Details

analyze4.0ms

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

simplify138.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (135.0ms)

Iter	Nodes	Cost
0	4949	35
1	4949	35

prune6.0ms

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: 2.9b

Counts

2 → 1

localize16.0ms

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))
2.7b	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1.0) (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0)))

rewrite137.0ms

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)
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)))
39.0ms	(/.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)))

series77.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(+.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)))
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)))

simplify157.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 0 (50.0ms)

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: 1.1b

Counts

478 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (+.f64 (+.f64 alpha beta) (*.f64 1.0 2.0)))
0.0b	(/.f64 (.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1.0) (/.f64 1 (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0)))) (+.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 1 (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0)))) (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)) 1.0))
2.7b	(.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1.0) (/.f64 1 (+.f64 (+.f64 alpha beta) (*.f64 1.0 2.0))))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

74×	`times-frac_binary64`
65×	`*-un-lft-identity_binary64`
54×	`add-exp-log_binary64`
49×	`add-sqr-sqrt_binary64`
42×	`add-cube-cbrt_binary64`
34×	`add-cbrt-cube_binary64`
24×	`div-exp_binary64`
18×	`associate-/r/_binary64`
15×	`associate-r_binary64`
14×	`cbrt-undiv_binary64`
13×	`flip3-+_binary64` `associate-/l*_binary64` `flip-+_binary64`
12×	`prod-exp_binary64`
11×	`distribute-lft-out_binary64`
10×	`associate-/r*_binary64`
9×	`div-inv_binary64`
7×	`associate-/l/_binary64` `pow1_binary64`
6×	`cbrt-unprod_binary64`
4×	`add-log-exp_binary64` `1-exp_binary64` `associate-l_binary64` `rec-exp_binary64` `frac-times_binary64` `associate-*l/_binary64`
3×	`unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64`
2×	`associate-*r/_binary64` `un-div-inv_binary64`
1×	`pow-prod-down_binary64` `inv-pow_binary64` `pow-flip_binary64` `*-commutative_binary64`

Counts

4 → 181

Calls

4 calls:

8.0ms	(/.f64 1 (+.f64 (+.f64 alpha beta) (*.f64 1.0 2.0)))
25.0ms	(/.f64 (.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1.0) (/.f64 1 (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0)))) (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0)))
32.0ms	(/.f64 (/.f64 (.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1.0) (/.f64 1 (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0)))) (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2.0 1.0)) 1.0))
22.0ms	(.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1.0) (/.f64 1 (+.f64 (+.f64 alpha beta) (*.f64 1.0 2.0))))

series79.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/.f64 1 (+.f64 (+.f64 alpha beta) (*.f64 1.0 2.0)))
26.0ms	(/.f64 (.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1.0) (/.f64 1 (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0)))) (+.f64 (+.f64 alpha beta) (.f64 2.0 1.0)))
32.0ms	(/.f64 (/.f64 (.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1.0) (/.f64 1 (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0)))) (+.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 1 (+.f64 (+.f64 alpha beta) (*.f64 1.0 2.0))))

simplify62.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5351	5555

prune295.0ms

Filtered

131 candidates to 193 candidates (-47.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	193	0	193
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	193	10	203

Merged error: 1.1b

Counts

203 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1.0)) (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0)))
0.2b	(.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1.0)) (/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1.0)) (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0))))
2.6b	(sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 alpha beta)) 1.0))
2.6b	(sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 alpha beta)) 1.0))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64`
56×	`add-sqr-sqrt_binary64`
46×	`times-frac_binary64`
45×	`sqrt-prod_binary64`
38×	`add-cube-cbrt_binary64`
27×	`associate-r_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`distribute-lft-out_binary64` `sqrt-div_binary64`
8×	`pow1_binary64`
7×	`flip3-+_binary64` `associate-l_binary64` `associate-/l*_binary64` `flip-+_binary64`
6×	`unswap-sqr_binary64`
4×	`add-log-exp_binary64` `associate-/r/_binary64`
3×	`associate-/r*_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `-commutative_binary64`

Counts

4 → 137

Calls

4 calls:

16.0ms	(/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1.0)) (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0)))
30.0ms	(.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1.0)) (/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1.0)) (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0))))
8.0ms	(sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 alpha beta)) 1.0))
8.0ms	(sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 alpha beta)) 1.0))

series100.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1.0)) (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0)))
15.0ms	(.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1.0)) (/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1.0)) (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0))))
12.0ms	(sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 alpha beta)) 1.0))
15.0ms	(sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 alpha beta)) 1.0))

simplify59.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4994	3486
1	4994	3486

prune232.0ms

Filtered

101 candidates to 149 candidates (-47.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	149	10	159

Merged error: 1.1b

Counts

159 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1.0) (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0)))) (cbrt.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1.0) (+.f64 (+.f64 alpha beta) (*.f64 1.0 2.0)))))
2.7b	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1.0) (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0)))
2.7b	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1.0) (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0)))
2.7b	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1.0) (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

137×	`*-un-lft-identity_binary64`
102×	`times-frac_binary64`
96×	`cbrt-prod_binary64`
95×	`add-sqr-sqrt_binary64`
71×	`add-cube-cbrt_binary64`
30×	`distribute-lft-out_binary64`
27×	`swap-sqr_binary64`
21×	`associate-r_binary64` `associate-l_binary64`
14×	`associate-/r/_binary64`
12×	`add-exp-log_binary64` `associate-/l*_binary64`
11×	`pow1_binary64`
10×	`flip3-+_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
9×	`associate-/r*_binary64` `unswap-sqr_binary64`
7×	`div-inv_binary64`
6×	`associate-/l/_binary64` `pow1/3_binary64`
4×	`cbrt-div_binary64` `add-log-exp_binary64`
3×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`cbrt-unprod_binary64` `associate-r/_binary64` `pow-plus_binary64` `prod-exp_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 204

Calls

4 calls:

37.0ms	(.f64 (cbrt.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1.0) (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0)))) (cbrt.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1.0) (+.f64 (+.f64 alpha beta) (*.f64 1.0 2.0)))))
17.0ms	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1.0) (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0)))
19.0ms	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1.0) (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0)))
16.0ms	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1.0) (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0)))

series105.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(.f64 (cbrt.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1.0) (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0)))) (cbrt.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1.0) (+.f64 (+.f64 alpha beta) (*.f64 1.0 2.0)))))
15.0ms	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1.0) (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0)))
18.0ms	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1.0) (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0)))
15.0ms	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 alpha beta)) 1.0) (+.f64 (+.f64 alpha beta) (.f64 1.0 2.0)))

simplify72.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5045	6835

prune675.0ms

Filtered

152 candidates to 216 candidates (-42.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	216	0	216
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	216	10	226

Merged error: 1.1b

Counts

226 → 10

regimes127.0ms

Accuracy

57.6% (1.0b remaining)

Error of 2.1b against oracle of 1.1b and baseline of 3.5b

bsearch17.0ms

Steps

Iters	Range		Point
8	2.856170016854068e+195	3.85392169788566e+198	6.064453308972152e+195

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	42
1	28	42

end0.0ms

sample739.0ms

Algorithm

intervals

Results

477.0ms	8000×	body	80	valid
130.0ms	8000×	pre	80	true

Details

analyze4.0ms

sample27.0ms

simplify138.0ms

prune6.0ms

localize16.0ms

rewrite137.0ms

series77.0ms

simplify157.0ms

prune1.1s

localize16.0ms

rewrite94.0ms

series79.0ms

simplify62.0ms

prune295.0ms

localize17.0ms

rewrite69.0ms

series100.0ms

simplify59.0ms

prune232.0ms

localize19.0ms

rewrite99.0ms

series105.0ms

simplify72.0ms

prune675.0ms

regimes127.0ms

bsearch17.0ms

simplify2.0ms

end0.0ms

sample739.0ms

Profiling