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

5.0ms	51×	body	640	valid
5.0ms	38×	body	1280	valid
4.0ms	144×	body	80	valid
1.0ms	17×	body	320	valid
0.0ms	6×	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

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: 26.9b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
2.1b	(-.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))
8.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series15.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(sqrt.f64 (+.f64 x 1))
11.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

simplify57.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5006	484

prune46.0ms

Filtered

30 candidates to 40 candidates (-33.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	37	3	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	3	41

Merged error: 0.1b

Counts

41 → 3

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

rewrite24.0ms

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:

3.0ms	(sqrt.f64 (+.f64 x 1))
8.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
10.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

series18.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify61.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4999	966
1	4999	966

prune97.0ms

Filtered

56 candidates to 84 candidates (-50.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	78	6	84
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	79	8	87

Merged error: 0.0b

Counts

87 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

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

11.0ms	(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)))
11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
42.0ms	(*.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)))))

series43.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(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)))
14.0ms	(*.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)))))

simplify86.0ms

Algorithm

egg-herbie

Counts

290 → 290

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4894	4164
1	4894	4164

prune250.0ms

Filtered

129 candidates to 290 candidates (-124.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	288	2	290
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	290	8	298

Merged error: 0b

Counts

298 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.1b	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.3b	(pow.f64 (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 4) (/.f64 -1 2))
0.5b	(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 4)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity_binary64`
34×	`sqrt-prod_binary64`
31×	`unpow-prod-down_binary64`
19×	`add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64`
16×	`pow-unpow_binary64` `distribute-lft-out_binary64`
9×	`times-frac_binary64`
7×	`pow1_binary64` `add-exp-log_binary64`
6×	`add-log-exp_binary64`
5×	`pow-exp_binary64`
4×	`pow-pow_binary64` `add-cbrt-cube_binary64`
3×	`pow-to-exp_binary64` `sqr-pow_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`sqrt-pow2_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 97

Calls

4 calls:

8.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
8.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
13.0ms	(pow.f64 (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 4) (/.f64 -1 2))
10.0ms	(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 4)

series66.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
10.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
29.0ms	(pow.f64 (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 4) (/.f64 -1 2))
20.0ms	(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 4)

simplify33.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	4893	1608
1	4893	1608

prune104.0ms

Filtered

74 candidates to 109 candidates (-47.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	109	8	117

Merged error: 0b

Counts

117 → 8

regimes76.0ms

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

sample595.0ms

Algorithm

intervals

Results

211.0ms	1696×	body	1280	valid
124.0ms	1207×	body	640	valid
112.0ms	4211×	body	80	valid
43.0ms	606×	body	320	valid
13.0ms	280×	body	160	valid

Details

analyze2.0ms

sample20.0ms

simplify7.0ms

prune2.0ms

localize5.0ms

rewrite13.0ms

series15.0ms

simplify57.0ms

prune46.0ms

localize8.0ms

rewrite24.0ms

series18.0ms

simplify61.0ms

prune97.0ms

localize9.0ms

rewrite92.0ms

series43.0ms

simplify86.0ms

prune250.0ms

localize14.0ms

rewrite42.0ms

series66.0ms

simplify33.0ms

prune104.0ms

regimes76.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample595.0ms

Profiling