Details

analyze1.2s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	62.4%	12.6%	5
25%	56.2%	18.8%	6
28.1%	50%	22%	7
28.1%	46.8%	25.1%	8
29.7%	41.4%	29%	9
29.7%	39.4%	30.9%	10
31.1%	35.8%	33.1%	11
31.1%	34.4%	34.5%	12
31.5%	32.9%	35.6%	13
31.5%	32.1%	36.4%	14

sample187.0ms

Algorithm

intervals

Results

61.0ms	122×	body	1280	valid
37.0ms	37×	body	1280	nan
20.0ms	49×	body	640	valid
17.0ms	22×	body	640	nan
12.0ms	72×	body	80	overflowed
7.0ms	23×	body	320	valid
5.0ms	55×	body	80	valid
4.0ms	6×	body	640	invalid
4.0ms	3×	body	1280	invalid
3.0ms	7×	body	320	nan
1.0ms	4×	body	320	invalid
1.0ms	7×	body	160	valid
1.0ms	18×	body	80	nan
1.0ms	4×	body	160	nan
1.0ms	5×	body	80	invalid
0.0ms	1×	body	160	invalid

simplify57.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4912	13
1	4912	13

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: 30.4b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(pow.f64 x (/.f64 1 n))
1.1b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
13×	`pow-unpow_binary64` `unpow-prod-down_binary64`
10×	`add-cube-cbrt_binary64`
9×	`difference-of-squares_binary64` `times-frac_binary64`
7×	`sqr-pow_binary64`
4×	`add-log-exp_binary64`
3×	`pow1_binary64` `add-exp-log_binary64` `distribute-lft-out--_binary64`
2×	`add-cbrt-cube_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `pow-pow_binary64` `div-inv_binary64` `flip--_binary64` `pow-exp_binary64`

Counts

2 → 50

Calls

2 calls:

4.0ms	(pow.f64 x (/.f64 1 n))
10.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

series44.0ms

Counts

2 → 6

Calls

2 calls:

10.0ms	(pow.f64 x (/.f64 1 n))
34.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

simplify61.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4913	797
1	4913	797

prune55.0ms

Filtered

44 candidates to 56 candidates (-27.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	53	3	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	3	57

Merged error: 19.3b

Counts

57 → 3

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(exp.f64 (/.f64 (log.f64 x) n))
0.3b	(/.f64 (log.f64 x) n)
1.1b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
24×	`times-frac_binary64`
22×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
16×	`exp-prod_binary64`
10×	`pow1_binary64`
7×	`log-pow_binary64`
6×	`add-log-exp_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`associate-/l*_binary64`
3×	`associate-/r*_binary64` `difference-of-squares_binary64` `div-inv_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `sqr-pow_binary64` `rem-exp-log_binary64` `clear-num_binary64` `unpow-prod-down_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `flip--_binary64` `exp-to-pow_binary64`

Counts

3 → 71

Calls

3 calls:

4.0ms	(exp.f64 (/.f64 (log.f64 x) n))
4.0ms	(/.f64 (log.f64 x) n)
10.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n)))

series45.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(exp.f64 (/.f64 (log.f64 x) n))
7.0ms	(/.f64 (log.f64 x) n)
28.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n)))

simplify32.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4905	819
1	4905	819

prune44.0ms

Filtered

57 candidates to 80 candidates (-40.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	80	3	83

Merged error: 19.3b

Counts

83 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp.f64 (/.f64 (log.f64 x) n))
0.3b	(/.f64 (log.f64 x) n)
0.3b	(/.f64 (log.f64 x) n)
3.6b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (*.f64 (sqrt.f64 (exp.f64 (/.f64 (log.f64 x) n))) (sqrt.f64 (exp.f64 (/.f64 (log.f64 x) n)))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac_binary64`
32×	`add-sqr-sqrt_binary64`
30×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
16×	`exp-prod_binary64`
15×	`pow1_binary64`
11×	`log-pow_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
7×	`add-log-exp_binary64`
6×	`associate-/r*_binary64`
4×	`div-inv_binary64`
3×	`difference-of-squares_binary64`
2×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `sqr-pow_binary64` `rem-exp-log_binary64` `unpow-prod-down_binary64` `flip--_binary64` `exp-to-pow_binary64`

Counts

4 → 101

Calls

4 calls:

4.0ms	(exp.f64 (/.f64 (log.f64 x) n))
4.0ms	(/.f64 (log.f64 x) n)
4.0ms	(/.f64 (log.f64 x) n)
7.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (*.f64 (sqrt.f64 (exp.f64 (/.f64 (log.f64 x) n))) (sqrt.f64 (exp.f64 (/.f64 (log.f64 x) n)))))

series52.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(exp.f64 (/.f64 (log.f64 x) n))
7.0ms	(/.f64 (log.f64 x) n)
7.0ms	(/.f64 (log.f64 x) n)
29.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (*.f64 (sqrt.f64 (exp.f64 (/.f64 (log.f64 x) n))) (sqrt.f64 (exp.f64 (/.f64 (log.f64 x) n)))))

simplify62.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4888	1055
1	4888	1055

prune58.0ms

Filtered

80 candidates to 113 candidates (-41.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	112	4	116

Merged error: 19.3b

Counts

116 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(/.f64 1 (*.f64 x n))
0.8b	(/.f64 (log.f64 x) (.f64 x (.f64 n n)))
2.5b	(-.f64 (/.f64 1 (.f64 x n)) (/.f64 1/2 (.f64 x (*.f64 x n))))
8.1b	(.f64 x (.f64 n n))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-exp-log_binary64`
23×	`add-cbrt-cube_binary64`
14×	`*-un-lft-identity_binary64` `pow1_binary64`
12×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64` `prod-exp_binary64` `times-frac_binary64`
7×	`cbrt-unprod_binary64` `associate-/l*_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64`
5×	`cbrt-undiv_binary64`
4×	`pow-prod-down_binary64`
3×	`associate-l_binary64` `distribute-lft-out--_binary64` `div-inv_binary64`
2×	`associate-/r*_binary64` `1-exp_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64` `pow-flip_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `associate-r_binary64` `unswap-sqr_binary64` `inv-pow_binary64` `difference-of-squares_binary64` `flip--_binary64` `frac-sub_binary64` `*-commutative_binary64`

Counts

4 → 88

Calls

4 calls:

5.0ms	(/.f64 1 (*.f64 x n))
7.0ms	(/.f64 (log.f64 x) (.f64 x (.f64 n n)))
11.0ms	(-.f64 (/.f64 1 (.f64 x n)) (/.f64 1/2 (.f64 x (*.f64 x n))))
6.0ms	(.f64 x (.f64 n n))

series30.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/.f64 1 (*.f64 x n))
14.0ms	(/.f64 (log.f64 x) (.f64 x (.f64 n n)))
6.0ms	(-.f64 (/.f64 1 (.f64 x n)) (/.f64 1/2 (.f64 x (*.f64 x n))))
7.0ms	(.f64 x (.f64 n n))

simplify39.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5260	884

prune42.0ms

Filtered

56 candidates to 100 candidates (-78.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	95	5	100
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	95	9	104

Merged error: 18.7b

Counts

104 → 9

regimes120.0ms

Accuracy

85.8% (1.6b remaining)

Error of 23.3b against oracle of 21.8b and baseline of 32.9b

bsearch98.0ms

Steps

Iters	Range		Point
7	8733.533672405438	842852.0075109552	829455.0002747169
9	-83187900.77998409	-23.96138598826094	-19797961.77181827

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	69	52
1	69	52

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.0s	3731×	body	1280	valid
1.1s	1036×	body	1280	nan
713.0ms	1662×	body	640	valid
601.0ms	870×	body	640	nan
453.0ms	2605×	body	80	overflowed
210.0ms	700×	body	320	valid
183.0ms	451×	body	320	nan
179.0ms	262×	body	640	invalid
157.0ms	117×	body	1280	invalid
134.0ms	1553×	body	80	valid
67.0ms	354×	body	160	valid
67.0ms	174×	body	320	invalid
56.0ms	242×	body	160	nan
32.0ms	520×	body	80	nan
24.0ms	197×	body	80	invalid
19.0ms	81×	body	160	invalid

Details

analyze1.2s

sample187.0ms

simplify57.0ms

prune2.0ms

localize8.0ms

rewrite16.0ms

series44.0ms

simplify61.0ms

prune55.0ms

localize12.0ms

rewrite20.0ms

series45.0ms

simplify32.0ms

prune44.0ms

localize14.0ms

rewrite23.0ms

series52.0ms

simplify62.0ms

prune58.0ms

localize13.0ms

rewrite31.0ms

series30.0ms

simplify39.0ms

prune42.0ms

regimes120.0ms

bsearch98.0ms

simplify2.0ms

end0.0ms

sample6.3s

Profiling