Details

analyze1.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	0%	50%	2

sample30.0ms

Algorithm

intervals

Results

10.0ms	68×	body	640	valid
6.0ms	33×	body	1280	valid
4.0ms	118×	body	80	valid
2.0ms	22×	body	320	valid
1.0ms	15×	body	160	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (13.0ms)

Iter	Nodes	Cost
0	265	11
1	265	11

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: 21.8b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1.0))
0.2b	(/.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))
0.3b	(/.f64 1.0 (sqrt.f64 x))
3.7b	(-.f64 (/.f64 1.0 (sqrt.f64 x)) (/.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

75×	`*-un-lft-identity_binary64`
73×	`add-sqr-sqrt_binary64`
69×	`times-frac_binary64`
50×	`sqrt-prod_binary64`
42×	`add-cube-cbrt_binary64`
13×	`associate-/r*_binary64`
11×	`distribute-lft-out--_binary64`
9×	`difference-of-squares_binary64`
8×	`distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `associate-/l*_binary64`
5×	`pow1_binary64`
4×	`div-inv_binary64` `sqrt-div_binary64`
2×	`flip3-+_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `flip3--_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `frac-sub_binary64`

Counts

4 → 132

Calls

4 calls:

4.0ms	(sqrt.f64 (+.f64 x 1.0))
6.0ms	(/.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))
4.0ms	(/.f64 1.0 (sqrt.f64 x))
31.0ms	(-.f64 (/.f64 1.0 (sqrt.f64 x)) (/.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))

series43.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(sqrt.f64 (+.f64 x 1.0))
8.0ms	(/.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))
10.0ms	(/.f64 1.0 (sqrt.f64 x))
20.0ms	(-.f64 (/.f64 1.0 (sqrt.f64 x)) (/.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))

simplify36.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5076	1839

prune182.0ms

Filtered

103 candidates to 144 candidates (-39.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	133	11	144
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	134	11	145

Merged error: 21.0b

Counts

145 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1.0 (sqrt.f64 (+.f64 1.0 x)))
0.3b	(/.f64 (-.f64 (/.f64 1.0 (/.f64 x 1.0)) (/.f64 1.0 (/.f64 (+.f64 1.0 x) 1.0))) (+.f64 (/.f64 1.0 (sqrt.f64 x)) (/.f64 1.0 (sqrt.f64 (+.f64 1.0 x)))))
0.3b	(/.f64 1.0 (sqrt.f64 x))
3.7b	(-.f64 (/.f64 1.0 (/.f64 x 1.0)) (/.f64 1.0 (/.f64 (+.f64 1.0 x) 1.0)))

rewrite372.0ms

Algorithm

rewrite-expression-head

Rules

2937×	`times-frac_binary64`
2554×	`*-un-lft-identity_binary64`
1354×	`add-sqr-sqrt_binary64`
778×	`add-cube-cbrt_binary64`
708×	`distribute-lft-out_binary64`
508×	`sqrt-prod_binary64`
368×	`distribute-lft-out--_binary64`
211×	`div-inv_binary64`
144×	`difference-of-squares_binary64`
64×	`distribute-rgt-out--_binary64`
45×	`associate-/l*_binary64`
37×	`associate-/r/_binary64`
27×	`associate-/r*_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64`
4×	`pow1_binary64`
3×	`associate-/l/_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `flip--_binary64` `flip-+_binary64` `frac-sub_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `frac-add_binary64` `div-sub_binary64`

Counts

4 → 750

Calls

4 calls:

6.0ms	(/.f64 1.0 (sqrt.f64 (+.f64 1.0 x)))
135.0ms	(/.f64 (-.f64 (/.f64 1.0 (/.f64 x 1.0)) (/.f64 1.0 (/.f64 (+.f64 1.0 x) 1.0))) (+.f64 (/.f64 1.0 (sqrt.f64 x)) (/.f64 1.0 (sqrt.f64 (+.f64 1.0 x)))))
4.0ms	(/.f64 1.0 (sqrt.f64 x))
90.0ms	(-.f64 (/.f64 1.0 (/.f64 x 1.0)) (/.f64 1.0 (/.f64 (+.f64 1.0 x) 1.0)))

series54.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/.f64 1.0 (sqrt.f64 (+.f64 1.0 x)))
30.0ms	(/.f64 (-.f64 (/.f64 1.0 (/.f64 x 1.0)) (/.f64 1.0 (/.f64 (+.f64 1.0 x) 1.0))) (+.f64 (/.f64 1.0 (sqrt.f64 x)) (/.f64 1.0 (sqrt.f64 (+.f64 1.0 x)))))
10.0ms	(/.f64 1.0 (sqrt.f64 x))
5.0ms	(-.f64 (/.f64 1.0 (/.f64 x 1.0)) (/.f64 1.0 (/.f64 (+.f64 1.0 x) 1.0)))

simplify189.0ms

Algorithm

egg-herbie

Counts

762 → 762

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4983	23232
1	4983	23232

prune945.0ms

Filtered

283 candidates to 762 candidates (-169.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	759	3	762
Fresh	9	1	10
Picked	1	0	1
Done	0	0	0
Total	769	4	773

Merged error: 3.9b

Counts

773 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1.0 (sqrt.f64 (+.f64 1.0 x)))
0.2b	(/.f64 (/.f64 (-.f64 (.f64 1.0 (/.f64 (+.f64 1.0 x) 1.0)) (/.f64 x 1)) (.f64 (/.f64 x 1.0) (/.f64 (+.f64 1.0 x) 1.0))) (+.f64 (/.f64 1.0 (sqrt.f64 x)) (/.f64 1.0 (sqrt.f64 (+.f64 1.0 x)))))
0.3b	(/.f64 1.0 (sqrt.f64 x))
3.2b	(-.f64 (*.f64 1.0 (/.f64 (+.f64 1.0 x) 1.0)) (/.f64 x 1))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

422×	`times-frac_binary64`
403×	`*-un-lft-identity_binary64`
160×	`sqrt-prod_binary64`
158×	`distribute-lft-out_binary64`
142×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
50×	`associate-/r/_binary64`
40×	`div-inv_binary64`
33×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
27×	`associate-/r*_binary64`
17×	`cbrt-undiv_binary64` `div-exp_binary64`
16×	`associate-r/_binary64` `associate-/l_binary64`
15×	`frac-times_binary64` `associate-*l/_binary64`
6×	`add-log-exp_binary64`
4×	`pow1_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
3×	`clear-num_binary64` `frac-2neg_binary64`
2×	`flip3-+_binary64` `div-sub_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `frac-add_binary64` `flip--_binary64` `frac-sub_binary64`

Counts

4 → 287

Calls

4 calls:

6.0ms	(/.f64 1.0 (sqrt.f64 (+.f64 1.0 x)))
56.0ms	(/.f64 (/.f64 (-.f64 (.f64 1.0 (/.f64 (+.f64 1.0 x) 1.0)) (/.f64 x 1)) (.f64 (/.f64 x 1.0) (/.f64 (+.f64 1.0 x) 1.0))) (+.f64 (/.f64 1.0 (sqrt.f64 x)) (/.f64 1.0 (sqrt.f64 (+.f64 1.0 x)))))
4.0ms	(/.f64 1.0 (sqrt.f64 x))
9.0ms	(-.f64 (*.f64 1.0 (/.f64 (+.f64 1.0 x) 1.0)) (/.f64 x 1))

series72.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/.f64 1.0 (sqrt.f64 (+.f64 1.0 x)))
48.0ms	(/.f64 (/.f64 (-.f64 (.f64 1.0 (/.f64 (+.f64 1.0 x) 1.0)) (/.f64 x 1)) (.f64 (/.f64 x 1.0) (/.f64 (+.f64 1.0 x) 1.0))) (+.f64 (/.f64 1.0 (sqrt.f64 x)) (/.f64 1.0 (sqrt.f64 (+.f64 1.0 x)))))
15.0ms	(/.f64 1.0 (sqrt.f64 x))
1.0ms	(-.f64 (*.f64 1.0 (/.f64 (+.f64 1.0 x) 1.0)) (/.f64 x 1))

simplify78.0ms

Algorithm

egg-herbie

Counts

299 → 299

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5022	9018

prune428.0ms

Filtered

158 candidates to 299 candidates (-89.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	297	2	299
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	299	4	303

Merged error: 3.9b

Counts

303 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1.0 (sqrt.f64 (+.f64 1.0 x)))
0.3b	(/.f64 1.0 (sqrt.f64 x))
0.4b	(/.f64 1.0 (*.f64 (/.f64 x 1.0) (/.f64 (+.f64 1.0 x) 1.0)))
3.8b	(/.f64 (/.f64 1.0 (*.f64 (/.f64 x 1.0) (/.f64 (+.f64 1.0 x) 1.0))) (+.f64 (/.f64 1.0 (sqrt.f64 x)) (/.f64 1.0 (sqrt.f64 (+.f64 1.0 x)))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

425×	`times-frac_binary64`
405×	`*-un-lft-identity_binary64`
160×	`sqrt-prod_binary64`
158×	`distribute-lft-out_binary64`
144×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
53×	`associate-/r/_binary64`
51×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
41×	`div-inv_binary64`
28×	`associate-/r*_binary64`
26×	`cbrt-undiv_binary64` `div-exp_binary64`
19×	`associate-/l*_binary64`
16×	`associate-r/_binary64` `frac-times_binary64` `associate-l/_binary64`
8×	`cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `clear-num_binary64` `frac-2neg_binary64`
2×	`flip3-+_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `frac-add_binary64`

Counts

4 → 304

Calls

4 calls:

6.0ms	(/.f64 1.0 (sqrt.f64 (+.f64 1.0 x)))
4.0ms	(/.f64 1.0 (sqrt.f64 x))
12.0ms	(/.f64 1.0 (*.f64 (/.f64 x 1.0) (/.f64 (+.f64 1.0 x) 1.0)))
43.0ms	(/.f64 (/.f64 1.0 (*.f64 (/.f64 x 1.0) (/.f64 (+.f64 1.0 x) 1.0))) (+.f64 (/.f64 1.0 (sqrt.f64 x)) (/.f64 1.0 (sqrt.f64 (+.f64 1.0 x)))))

series74.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/.f64 1.0 (sqrt.f64 (+.f64 1.0 x)))
10.0ms	(/.f64 1.0 (sqrt.f64 x))
4.0ms	(/.f64 1.0 (*.f64 (/.f64 x 1.0) (/.f64 (+.f64 1.0 x) 1.0)))
52.0ms	(/.f64 (/.f64 1.0 (*.f64 (/.f64 x 1.0) (/.f64 (+.f64 1.0 x) 1.0))) (+.f64 (/.f64 1.0 (sqrt.f64 x)) (/.f64 1.0 (sqrt.f64 (+.f64 1.0 x)))))

simplify83.0ms

Algorithm

egg-herbie

Counts

316 → 316

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5353	7345

prune372.0ms

Filtered

165 candidates to 316 candidates (-91.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	307	9	316
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	308	12	320

Merged error: 0.0b

Counts

320 → 12

regimes59.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	25
1	18	25

end0.0ms

sample815.0ms

Algorithm

intervals

Results

268.0ms	1869×	body	640	valid
204.0ms	1126×	body	1280	valid
157.0ms	4088×	body	80	valid
63.0ms	601×	body	320	valid
24.0ms	316×	body	160	valid

Details

analyze1.0ms

sample30.0ms

simplify16.0ms

prune9.0ms

localize8.0ms

rewrite50.0ms

series43.0ms

simplify36.0ms

prune182.0ms

localize13.0ms

rewrite372.0ms

series54.0ms

simplify189.0ms

prune945.0ms

localize16.0ms

rewrite96.0ms

series72.0ms

simplify78.0ms

prune428.0ms

localize12.0ms

rewrite87.0ms

series74.0ms

simplify83.0ms

prune372.0ms

regimes59.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample815.0ms

Profiling