114847819588e-93

simplify6.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	188	239
1	188	239

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	8000×	body	80	valid
1.2s	8541×	body	80	nan
845.0ms	4757×	body	80	invalid

Details

analyze1.9s

sample136.0ms

simplify46.0ms

prune8.0ms

localize20.0ms

rewrite40.0ms

series501.0ms

simplify97.0ms

prune222.0ms

localize24.0ms

rewrite47.0ms

series1.2s

simplify139.0ms

prune196.0ms

localize33.0ms

rewrite51.0ms

series1.4s

simplify124.0ms

prune191.0ms

localize35.0ms

rewrite82.0ms

series1.6s

simplify128.0ms

prune139.0ms

regimes503.0ms

bsearch190.0ms

simplify6.0ms

end0.0ms

sample4.2s

Profiling