Details

analyze2.1s

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

sample137.0ms

Algorithm

intervals

Results

50.0ms	256×	body	80	valid
32.0ms	220×	body	80	nan
27.0ms	146×	body	80	invalid

simplify40.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4965	27
1	4965	27

prune13.0ms

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: 26.6b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

7.0b	(.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))))
11.2b	(sqrt.f64 (/.f64 d l))
11.3b	(sqrt.f64 (/.f64 d h))
12.9b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite37.0ms

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:

15.0ms	(.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 l))
3.0ms	(sqrt.f64 (/.f64 d h))
11.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

series171.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(.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))))
13.0ms	(sqrt.f64 (/.f64 d l))
14.0ms	(sqrt.f64 (/.f64 d h))
32.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

simplify55.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5029	2281

prune265.0ms

Filtered

95 candidates to 137 candidates (-44.2%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	119	18	137
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	18	138

Merged error: 14.7b

Counts

138 → 18

localize27.0ms

Local error

Found 4 expressions with local error:

2.8b	(/.f64 (.f64 M D) (.f64 d 2))
7.0b	(.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))))
11.2b	(sqrt.f64 (/.f64 d l))
12.9b	(.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))
21.0ms	(.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))
12.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

series363.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/.f64 (.f64 M D) (.f64 d 2))
309.0ms	(.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))))
14.0ms	(sqrt.f64 (/.f64 d l))
30.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

simplify66.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4963	2791
1	4963	2791

prune227.0ms

Filtered

87 candidates to 136 candidates (-56.3%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	129	7	136
Fresh	2	15	17
Picked	1	0	1
Done	0	0	0
Total	132	22	154

Merged error: 14.0b

Counts

154 → 22

localize27.0ms

Local error

Found 4 expressions with local error:

2.8b	(/.f64 (.f64 M D) (.f64 d 2))
3.2b	(sqrt.f64 (/.f64 (cbrt.f64 d) l))
7.0b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
12.9b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

102×	`add-exp-log_binary64`
55×	`prod-exp_binary64`
46×	`add-cbrt-cube_binary64`
30×	`add-sqr-sqrt_binary64` `times-frac_binary64`
25×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
23×	`cbrt-unprod_binary64`
22×	`sqrt-prod_binary64`
20×	`div-exp_binary64`
18×	`associate-*r/_binary64`
16×	`associate-r_binary64`
14×	`pow-prod-down_binary64`
13×	`sqrt-div_binary64`
10×	`cbrt-prod_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×	`rem-sqrt-square_binary64` `div-inv_binary64`
2×	`pow-to-exp_binary64` `sub-neg_binary64` `associate-l_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 → 140

Calls

4 calls:

7.0ms	(/.f64 (.f64 M D) (.f64 d 2))
4.0ms	(sqrt.f64 (/.f64 (cbrt.f64 d) l))
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 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) 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))

series487.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
29.0ms	(sqrt.f64 (/.f64 (cbrt.f64 d) l))
421.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
30.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

simplify66.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5008	3478

prune258.0ms

Filtered

95 candidates to 152 candidates (-60.0%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	145	7	152
Fresh	3	18	21
Picked	1	0	1
Done	0	0	0
Total	149	25	174

Merged error: 11.9b

Counts

174 → 25

localize26.0ms

Local error

Found 4 expressions with local error:

3.2b	(sqrt.f64 (/.f64 (cbrt.f64 d) l))
5.5b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h)
5.9b	(/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)
7.0b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-exp-log_binary64`
51×	`prod-exp_binary64`
36×	`add-cbrt-cube_binary64`
29×	`add-sqr-sqrt_binary64`
25×	`pow1_binary64`
24×	`*-un-lft-identity_binary64`
23×	`times-frac_binary64`
22×	`sqrt-prod_binary64`
21×	`add-cube-cbrt_binary64`
19×	`cbrt-unprod_binary64`
17×	`associate-*r/_binary64` `div-exp_binary64`
14×	`pow-prod-down_binary64`
13×	`sqrt-div_binary64`
10×	`cbrt-prod_binary64` `pow-exp_binary64`
9×	`associate-r_binary64` `frac-times_binary64`
6×	`associate-*l/_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `flip--_binary64`
3×	`associate-/r*_binary64` `cbrt-undiv_binary64` `rem-sqrt-square_binary64`
2×	`pow-to-exp_binary64` `sub-neg_binary64` `associate-l_binary64` `difference-of-squares_binary64` `div-inv_binary64` `*-commutative_binary64`
1×	`pow1/2_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `distribute-lft-out--_binary64`

Counts

4 → 130

Calls

4 calls:

4.0ms	(sqrt.f64 (/.f64 (cbrt.f64 d) l))
8.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h)
10.0ms	(/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)
29.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)))

series503.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(sqrt.f64 (/.f64 (cbrt.f64 d) l))
27.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h)
30.0ms	(/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)
418.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)))

simplify68.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4972	3519
1	4972	3519

prune155.0ms

Filtered

92 candidates to 142 candidates (-54.3%)

Pruning

31 alts after pruning (31 fresh and 0 done)

	Pruned	Kept	Total
New	133	9	142
Fresh	2	22	24
Picked	1	0	1
Done	0	0	0
Total	136	31	167

Merged error: 10.8b

Counts

167 → 31

regimes1.3s

Accuracy

0% (3.5b remaining)

Error of 14.1b against oracle of 10.6b and baseline of 14.1b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	91	51
1	91	51

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.5s	8000×	body	80	valid
1.2s	8217×	body	80	nan
910.0ms	4759×	body	80	invalid

Details

analyze2.1s

sample137.0ms

simplify40.0ms

prune13.0ms

localize19.0ms

rewrite37.0ms

series171.0ms

simplify55.0ms

prune265.0ms

localize27.0ms

rewrite47.0ms

series363.0ms

simplify66.0ms

prune227.0ms

localize27.0ms

rewrite55.0ms

series487.0ms

simplify66.0ms

prune258.0ms

localize26.0ms

rewrite57.0ms

series503.0ms

simplify68.0ms

prune155.0ms

regimes1.3s

bsearch0.0ms

simplify3.0ms

end0.0ms

sample4.4s

Profiling