Details

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

sample27.0ms

Algorithm

intervals

Results

9.0ms	50×	body	640	valid
7.0ms	54×	body	1280	valid
3.0ms	125×	body	80	valid
1.0ms	15×	body	320	valid
1.0ms	12×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 31.0b

Counts

2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

2.7b	(-.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `sqrt-prod_binary64`
4×	`difference-of-squares_binary64`
3×	`add-log-exp_binary64` `distribute-lft-out--_binary64`
1×	`sub-neg_binary64` `pow1_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`

Counts

1 → 18

Calls

1 calls:

10.0ms

(-.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x))

series14.0ms

Counts

1 → 3

Calls

1 calls:

14.0ms

(-.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x))

simplify32.0ms

Algorithm

egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5102	335

prune33.0ms

Filtered

15 candidates to 21 candidates (-40.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	18	3	21
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	19	3	22

Merged error: 0.1b

Counts

22 → 3

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

48×	`*-un-lft-identity_binary64`
20×	`distribute-lft-out_binary64` `sqrt-prod_binary64`
18×	`times-frac_binary64`
13×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
6×	`associate-/r*_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-/l*_binary64`
2×	`flip3-+_binary64` `pow1_binary64` `associate-/r/_binary64` `flip-+_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

2 → 55

Calls

2 calls:

9.0ms	(+.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x))
11.0ms	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x)))

series21.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(+.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x))
13.0ms	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 x 1.0)) (sqrt.f64 x)))

simplify25.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5138	866

prune75.0ms

Filtered

43 candidates to 61 candidates (-41.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	56	5	61
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	57	7	64

Merged error: 0.0b

Counts

64 → 7

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))))
0.2b	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
0.2b	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
0.3b	(*.f64 (sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

297×	`*-un-lft-identity_binary64`
274×	`sqrt-prod_binary64`
157×	`times-frac_binary64`
119×	`add-sqr-sqrt_binary64`
116×	`distribute-lft-out_binary64`
88×	`add-cube-cbrt_binary64`
41×	`swap-sqr_binary64`
27×	`associate-r_binary64` `associate-l_binary64`
20×	`pow1_binary64`
14×	`associate-/r/_binary64`
12×	`associate-/r*_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`pow1/2_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64`
7×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64`
6×	`associate-/l*_binary64`
5×	`pow-prod-up_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `pow-sqr_binary64`
2×	`cbrt-undiv_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `associate-r/_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 250

Calls

4 calls:

12.0ms	(sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))))
11.0ms	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
11.0ms	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
42.0ms	(*.f64 (sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))))

series73.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))))
13.0ms	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
17.0ms	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
18.0ms	(*.f64 (sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))))

simplify83.0ms

Algorithm

egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4946	4249
1	4946	4249

prune284.0ms

Filtered

142 candidates to 262 candidates (-84.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	257	5	262
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	260	9	269

Merged error: 0.0b

Counts

269 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))))
0.2b	(/.f64 (sqrt.f64 1.0) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))))
0.2b	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
0.3b	(*.f64 (sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))) (/.f64 (sqrt.f64 1.0) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

298×	`sqrt-prod_binary64`
262×	`*-un-lft-identity_binary64`
181×	`times-frac_binary64`
154×	`add-sqr-sqrt_binary64`
101×	`add-cube-cbrt_binary64`
92×	`distribute-lft-out_binary64`
60×	`associate-r_binary64`
27×	`associate-l_binary64`
15×	`associate-/r*_binary64` `unswap-sqr_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`associate-/r/_binary64`
9×	`associate-/l*_binary64`
7×	`pow1_binary64` `sqrt-div_binary64`
5×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64`
3×	`cbrt-undiv_binary64` `sqrt-undiv_binary64` `div-exp_binary64`
2×	`cbrt-unprod_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `swap-sqr_binary64` `rem-square-sqrt_binary64` `associate-r/_binary64` `sqrt-unprod_binary64` `sqrt-pow1_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 282

Calls

4 calls:

12.0ms	(sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))))
15.0ms	(/.f64 (sqrt.f64 1.0) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))))
11.0ms	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
59.0ms	(*.f64 (sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))) (/.f64 (sqrt.f64 1.0) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))))

series85.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))))
25.0ms	(/.f64 (sqrt.f64 1.0) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x))))
13.0ms	(/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))
23.0ms	(*.f64 (sqrt.f64 (/.f64 1.0 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))) (/.f64 (sqrt.f64 1.0) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1.0 x)) (sqrt.f64 x)))))

simplify251.0ms

Algorithm

egg-herbie

Counts

294 → 294

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5128	6047

prune310.0ms

Filtered

148 candidates to 294 candidates (-98.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	293	1	294
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	293	10	303

Merged error: 0b

Counts

303 → 10

regimes95.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	9
1	9	9

end0.0ms

sample606.0ms

Algorithm

intervals

Results

212.0ms	1715×	body	1280	valid
129.0ms	1304×	body	640	valid
109.0ms	3997×	body	80	valid
46.0ms	643×	body	320	valid
16.0ms	341×	body	160	valid
0.0ms	1×	body	80	nan

Details

analyze2.0ms

sample27.0ms

simplify7.0ms

prune2.0ms

localize5.0ms

rewrite10.0ms

series14.0ms

simplify32.0ms

prune33.0ms

localize6.0ms

rewrite22.0ms

series21.0ms

simplify25.0ms

prune75.0ms

localize9.0ms

rewrite96.0ms

series73.0ms

simplify83.0ms

prune284.0ms

localize12.0ms

rewrite116.0ms

series85.0ms

simplify251.0ms

prune310.0ms

regimes95.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample606.0ms

Profiling