Details

analyze126.0ms

Algorithm

Search

True	Other	False	Iter
0%	28.1%	71.9%	0
0%	28.1%	71.9%	1
0%	28.1%	71.9%	2
0%	28.1%	71.9%	3
3.5%	24.6%	71.9%	4
5.3%	22.8%	71.9%	5
10.5%	17.5%	71.9%	6
14%	14%	71.9%	7
19.1%	9%	71.9%	8
24.6%	3.5%	71.9%	9
25.1%	3%	71.9%	10
25.8%	2.3%	71.9%	11
26.3%	1.8%	71.9%	12
26.6%	1.5%	71.9%	13
26.9%	1.2%	71.9%	14

sample37.0ms

Algorithm

intervals

Results

11.0ms	209×	body	80	valid
5.0ms	256×	pre	80	true
4.0ms	15×	body	1280	valid
4.0ms	17×	body	640	valid
2.0ms	10×	body	320	valid
1.0ms	5×	body	160	valid

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5221	29

prune5.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 20.2b

Counts

2 → 1

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b

(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))

1.8b

(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

17.2b

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac_binary64`
47×	`*-un-lft-identity_binary64`
25×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
17×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`associate-/r/_binary64`
11×	`flip3-+_binary64` `distribute-lft-out_binary64` `flip-+_binary64`
10×	`associate-/l*_binary64`
9×	`associate-/l/_binary64`
7×	`associate-/r*_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64`
5×	`add-log-exp_binary64`
4×	`frac-times_binary64`
3×	`pow1_binary64` `flip3--_binary64` `flip--_binary64`
2×	`cbrt-unprod_binary64` `associate-r/_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-l/_binary64`
1×	`+-commutative_binary64` `sum-log_binary64`

Counts

3 → 111

Calls

3 calls:

22.0ms

(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))

32.0ms

(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

15.0ms

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series191.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms

(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))

96.0ms

(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

22.0ms

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify61.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5570	3519

prune160.0ms

Filtered

91 candidates to 120 candidates (-31.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	111	9	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	112	9	121

Merged error: 6.6b

Counts

121 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.0b	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
1.3b	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
3.3b	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

321×	`times-frac_binary64`
290×	`*-un-lft-identity_binary64`
211×	`add-sqr-sqrt_binary64`
140×	`add-cube-cbrt_binary64`
90×	`associate-r_binary64`
44×	`distribute-lft-out_binary64`
31×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
26×	`associate-/l*_binary64`
24×	`associate-/r/_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
15×	`flip3-+_binary64` `flip-+_binary64`
12×	`div-inv_binary64`
7×	`associate-/r*_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64` `pow1_binary64`
4×	`associate-l_binary64`
3×	`associate-/l/_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `div-sub_binary64` `prod-exp_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `flip3--_binary64` `associate-r/_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 295

Calls

4 calls:

11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
22.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
38.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
28.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

series234.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
42.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
75.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
98.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

simplify91.0ms

Algorithm

egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5049	8873

prune376.0ms

Filtered

200 candidates to 307 candidates (-53.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	302	5	307
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	306	10	316

Merged error: 6.6b

Counts

316 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow.f64 (+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1) 3)
0.1b	(cbrt.f64 (pow.f64 (+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1) 3))
1.3b	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
3.3b	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

147×	`times-frac_binary64`
137×	`*-un-lft-identity_binary64`
102×	`add-sqr-sqrt_binary64`
90×	`associate-r_binary64`
69×	`add-cube-cbrt_binary64`
22×	`distribute-lft-out_binary64`
14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`difference-of-squares_binary64` `distribute-lft-out--_binary64` `cbrt-prod_binary64`
10×	`flip3-+_binary64` `associate-/r/_binary64` `flip-+_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
5×	`div-inv_binary64`
4×	`associate-l_binary64` `cube-div_binary64`
3×	`pow-unpow_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-exp_binary64`
2×	`cbrt-div_binary64` `sqr-pow_binary64` `frac-times_binary64` `unpow3_binary64` `associate-*l/_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `rem-cbrt-cube_binary64` `associate-r/_binary64` `pow1/3_binary64` `pow-pow_binary64` `rem-cube-cbrt_binary64` `+-commutative_binary64` `pow-exp_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 176

Calls

4 calls:

28.0ms	(pow.f64 (+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1) 3)
28.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1) 3))
42.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
29.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

series549.0ms

Counts

4 → 12

Calls

4 calls:

282.0ms	(pow.f64 (+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1) 3)
97.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1) 3))
74.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
95.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

simplify90.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5014	5514

prune225.0ms

Filtered

116 candidates to 188 candidates (-62.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	183	5	188
Fresh	3	5	8
Picked	1	0	1
Done	0	1	1
Total	187	11	198

Merged error: 6.6b

Counts

198 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))))
0.4b	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i)))))
0.4b	(/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
7.2b	(+.f64 (.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i)))))) 1)

rewrite222.0ms

Algorithm

rewrite-expression-head

Rules

603×	`times-frac_binary64`
484×	`*-un-lft-identity_binary64`
408×	`add-sqr-sqrt_binary64`
260×	`add-cube-cbrt_binary64`
219×	`sqrt-prod_binary64`
153×	`associate-r_binary64`
67×	`distribute-lft-out_binary64`
45×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
38×	`associate-/r/_binary64`
34×	`associate-l_binary64`
32×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
25×	`associate-/l*_binary64`
21×	`flip3-+_binary64` `flip-+_binary64`
19×	`div-inv_binary64`
15×	`unswap-sqr_binary64`
14×	`associate-/r*_binary64`
13×	`cbrt-undiv_binary64` `div-exp_binary64`
8×	`sqrt-div_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
3×	`associate-/l/_binary64`
2×	`div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `+-commutative_binary64` `frac-times_binary64` `associate-l/_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 485

Calls

4 calls:

110.0ms	(.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))))
22.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i)))))
14.0ms	(/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
43.0ms	(+.f64 (.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i)))))) 1)

series267.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))))
47.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i)))))
44.0ms	(/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
101.0ms	(+.f64 (.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i)))))) 1)

simplify118.0ms

Algorithm

egg-herbie

Counts

497 → 497

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5205	18503

prune880.0ms

Filtered

257 candidates to 497 candidates (-93.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	493	4	497
Fresh	4	5	9
Picked	1	0	1
Done	0	1	1
Total	498	10	508

Merged error: 6.6b

Counts

508 → 10

regimes231.0ms

Accuracy

19.8% (5.0b remaining)

Error of 10.9b against oracle of 5.9b and baseline of 12.2b

bsearch27.0ms

Steps

Iters	Range		Point
7	4.920182458003253e+165	5.385702093629972e+167	6.078461969447068e+166

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	65	65
1	65	65

end0.0ms

sample1.1s

Algorithm

intervals

Results

358.0ms	6379×	body	80	valid
173.0ms	8000×	pre	80	true
146.0ms	517×	body	1280	valid
126.0ms	558×	body	640	valid
59.0ms	348×	body	320	valid
22.0ms	198×	body	160	valid

Details

analyze126.0ms

sample37.0ms

simplify52.0ms

prune5.0ms

localize15.0ms

rewrite73.0ms

series191.0ms

simplify61.0ms

prune160.0ms

localize15.0ms

rewrite117.0ms

series234.0ms

simplify91.0ms

prune376.0ms

localize15.0ms

rewrite142.0ms

series549.0ms

simplify90.0ms

prune225.0ms

localize17.0ms

rewrite222.0ms

series267.0ms

simplify118.0ms

prune880.0ms

regimes231.0ms

bsearch27.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling