Details

analyze508.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.3%	24.4%	11
31.4%	44.3%	24.4%	12
31.4%	44%	24.5%	13
31.5%	43.8%	24.8%	14

sample66.0ms

Algorithm

intervals

Results

34.0ms	77×	body	1280	valid
12.0ms	53×	body	640	valid
4.0ms	24×	body	320	valid
4.0ms	89×	body	80	valid
1.0ms	13×	body	160	valid

simplify471.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5131	12

prune4.0ms

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: 41.3b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2.0 x)) 1.0) (-.f64 (exp.f64 x) 1.0)))
0.0b	(/.f64 (-.f64 (exp.f64 (*.f64 2.0 x)) 1.0) (-.f64 (exp.f64 x) 1.0))
3.8b	(-.f64 (exp.f64 (*.f64 2.0 x)) 1.0)
3.8b	(-.f64 (exp.f64 x) 1.0)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt_binary64`
75×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`sqrt-prod_binary64`
27×	`add-cube-cbrt_binary64`
24×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-/r_binary64` `pow1_binary64` `flip3--_binary64` `associate-/l_binary64` `flip--_binary64`
4×	`associate-/r/_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `rem-sqrt-square_binary64` `div-inv_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `sqrt-div_binary64`

Counts

4 → 121

Calls

4 calls:

10.0ms	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2.0 x)) 1.0) (-.f64 (exp.f64 x) 1.0)))
10.0ms	(/.f64 (-.f64 (exp.f64 (*.f64 2.0 x)) 1.0) (-.f64 (exp.f64 x) 1.0))
14.0ms	(-.f64 (exp.f64 (*.f64 2.0 x)) 1.0)
7.0ms	(-.f64 (exp.f64 x) 1.0)

series40.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2.0 x)) 1.0) (-.f64 (exp.f64 x) 1.0)))
10.0ms	(/.f64 (-.f64 (exp.f64 (*.f64 2.0 x)) 1.0) (-.f64 (exp.f64 x) 1.0))
3.0ms	(-.f64 (exp.f64 (*.f64 2.0 x)) 1.0)
12.0ms	(-.f64 (exp.f64 x) 1.0)

simplify42.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5066	2150

prune160.0ms

Filtered

96 candidates to 133 candidates (-38.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	130	3	133
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	131	3	134

Merged error: 0b

Counts

134 → 3

localize9.0ms

Local error

Found 1 expressions with local error:

9.2b	(sqrt.f64 (+.f64 2.0 (.f64 x (+.f64 (.f64 x 0.5) 1.0))))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
2×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `add-log-exp_binary64` `pow1/2_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`

Counts

1 → 15

Calls

1 calls:

3.0ms

(sqrt.f64 (+.f64 2.0 (*.f64 x (+.f64 (*.f64 x 0.5) 1.0))))

series7.0ms

Counts

1 → 3

Calls

1 calls:

7.0ms

(sqrt.f64 (+.f64 2.0 (*.f64 x (+.f64 (*.f64 x 0.5) 1.0))))

simplify26.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5259	280

prune25.0ms

Filtered

15 candidates to 18 candidates (-20.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	18	0	18
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	18	3	21

Merged error: 0b

Counts

21 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

3.8b	(-.f64 (sqrt.f64 (pow.f64 (exp.f64 x) 2.0)) (sqrt.f64 1.0))
3.8b	(-.f64 (exp.f64 x) 1.0)
3.8b	(-.f64 (exp.f64 x) 1.0)
3.8b	(-.f64 (exp.f64 x) 1.0)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
12×	`add-log-exp_binary64` `sqrt-prod_binary64`
11×	`difference-of-squares_binary64`
5×	`distribute-lft-out--_binary64`
4×	`sub-neg_binary64` `pow1_binary64` `flip3--_binary64` `diff-log_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
2×	`sqr-pow_binary64` `unpow-prod-down_binary64`

Counts

4 → 60

Calls

4 calls:

9.0ms	(-.f64 (sqrt.f64 (pow.f64 (exp.f64 x) 2.0)) (sqrt.f64 1.0))
5.0ms	(-.f64 (exp.f64 x) 1.0)
5.0ms	(-.f64 (exp.f64 x) 1.0)
7.0ms	(-.f64 (exp.f64 x) 1.0)

series11.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(-.f64 (sqrt.f64 (pow.f64 (exp.f64 x) 2.0)) (sqrt.f64 1.0))
2.0ms	(-.f64 (exp.f64 x) 1.0)
2.0ms	(-.f64 (exp.f64 x) 1.0)
2.0ms	(-.f64 (exp.f64 x) 1.0)

simplify80.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4871	674
1	4871	674

prune103.0ms

Filtered

52 candidates to 72 candidates (-38.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	72	3	75

Merged error: 0b

Counts

75 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (-.f64 (pow.f64 (exp.f64 x) 2.0) 1.0) 3)
0.0b	(cbrt.f64 (pow.f64 (-.f64 (pow.f64 (exp.f64 x) 2.0) 1.0) 3))
3.8b	(-.f64 (pow.f64 (exp.f64 x) 2.0) 1.0)
3.8b	(-.f64 (exp.f64 x) 1.0)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
20×	`cbrt-prod_binary64`
19×	`unpow-prod-down_binary64`
16×	`difference-of-squares_binary64`
14×	`cube-prod_binary64`
10×	`add-cube-cbrt_binary64`
8×	`add-log-exp_binary64`
7×	`sqr-pow_binary64`
6×	`distribute-lft-out--_binary64`
5×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`flip3--_binary64` `cube-div_binary64` `flip--_binary64`
3×	`pow-unpow_binary64`
2×	`cbrt-div_binary64` `sub-neg_binary64` `diff-log_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `rem-cbrt-cube_binary64` `pow1/3_binary64` `pow-pow_binary64` `rem-cube-cbrt_binary64` `pow-exp_binary64`

Counts

4 → 92

Calls

4 calls:

8.0ms	(pow.f64 (-.f64 (pow.f64 (exp.f64 x) 2.0) 1.0) 3)
8.0ms	(cbrt.f64 (pow.f64 (-.f64 (pow.f64 (exp.f64 x) 2.0) 1.0) 3))
6.0ms	(-.f64 (pow.f64 (exp.f64 x) 2.0) 1.0)
5.0ms	(-.f64 (exp.f64 x) 1.0)

series30.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(pow.f64 (-.f64 (pow.f64 (exp.f64 x) 2.0) 1.0) 3)
8.0ms	(cbrt.f64 (pow.f64 (-.f64 (pow.f64 (exp.f64 x) 2.0) 1.0) 3))
5.0ms	(-.f64 (pow.f64 (exp.f64 x) 2.0) 1.0)
3.0ms	(-.f64 (exp.f64 x) 1.0)

simplify28.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5001	1138

prune84.0ms

Filtered

63 candidates to 104 candidates (-65.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	104	3	107

Merged error: 0b

Counts

107 → 3

regimes37.0ms

Accuracy

98.8% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 20.9b

bsearch15.0ms

Steps

Iters	Range		Point
8	-0.04656747277699857	-3.260266735920925e-06	-0.0001300712652255136

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	29
1	37	29

end0.0ms

sample1.6s

Algorithm

intervals

Results

822.0ms	2254×	body	1280	valid
395.0ms	1691×	body	640	valid
126.0ms	2820×	body	80	valid
126.0ms	804×	body	320	valid
43.0ms	431×	body	160	valid
0.0ms	4×	body	80	invalid

Details

analyze508.0ms

sample66.0ms

simplify471.0ms

prune4.0ms

localize10.0ms

rewrite48.0ms

series40.0ms

simplify42.0ms

prune160.0ms

localize9.0ms

rewrite3.0ms

series7.0ms

simplify26.0ms

prune25.0ms

localize17.0ms

rewrite28.0ms

series11.0ms

simplify80.0ms

prune103.0ms

localize10.0ms

rewrite29.0ms

series30.0ms

simplify28.0ms

prune84.0ms

regimes37.0ms

bsearch15.0ms

simplify2.0ms

end0.0ms

sample1.6s

Profiling