Details

analyze3.0ms

Algorithm

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
0%	56.2%	43.8%	2
42.1%	14%	43.8%	3
42.1%	14%	43.8%	4
52.7%	3.5%	43.8%	5
56.2%	0%	43.8%	6

sample27.0ms

Algorithm

intervals

Results

15.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify137.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (134.0ms)

Iter	Nodes	Cost
0	4949	35
1	4949	35

prune9.0ms

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: 3.9b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)) 1.0)
0.0b	(/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0))) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)))
0.1b	(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0))) (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0)) 1.0))
3.6b	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0)))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

804×	`times-frac_binary64`
586×	`*-un-lft-identity_binary64`
340×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
123×	`distribute-lft-out_binary64`
82×	`associate-/l*_binary64`
54×	`associate-/r/_binary64`
29×	`flip3-+_binary64` `flip-+_binary64`
27×	`div-inv_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`add-log-exp_binary64`
10×	`associate-/r*_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
6×	`sum-log_binary64`
4×	`associate-/l/_binary64` `pow1_binary64`
3×	`clear-num_binary64` `frac-2neg_binary64`
1×	`associate-+l+_binary64` `+-commutative_binary64`

Counts

4 → 465

Calls

4 calls:

9.0ms	(+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)) 1.0)
25.0ms	(/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0))) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)))
40.0ms	(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0))) (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0)) 1.0))
16.0ms	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0)))

series79.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)) 1.0)
26.0ms	(/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0))) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)))
34.0ms	(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0))) (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0)) 1.0))
15.0ms	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0)))

simplify162.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4973	23485
1	4973	23485

prune1.1s

Filtered

288 candidates to 477 candidates (-65.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	467	10	477
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	468	10	478

Merged error: 1.4b

Counts

478 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 alpha beta) (*.f64 beta alpha))
0.0b	(/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0))) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)))
0.1b	(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0))) (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0))) (+.f64 (+.f64 alpha beta) (+.f64 1.0 (.f64 1.0 2.0))))
3.6b	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0)))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

954×	`times-frac_binary64`
828×	`*-un-lft-identity_binary64`
383×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
253×	`distribute-lft-out_binary64`
82×	`associate-/l*_binary64`
66×	`associate-/r/_binary64`
37×	`flip3-+_binary64` `flip-+_binary64`
31×	`div-inv_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`associate-/r*_binary64`
10×	`cbrt-undiv_binary64` `div-exp_binary64`
9×	`add-log-exp_binary64`
4×	`associate-/l/_binary64` `pow1_binary64` `frac-add_binary64`
3×	`clear-num_binary64` `frac-2neg_binary64` `sum-log_binary64`
1×	`associate-+l+_binary64` `+-commutative_binary64`

Counts

4 → 528

Calls

4 calls:

7.0ms	(+.f64 (+.f64 alpha beta) (*.f64 beta alpha))
22.0ms	(/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0))) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)))
41.0ms	(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0))) (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0))) (+.f64 (+.f64 alpha beta) (+.f64 1.0 (.f64 1.0 2.0))))
16.0ms	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0)))

series81.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+.f64 (+.f64 alpha beta) (*.f64 beta alpha))
26.0ms	(/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0))) (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)))
35.0ms	(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0))) (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0))) (+.f64 (+.f64 alpha beta) (+.f64 1.0 (.f64 1.0 2.0))))
15.0ms	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0)))

simplify170.0ms

Algorithm

egg-herbie

Counts

540 → 540

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5600	27238

prune1.0s

Filtered

289 candidates to 540 candidates (-86.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	540	0	540
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	540	10	550

Merged error: 1.4b

Counts

550 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1.0) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0)))) (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0)))
0.1b	(/.f64 (/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1.0) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0)))) (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)) 1.0))
0.7b	(/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1.0) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0))))
3.4b	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1.0) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0))))

rewrite858.0ms

Algorithm

rewrite-expression-head

Rules

12132×	`times-frac_binary64`
7340×	`*-un-lft-identity_binary64`
4744×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
3270×	`sqrt-prod_binary64`
1298×	`distribute-lft-out_binary64`
784×	`associate-/l*_binary64`
298×	`associate-/r/_binary64`
284×	`sqrt-div_binary64`
150×	`flip3-+_binary64` `flip-+_binary64`
149×	`div-inv_binary64`
34×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
20×	`cbrt-undiv_binary64` `div-exp_binary64`
19×	`associate-/r*_binary64`
5×	`associate-/l/_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 3894

Calls

4 calls:

69.0ms	(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1.0) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0)))) (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0)))
173.0ms	(/.f64 (/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1.0) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0)))) (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)) 1.0))
30.0ms	(/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1.0) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0))))
17.0ms	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1.0) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0))))

series94.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1.0) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0)))) (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0)))
35.0ms	(/.f64 (/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1.0) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0)))) (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)) 1.0))
15.0ms	(/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1.0) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0))))
17.0ms	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1.0) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0))))

simplify1.7s

Algorithm

egg-herbie

Counts

3906 → 3906

Iterations

Useful iterations: 0 (110.0ms)

Iter	Nodes	Cost
0	5589	286573

prune40.4s

Filtered

1515 candidates to 3906 candidates (-157.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	3905	1	3906
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	3906	10	3916

Merged error: 1.4b

Counts

3916 → 10

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(/.f64 (.f64 (cbrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1.0)) (cbrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1.0))) (/.f64 (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0)) (cbrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 alpha beta)) 1.0))))
3.9b	(cbrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 alpha beta)) 1.0))
3.9b	(cbrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1.0))
3.9b	(cbrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1.0))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

69×	`times-frac_binary64`
53×	`*-un-lft-identity_binary64`
36×	`cbrt-prod_binary64`
35×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
27×	`associate-/r*_binary64`
22×	`cbrt-div_binary64`
16×	`add-exp-log_binary64`
11×	`flip3-+_binary64` `flip-+_binary64`
10×	`add-cbrt-cube_binary64`
9×	`distribute-lft-out_binary64`
8×	`associate-/l/_binary64`
6×	`cbrt-undiv_binary64` `div-exp_binary64`
5×	`associate-/r/_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `frac-times_binary64`
3×	`pow1/3_binary64` `div-inv_binary64`
2×	`cbrt-unprod_binary64` `associate-r/_binary64` `prod-exp_binary64` `associate-l/_binary64`
1×	`clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64`

Counts

4 → 124

Calls

4 calls:

38.0ms	(/.f64 (.f64 (cbrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1.0)) (cbrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1.0))) (/.f64 (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0)) (cbrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 alpha beta)) 1.0))))
8.0ms	(cbrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 alpha beta)) 1.0))
8.0ms	(cbrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1.0))
8.0ms	(cbrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1.0))

series68.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/.f64 (.f64 (cbrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1.0)) (cbrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1.0))) (/.f64 (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0)) (cbrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 alpha beta)) 1.0))))
17.0ms	(cbrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 alpha beta)) 1.0))
17.0ms	(cbrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1.0))
17.0ms	(cbrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1.0))

simplify259.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4951	3974
1	4951	3974

prune270.0ms

Filtered

114 candidates to 136 candidates (-19.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	136	10	146

Merged error: 1.4b

Counts

146 → 10

regimes139.0ms

Accuracy

53.9% (1.2b remaining)

Error of 2.3b against oracle of 1.2b and baseline of 3.7b

bsearch20.0ms

Steps

Iters	Range		Point
9	3.389125203548831e+214	2.357313965399137e+221	7.156274647039849e+214

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	85	89
1	85	89

end0.0ms

sample754.0ms

Algorithm

intervals

Results

480.0ms	8000×	body	80	valid
135.0ms	8000×	pre	80	true

Details

analyze3.0ms

sample27.0ms

simplify137.0ms

prune9.0ms

localize12.0ms

rewrite125.0ms

series79.0ms

simplify162.0ms

prune1.1s

localize16.0ms

rewrite132.0ms

series81.0ms

simplify170.0ms

prune1.0s

localize17.0ms

rewrite858.0ms

series94.0ms

simplify1.7s

prune40.4s

localize22.0ms

rewrite69.0ms

series68.0ms

simplify259.0ms

prune270.0ms

regimes139.0ms

bsearch20.0ms

simplify3.0ms

end0.0ms

sample754.0ms

Profiling