Details

analyze42.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	31.2%	6.3%	6
68.7%	21.9%	9.5%	7
68.7%	17.2%	14.1%	8
71.8%	11.7%	16.5%	9
71.8%	9%	19.2%	10
73.4%	6%	20.6%	11
73.4%	4.6%	22%	12
74.1%	3.1%	22.8%	13
74.1%	2.3%	23.5%	14

sample34.0ms

Algorithm

intervals

Results

16.0ms	87×	body	1280	valid
5.0ms	47×	body	640	valid
2.0ms	87×	body	80	valid
2.0ms	23×	body	320	valid
1.0ms	12×	body	160	valid
0.0ms	3×	body	80	invalid

simplify68.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4778	6
1	4778	6

prune3.0ms

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

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp.f64 (*.f64 a x))
3.6b	(-.f64 (exp.f64 (*.f64 a x)) 1.0)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp_binary64`
4×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
2×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `rem-exp-log_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `exp-to-pow_binary64` `exp-prod_binary64`

Counts

2 → 23

Calls

2 calls:

2.0ms	(exp.f64 (*.f64 a x))
4.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1.0)

series13.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(exp.f64 (*.f64 a x))
9.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1.0)

simplify70.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4915	224
1	4915	224

prune42.0ms

Filtered

20 candidates to 29 candidates (-45.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	24	5	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	25	5	30

Merged error: 3.9b

Counts

30 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

1.2b	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
5.2b	(.f64 x (.f64 1/6 (pow.f64 a 3)))
8.6b	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))
9.5b	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
10×	`pow1_binary64`
9×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64` `prod-exp_binary64`
7×	`associate-r_binary64`
6×	`add-log-exp_binary64`
5×	`cbrt-unprod_binary64`
4×	`associate-*r/_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `flip-+_binary64` `*-commutative_binary64`
2×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64`
1×	`pow-to-exp_binary64` `+-commutative_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

4 → 74

Calls

4 calls:

6.0ms	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
7.0ms	(.f64 x (.f64 1/6 (pow.f64 a 3)))
7.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))
10.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))

series85.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
16.0ms	(.f64 x (.f64 1/6 (pow.f64 a 3)))
11.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))
29.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))

simplify30.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5186	1359

prune97.0ms

Filtered

54 candidates to 86 candidates (-59.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	84	7	91

Merged error: 2.2b

Counts

91 → 7

localize8.0ms

Local error

Found 3 expressions with local error:

2.4b	(+.f64 (.f64 x a) (.f64 1/2 (.f64 x (.f64 x (*.f64 a a)))))
3.7b	(.f64 x (.f64 x (*.f64 a a)))
10.3b	(.f64 x (.f64 a a))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
6×	`associate-l_binary64` `add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-cube-cbrt_binary64`
2×	`associate-r_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `unswap-sqr_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

3 → 51

Calls

3 calls:

6.0ms	(+.f64 (.f64 x a) (.f64 1/2 (.f64 x (.f64 x (*.f64 a a)))))
8.0ms	(.f64 x (.f64 x (*.f64 a a)))
6.0ms	(.f64 x (.f64 a a))

series33.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(+.f64 (.f64 x a) (.f64 1/2 (.f64 x (.f64 x (*.f64 a a)))))
8.0ms	(.f64 x (.f64 x (*.f64 a a)))
9.0ms	(.f64 x (.f64 a a))

simplify29.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	4968	476
1	4968	476

prune56.0ms

Filtered

35 candidates to 60 candidates (-71.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	59	1	60
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	62	5	67

Merged error: 0.1b

Counts

67 → 5

localize8.0ms

Local error

Found 3 expressions with local error:

0.3b	(pow.f64 (*.f64 x a) 6)
2.4b	(+.f64 (.f64 x a) (.f64 1/2 (cbrt.f64 (pow.f64 (*.f64 x a) 6))))
17.3b	(cbrt.f64 (pow.f64 (*.f64 x a) 6))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

6×	`pow1_binary64` `add-exp-log_binary64`
5×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `cbrt-prod_binary64`
3×	`pow-unpow_binary64` `add-cbrt-cube_binary64`
2×	`pow-pow_binary64` `sqr-pow_binary64` `unpow-prod-down_binary64` `pow-exp_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `flip3-+_binary64` `pow1/3_binary64` `prod-exp_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

3 → 41

Calls

3 calls:

4.0ms	(pow.f64 (*.f64 x a) 6)
4.0ms	(+.f64 (.f64 x a) (.f64 1/2 (cbrt.f64 (pow.f64 (*.f64 x a) 6))))
2.0ms	(cbrt.f64 (pow.f64 (*.f64 x a) 6))

series39.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(pow.f64 (*.f64 x a) 6)
14.0ms	(+.f64 (.f64 x a) (.f64 1/2 (cbrt.f64 (pow.f64 (*.f64 x a) 6))))
9.0ms	(cbrt.f64 (pow.f64 (*.f64 x a) 6))

simplify60.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5156	413

prune44.0ms

Filtered

36 candidates to 50 candidates (-38.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	49	1	50
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	50	5	55

Merged error: 0.1b

Counts

55 → 5

regimes328.0ms

Accuracy

98.3% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 21.9b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	26
1	30	26

end0.0ms

sample955.0ms

Algorithm

intervals

Results

489.0ms	2679×	body	1280	valid
157.0ms	1326×	body	640	valid
72.0ms	2826×	body	80	valid
61.0ms	758×	body	320	valid
22.0ms	411×	body	160	valid
3.0ms	130×	body	80	invalid

Details

analyze42.0ms

sample34.0ms

simplify68.0ms

prune3.0ms

localize9.0ms

rewrite7.0ms

series13.0ms

simplify70.0ms

prune42.0ms

localize12.0ms

rewrite32.0ms

series85.0ms

simplify30.0ms

prune97.0ms

localize8.0ms

rewrite21.0ms

series33.0ms

simplify29.0ms

prune56.0ms

localize8.0ms

rewrite11.0ms

series39.0ms

simplify60.0ms

prune44.0ms

regimes328.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample955.0ms

Profiling