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

sample139.0ms

Algorithm

intervals

Results

45.0ms	256×	body	80	valid
40.0ms	255×	body	80	nan
25.0ms	134×	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

prune10.0ms

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: 26.0b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

5.8b	(.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))))
9.9b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
11.2b	(sqrt.f64 (/.f64 d h))
11.5b	(sqrt.f64 (/.f64 d l))

rewrite42.0ms

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))))
12.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
6.0ms	(sqrt.f64 (/.f64 d h))
3.0ms	(sqrt.f64 (/.f64 d l))

series174.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(.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))))
32.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
14.0ms	(sqrt.f64 (/.f64 d h))
14.0ms	(sqrt.f64 (/.f64 d l))

simplify54.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5029	2281

prune270.0ms

Filtered

97 candidates to 137 candidates (-41.2%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	117	20	137
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	118	20	138

Merged error: 11.5b

Counts

138 → 20

localize24.0ms

Local error

Found 4 expressions with local error:

3.9b	(/.f64 (.f64 M D) (.f64 d 2))
5.8b	(.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))))
9.9b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
11.5b	(sqrt.f64 (/.f64 d l))

rewrite50.0ms

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

series574.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
523.0ms	(.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))))
31.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
14.0ms	(sqrt.f64 (/.f64 d l))

simplify66.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4963	2791
1	4963	2791

prune240.0ms

Filtered

87 candidates to 136 candidates (-56.3%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	128	8	136
Fresh	2	17	19
Picked	1	0	1
Done	0	0	0
Total	131	25	156

Merged error: 10.3b

Counts

156 → 25

localize32.0ms

Local error

Found 4 expressions with local error:

1.6b	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
3.9b	(/.f64 (.f64 M D) (.f64 d 2))
5.8b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
9.9b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

102×	`add-exp-log_binary64`
55×	`prod-exp_binary64`
46×	`add-cbrt-cube_binary64`
37×	`sqrt-div_binary64`
30×	`associate-*r/_binary64` `add-sqr-sqrt_binary64` `times-frac_binary64`
29×	`frac-times_binary64`
25×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
23×	`cbrt-unprod_binary64`
22×	`sqrt-prod_binary64`
20×	`div-exp_binary64`
16×	`associate-r_binary64` `associate-*l/_binary64`
14×	`pow-prod-down_binary64`
10×	`cbrt-prod_binary64` `pow-exp_binary64`
8×	`flip3--_binary64` `flip--_binary64`
6×	`cbrt-undiv_binary64`
4×	`add-log-exp_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 → 152

Calls

4 calls:

4.0ms	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
37.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.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))

series616.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
543.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
31.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

simplify73.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4957	4465
1	4957	4465

prune295.0ms

Filtered

107 candidates to 164 candidates (-53.3%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	158	6	164
Fresh	6	18	24
Picked	1	0	1
Done	0	0	0
Total	165	24	189

Merged error: 8.1b

Counts

189 → 24

localize39.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 h)
3.9b	(/.f64 (.f64 M D) (.f64 d 2))
5.8b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 (cbrt.f64 l)) (cbrt.f64 (cbrt.f64 l))))) (sqrt.f64 (/.f64 d (cbrt.f64 (cbrt.f64 l))))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
9.9b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

113×	`add-exp-log_binary64`
96×	`sqrt-div_binary64`
81×	`frac-times_binary64`
78×	`associate-*r/_binary64`
64×	`prod-exp_binary64`
57×	`add-cbrt-cube_binary64`
36×	`associate-*l/_binary64`
35×	`pow1_binary64`
32×	`cbrt-unprod_binary64`
23×	`pow-prod-down_binary64`
20×	`div-exp_binary64`
16×	`flip3--_binary64` `associate-r_binary64` `flip--_binary64`
13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
10×	`times-frac_binary64` `pow-exp_binary64`
6×	`cbrt-undiv_binary64`
4×	`add-log-exp_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 → 158

Calls

4 calls:

1.0ms	(cbrt.f64 h)
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
49.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 (cbrt.f64 l)) (cbrt.f64 (cbrt.f64 l))))) (sqrt.f64 (/.f64 d (cbrt.f64 (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))

series466.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(cbrt.f64 h)
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
414.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 (cbrt.f64 l)) (cbrt.f64 (cbrt.f64 l))))) (sqrt.f64 (/.f64 d (cbrt.f64 (cbrt.f64 l))))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
31.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

simplify84.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5025	6596

prune224.0ms

Filtered

109 candidates to 170 candidates (-56.0%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	166	4	170
Fresh	0	23	23
Picked	1	0	1
Done	0	0	0
Total	167	27	194

Merged error: 7.4b

Counts

194 → 27

regimes1.4s

Accuracy

15.4% (5.9b remaining)

Error of 15.2b against oracle of 9.3b and baseline of 16.3b

bsearch3.0ms

simplify7.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	253	226
1	253	226

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.4s	8000×	body	80	valid
1.2s	8433×	body	80	nan
898.0ms	4870×	body	80	invalid

Details

analyze2.0s

sample139.0ms

simplify40.0ms

prune10.0ms

localize18.0ms

rewrite42.0ms

series174.0ms

simplify54.0ms

prune270.0ms

localize24.0ms

rewrite50.0ms

series574.0ms

simplify66.0ms

prune240.0ms

localize32.0ms

rewrite68.0ms

series616.0ms

simplify73.0ms

prune295.0ms

localize39.0ms

rewrite81.0ms

series466.0ms

simplify84.0ms

prune224.0ms

regimes1.4s

bsearch3.0ms

simplify7.0ms

end0.0ms

sample4.3s

Profiling