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

sample134.0ms

Algorithm

intervals

Results

45.0ms	256×	body	80	valid
35.0ms	220×	body	80	nan
26.0ms	146×	body	80	invalid

simplify44.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4965	27
1	4965	27

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: 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))

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

series371.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(.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))))
14.0ms	(sqrt.f64 (/.f64 d l))
14.0ms	(sqrt.f64 (/.f64 d h))
231.0ms	(.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

prune206.0ms

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

localize24.0ms

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))

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:

7.0ms	(/.f64 (.f64 M D) (.f64 d 2))
22.0ms	(.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))

series373.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
318.0ms	(.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))
35.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

simplify63.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4963	2791
1	4963	2791

prune164.0ms

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

localize30.0ms

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))

rewrite53.0ms

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))
24.0ms	(.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))

series502.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
28.0ms	(sqrt.f64 (/.f64 (cbrt.f64 d) l))
433.0ms	(.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))))
34.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

simplify69.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5008	3478

prune192.0ms

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

localize30.0ms

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)))

rewrite56.0ms

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)
27.0ms	(.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)))

series532.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt.f64 (/.f64 (cbrt.f64 d) l))
25.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h)
31.0ms	(/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)
446.0ms	(.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)))

simplify73.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4972	3519
1	4972	3519

prune118.0ms

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

regimes992.0ms

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 (2.0ms)

Iter	Nodes	Cost
0	91	51
1	91	51

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	8000×	body	80	valid
1.2s	8217×	body	80	nan
859.0ms	4759×	body	80	invalid

Details

analyze2.0s

sample134.0ms

simplify44.0ms

prune8.0ms

localize19.0ms

rewrite40.0ms

series371.0ms

simplify55.0ms

prune206.0ms

localize24.0ms

rewrite50.0ms

series373.0ms

simplify63.0ms

prune164.0ms

localize30.0ms

rewrite53.0ms

series502.0ms

simplify69.0ms

prune192.0ms

localize30.0ms

rewrite56.0ms

series532.0ms

simplify73.0ms

prune118.0ms

regimes992.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample4.2s

Profiling