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

sample20.0ms

Algorithm

intervals

Results

6.0ms	48×	body	1280	valid
4.0ms	43×	body	640	valid
4.0ms	147×	body	80	valid
1.0ms	10×	body	320	valid
0.0ms	8×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	70	7
1	70	7

prune6.0ms

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: 26.4b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
2.5b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `difference-of-squares_binary64`
3×	`pow1_binary64` `add-cube-cbrt_binary64` `distribute-lft-out--_binary64`
2×	`distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `flip3--_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `flip-+_binary64`

Counts

2 → 34

Calls

2 calls:

3.0ms	(sqrt.f64 (+.f64 x 1))
9.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series16.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(sqrt.f64 (+.f64 x 1))
12.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

simplify56.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5006	484

prune32.0ms

Filtered

30 candidates to 40 candidates (-33.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	38	2	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	2	41

Merged error: 0.1b

Counts

41 → 2

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.0b	(sqrt.f64 (+.f64 x 1))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64`
24×	`sqrt-prod_binary64`
21×	`distribute-lft-out_binary64`
18×	`times-frac_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
7×	`add-exp-log_binary64`
6×	`associate-/r*_binary64`
5×	`add-log-exp_binary64` `pow1_binary64` `add-cbrt-cube_binary64`
3×	`flip3-+_binary64` `associate-/l*_binary64` `flip-+_binary64`
2×	`associate-/r/_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `div-inv_binary64` `+-commutative_binary64` `pow-flip_binary64` `sum-log_binary64`

Counts

3 → 75

Calls

3 calls:

8.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))
12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

series19.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
4.0ms	(sqrt.f64 (+.f64 x 1))
8.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

simplify59.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4999	966
1	4999	966

prune63.0ms

Filtered

56 candidates to 84 candidates (-50.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	77	7	84
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	77	9	86

Merged error: 0.0b

Counts

86 → 9

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.3b	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

308×	`*-un-lft-identity_binary64`
290×	`sqrt-prod_binary64`
168×	`times-frac_binary64`
136×	`add-sqr-sqrt_binary64`
116×	`distribute-lft-out_binary64`
88×	`add-cube-cbrt_binary64`
43×	`swap-sqr_binary64`
31×	`pow1_binary64`
27×	`associate-r_binary64` `associate-l_binary64` `sqrt-pow1_binary64`
16×	`unswap-sqr_binary64`
14×	`add-exp-log_binary64` `associate-/r/_binary64`
12×	`associate-/r*_binary64`
11×	`inv-pow_binary64` `pow-flip_binary64`
10×	`add-cbrt-cube_binary64`
9×	`pow1/2_binary64` `pow-prod-up_binary64` `div-inv_binary64`
7×	`flip3-+_binary64` `flip-+_binary64`
6×	`associate-/l*_binary64`
5×	`pow-prod-down_binary64` `pow-sqr_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64` `div-exp_binary64`
3×	`rem-sqrt-square_binary64`
2×	`1-exp_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-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 → 278

Calls

4 calls:

12.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
13.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
38.0ms	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

series45.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
8.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
8.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
9.0ms	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

simplify88.0ms

Algorithm

egg-herbie

Counts

290 → 290

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4894	4164
1	4894	4164

prune170.0ms

Filtered

128 candidates to 290 candidates (-126.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	285	5	290
Fresh	5	2	7
Picked	0	1	1
Done	0	1	1
Total	290	9	299

Merged error: 0b

Counts

299 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.3b	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 3)))
0.3b	(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 3))
0.4b	(pow.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 3)

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

325×	`sqrt-prod_binary64`
290×	`*-un-lft-identity_binary64`
199×	`add-sqr-sqrt_binary64`
182×	`times-frac_binary64`
160×	`cbrt-prod_binary64`
100×	`distribute-lft-out_binary64`
97×	`unpow-prod-down_binary64` `cube-prod_binary64`
96×	`add-cube-cbrt_binary64`
63×	`associate-r_binary64`
44×	`unswap-sqr_binary64`
27×	`associate-l_binary64`
16×	`associate-/r/_binary64`
11×	`add-exp-log_binary64`
10×	`pow1_binary64`
8×	`flip3-+_binary64` `add-cbrt-cube_binary64` `div-inv_binary64` `flip-+_binary64`
7×	`sqr-pow_binary64`
6×	`associate-/r*_binary64` `sqrt-div_binary64`
5×	`pow-pow_binary64`
4×	`add-log-exp_binary64` `cube-div_binary64`
3×	`cbrt-div_binary64` `pow-unpow_binary64` `sqrt-pow1_binary64` `associate-/l*_binary64` `unpow3_binary64` `cube-mult_binary64`
2×	`inv-pow_binary64` `div-exp_binary64` `pow-flip_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `pow1/2_binary64` `rem-cbrt-cube_binary64` `cbrt-unprod_binary64` `sqrt-pow2_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `pow1/3_binary64` `clear-num_binary64` `rem-cube-cbrt_binary64` `prod-exp_binary64` `frac-2neg_binary64` `rec-exp_binary64` `frac-times_binary64` `pow-exp_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 340

Calls

4 calls:

11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
58.0ms	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 3)))
16.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 3))
15.0ms	(pow.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 3)

series52.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
8.0ms	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 3)))
13.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 3))
22.0ms	(pow.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 3)

simplify90.0ms

Algorithm

egg-herbie

Counts

352 → 352

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5015	6162

prune168.0ms

Filtered

116 candidates to 352 candidates (-203.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	352	0	352
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	352	9	361

Merged error: 0b

Counts

361 → 9

regimes34.0ms

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	10	9
1	10	9

end0.0ms

sample644.0ms

Algorithm

intervals

Results

241.0ms	1757×	body	1280	valid
128.0ms	1215×	body	640	valid
114.0ms	4126×	body	80	valid
49.0ms	598×	body	320	valid
16.0ms	304×	body	160	valid
0.0ms	3×	body	80	nan

Details

analyze2.0ms

sample20.0ms

simplify7.0ms

prune6.0ms

localize5.0ms

rewrite13.0ms

series16.0ms

simplify56.0ms

prune32.0ms

localize6.0ms

rewrite26.0ms

series19.0ms

simplify59.0ms

prune63.0ms

localize8.0ms

rewrite92.0ms

series45.0ms

simplify88.0ms

prune170.0ms

localize11.0ms

rewrite127.0ms

series52.0ms

simplify90.0ms

prune168.0ms

regimes34.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample644.0ms

Profiling