Details

analyze1.0ms

Algorithm

Search

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

sample29.0ms

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

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (12.0ms)

Iter	Nodes	Cost
0	265	11
1	265	11

prune4.0ms

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

localize7.0ms

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))))

rewrite53.0ms

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:

3.0ms	(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))
34.0ms	(-.f64 (/.f64 1.0 (sqrt.f64 x)) (/.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))

series38.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(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))
17.0ms	(-.f64 (/.f64 1.0 (sqrt.f64 x)) (/.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))

simplify40.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5076	1839

prune180.0ms

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

localize15.0ms

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)))

rewrite370.0ms

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:

7.0ms	(/.f64 1.0 (sqrt.f64 (+.f64 1.0 x)))
137.0ms	(/.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)))

series57.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/.f64 1.0 (sqrt.f64 (+.f64 1.0 x)))
34.0ms	(/.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)))

simplify254.0ms

Algorithm

egg-herbie

Counts

762 → 762

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4983	23232
1	4983	23232

prune869.0ms

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

localize19.0ms

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))

rewrite98.0ms

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:

9.0ms	(/.f64 1.0 (sqrt.f64 (+.f64 1.0 x)))
54.0ms	(/.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))
10.0ms	(-.f64 (*.f64 1.0 (/.f64 (+.f64 1.0 x) 1.0)) (/.f64 x 1))

series68.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/.f64 1.0 (sqrt.f64 (+.f64 1.0 x)))
49.0ms	(/.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)))))
10.0ms	(/.f64 1.0 (sqrt.f64 x))
1.0ms	(-.f64 (*.f64 1.0 (/.f64 (+.f64 1.0 x) 1.0)) (/.f64 x 1))

simplify72.0ms

Algorithm

egg-herbie

Counts

299 → 299

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5022	9018

prune600.0ms

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)))))

rewrite92.0ms

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))
10.0ms	(/.f64 1.0 (*.f64 (/.f64 x 1.0) (/.f64 (+.f64 1.0 x) 1.0)))
46.0ms	(/.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)))))

series68.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/.f64 1.0 (sqrt.f64 (+.f64 1.0 x)))
10.0ms	(/.f64 1.0 (sqrt.f64 x))
3.0ms	(/.f64 1.0 (*.f64 (/.f64 x 1.0) (/.f64 (+.f64 1.0 x) 1.0)))
45.0ms	(/.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)))))

simplify79.0ms

Algorithm

egg-herbie

Counts

316 → 316

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5353	7345

prune363.0ms

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

sample820.0ms

Algorithm

intervals

Results

275.0ms	1869×	body	640	valid
206.0ms	1126×	body	1280	valid
153.0ms	4088×	body	80	valid
64.0ms	601×	body	320	valid
26.0ms	316×	body	160	valid

Details

analyze1.0ms

sample29.0ms

simplify15.0ms

prune4.0ms

localize7.0ms

rewrite53.0ms

series38.0ms

simplify40.0ms

prune180.0ms

localize15.0ms

rewrite370.0ms

series57.0ms

simplify254.0ms

prune869.0ms

localize19.0ms

rewrite98.0ms

series68.0ms

simplify72.0ms

prune600.0ms

localize12.0ms

rewrite92.0ms

series68.0ms

simplify79.0ms

prune363.0ms

regimes59.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample820.0ms

Profiling