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

sample150.0ms

Algorithm

intervals

Results

47.0ms	256×	body	128	valid
43.0ms	268×	body	128	nan
30.0ms	157×	body	128	invalid

simplify38.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5139	41

prune5.0ms

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: 27.1b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

5.7b	(.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))))
11.1b	(sqrt.f64 (/.f64 d h))
12.6b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
15.1b	(sqrt.f64 (/.f64 d l))

rewrite53.0ms

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))
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))

series835.0ms

Counts

4 → 12

Calls

4 calls:

534.0ms	(.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))))
72.0ms	(sqrt.f64 (/.f64 d h))
160.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
68.0ms	(sqrt.f64 (/.f64 d l))

simplify82.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5046	3491

prune215.0ms

Filtered

97 candidates to 137 candidates (-41.2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	120	17	137
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	121	17	138

Merged error: 11.9b

Counts

138 → 17

localize25.0ms

Local error

Found 4 expressions with local error:

4.6b	(/.f64 (.f64 M D) (.f64 d 2))
5.7b	(.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))))
12.6b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
15.1b	(sqrt.f64 (/.f64 d l))

rewrite67.0ms

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

series2.1s

Counts

4 → 12

Calls

4 calls:

44.0ms	(/.f64 (.f64 M D) (.f64 d 2))
1.8s	(.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))))
168.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
73.0ms	(sqrt.f64 (/.f64 d l))

simplify92.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4953	4317
1	4953	4317

prune179.0ms

Filtered

87 candidates to 136 candidates (-56.3%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	127	9	136
Fresh	3	13	16
Picked	1	0	1
Done	0	0	0
Total	131	22	153

Merged error: 11.0b

Counts

153 → 22

localize31.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 h)
4.6b	(/.f64 (.f64 M D) (.f64 d 2))
5.7b	(.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))))
12.6b	(.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`
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 h)
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
28.0ms	(.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))

series2.5s

Counts

4 → 12

Calls

4 calls:

160.0ms	(cbrt.f64 h)
44.0ms	(/.f64 (.f64 M D) (.f64 d 2))
2.1s	(.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))))
165.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

simplify99.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5026	5004

prune175.0ms

Filtered

74 candidates to 128 candidates (-73.0%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	123	5	128
Fresh	3	18	21
Picked	1	0	1
Done	0	0	0
Total	127	23	150

Merged error: 7.9b

Counts

150 → 23

localize33.0ms

Local error

Found 4 expressions with local error:

3.5b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h)
4.6b	(/.f64 (.f64 M D) (.f64 d 2))
5.7b	(.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)) h) l)))
7.9b	(/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)

rewrite121.0ms

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:

16.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h)
12.0ms	(/.f64 (.f64 M D) (.f64 d 2))
35.0ms	(.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)) h) l)))
10.0ms	(/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)

series2.5s

Counts

4 → 12

Calls

4 calls:

136.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h)
42.0ms	(/.f64 (.f64 M D) (.f64 d 2))
2.1s	(.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)) h) l)))
156.0ms	(/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)

simplify101.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4964	5310
1	4964	5310

prune130.0ms

Filtered

72 candidates to 128 candidates (-77.8%)

Pruning

25 alts after pruning (24 fresh and 1 done)

	Pruned	Kept	Total
New	125	3	128
Fresh	1	21	22
Picked	0	1	1
Done	0	0	0
Total	126	25	151

Merged error: 7.8b

Counts

151 → 25

regimes508.0ms

Accuracy

2.5% (4.4b remaining)

Error of 14.6b against oracle of 10.2b and baseline of 14.7b

bsearch2.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	143	139
1	143	139

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.5s	8000×	body	128	valid
1.2s	8440×	body	128	nan
897.0ms	4723×	body	128	invalid

Details

analyze2.0s

sample150.0ms

simplify38.0ms

prune5.0ms

localize20.0ms

rewrite53.0ms

series835.0ms

simplify82.0ms

prune215.0ms

localize25.0ms

rewrite67.0ms

series2.1s

simplify92.0ms

prune179.0ms

localize31.0ms

rewrite68.0ms

series2.5s

simplify99.0ms

prune175.0ms

localize33.0ms

rewrite121.0ms

series2.5s

simplify101.0ms

prune130.0ms

regimes508.0ms

bsearch2.0ms

simplify4.0ms

end0.0ms

sample4.4s

Profiling