Details

analyze2.2s

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

sample145.0ms

Algorithm

intervals

Results

45.0ms	256×	body	80	valid
35.0ms	252×	body	80	nan
30.0ms	165×	body	80	invalid

simplify43.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4965	27
1	4965	27

prune14.0ms

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: 25.2b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

6.8b	(.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))))
9.3b	(sqrt.f64 (/.f64 d h))
11.5b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
13.1b	(sqrt.f64 (/.f64 d 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 h))
11.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
3.0ms	(sqrt.f64 (/.f64 d l))

series190.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(.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))))
15.0ms	(sqrt.f64 (/.f64 d h))
38.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
15.0ms	(sqrt.f64 (/.f64 d l))

simplify55.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5029	2281

prune276.0ms

Filtered

97 candidates to 137 candidates (-41.2%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	116	21	137
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	21	138

Merged error: 14.2b

Counts

138 → 21

localize24.0ms

Local error

Found 4 expressions with local error:

3.9b	(/.f64 (.f64 M D) (.f64 d 2))
6.8b	(.f64 (.f64 (sqrt.f64 (/.f64 d 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))))
9.3b	(sqrt.f64 (/.f64 d h))
11.5b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite48.0ms

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))
23.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 d 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))))
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))

series348.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/.f64 (.f64 M D) (.f64 d 2))
291.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 d 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))))
15.0ms	(sqrt.f64 (/.f64 d h))
34.0ms	(.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	5037	2813

prune227.0ms

Filtered

85 candidates to 136 candidates (-60.0%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	129	7	136
Fresh	5	15	20
Picked	1	0	1
Done	0	0	0
Total	135	22	157

Merged error: 11.5b

Counts

157 → 22

localize29.0ms

Local error

Found 4 expressions with local error:

2.4b	(sqrt.f64 (/.f64 d (cbrt.f64 h)))
3.9b	(/.f64 (.f64 M D) (.f64 d 2))
6.8b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 1 (cbrt.f64 h))) (sqrt.f64 (/.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))))
11.5b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite54.0ms

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:

4.0ms	(sqrt.f64 (/.f64 d (cbrt.f64 h)))
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
23.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 1 (cbrt.f64 h))) (sqrt.f64 (/.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))

series531.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(sqrt.f64 (/.f64 d (cbrt.f64 h)))
7.0ms	(/.f64 (.f64 M D) (.f64 d 2))
449.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 1 (cbrt.f64 h))) (sqrt.f64 (/.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))))
35.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

simplify74.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4998	3577
1	4998	3577

prune290.0ms

Filtered

97 candidates to 152 candidates (-56.7%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	147	5	152
Fresh	0	21	21
Picked	1	0	1
Done	0	0	0
Total	148	26	174

Merged error: 10.4b

Counts

174 → 26

localize29.0ms

Local error

Found 4 expressions with local error:

3.9b	(/.f64 (.f64 M D) (.f64 d 2))
4.9b	(/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)
6.2b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h)
6.8b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 1 (cbrt.f64 h))) (sqrt.f64 (/.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)) h) l)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

104×	`add-exp-log_binary64`
55×	`prod-exp_binary64`
48×	`add-cbrt-cube_binary64`
24×	`pow1_binary64`
23×	`cbrt-unprod_binary64`
21×	`div-exp_binary64`
17×	`associate-*r/_binary64`
14×	`pow-prod-down_binary64`
12×	`sqrt-div_binary64`
11×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
10×	`pow-exp_binary64`
9×	`associate-r_binary64` `frac-times_binary64`
8×	`add-cube-cbrt_binary64`
7×	`cbrt-undiv_binary64`
6×	`associate-*l/_binary64`
4×	`associate-/r*_binary64` `add-log-exp_binary64` `flip3--_binary64` `times-frac_binary64` `flip--_binary64`
2×	`pow-to-exp_binary64` `sub-neg_binary64` `associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `associate-/l_binary64` `div-inv_binary64` `-commutative_binary64`
1×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `distribute-lft-out--_binary64`

Counts

4 → 116

Calls

4 calls:

6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
10.0ms	(/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)
8.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h)
29.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 1 (cbrt.f64 h))) (sqrt.f64 (/.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)) h) l)))

series518.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/.f64 (.f64 M D) (.f64 d 2))
34.0ms	(/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)
29.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h)
448.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 1 (cbrt.f64 h))) (sqrt.f64 (/.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)) h) l)))

simplify55.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4970	3367
1	4970	3367

prune131.0ms

Filtered

72 candidates to 128 candidates (-77.8%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	120	8	128
Fresh	5	20	25
Picked	1	0	1
Done	0	0	0
Total	126	28	154

Merged error: 10.1b

Counts

154 → 28

regimes1.2s

Accuracy

-2.5% (5.0b remaining)

Error of 14.4b against oracle of 9.3b and baseline of 14.2b

bsearch341.0ms

Steps

Iters	Range		Point
5	3.3340091192664687e-15	8.74708550056944e-15	4.693898141863818e-15
9	-1.4780598355263286e-297	-1.914532670783506e-304	-1.9552656861105664e-304

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	164	139
1	164	139

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	8000×	body	80	valid
1.2s	8169×	body	80	nan
872.0ms	4878×	body	80	invalid

Details

analyze2.2s

sample145.0ms

simplify43.0ms

prune14.0ms

localize19.0ms

rewrite37.0ms

series190.0ms

simplify55.0ms

prune276.0ms

localize24.0ms

rewrite48.0ms

series348.0ms

simplify66.0ms

prune227.0ms

localize29.0ms

rewrite54.0ms

series531.0ms

simplify74.0ms

prune290.0ms

localize29.0ms

rewrite59.0ms

series518.0ms

simplify55.0ms

prune131.0ms

regimes1.2s

bsearch341.0ms

simplify4.0ms

end0.0ms

sample4.2s

Profiling