Details

analyze46.0ms

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

sample36.0ms

Algorithm

intervals

Results

19.0ms	97×	body	1280	valid
5.0ms	41×	body	640	valid
2.0ms	25×	body	320	valid
2.0ms	78×	body	80	valid
1.0ms	15×	body	160	valid
0.0ms	6×	body	80	invalid

simplify67.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (64.0ms)

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: 29.1b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp.f64 (*.f64 a x))
4.3b	(-.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:

4.0ms	(exp.f64 (*.f64 a x))
9.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1.0)

simplify75.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4915	224
1	4915	224

prune44.0ms

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: 4.7b

Counts

30 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

1.7b	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
6.4b	(.f64 x (.f64 1/6 (pow.f64 a 3)))
6.4b	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
10.6b	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

rewrite33.0ms

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:

5.0ms	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
6.0ms	(.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)))))
8.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

series81.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
13.0ms	(.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)))))
11.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

simplify33.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5186	1359

prune84.0ms

Filtered

54 candidates to 86 candidates (-59.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	86	5	91

Merged error: 2.6b

Counts

91 → 5

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(.f64 1/2 (.f64 (.f64 a a) (.f64 x x)))
4.2b	(+.f64 (.f64 a x) (.f64 1/2 (.f64 (.f64 a a) (*.f64 x x))))
15.5b	(.f64 (.f64 a a) (*.f64 x x))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

49×	`pow1_binary64`
33×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
27×	`pow-prod-down_binary64`
21×	`cbrt-unprod_binary64` `prod-exp_binary64`
5×	`add-log-exp_binary64`
4×	`-un-lft-identity_binary64` `pow-prod-up_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64` `pow-plus_binary64` `add-sqr-sqrt_binary64`
2×	`associate-r_binary64` `pow-sqr_binary64` `pow2_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `unswap-sqr_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

3 → 67

Calls

3 calls:

14.0ms	(.f64 1/2 (.f64 (.f64 a a) (.f64 x x)))
5.0ms	(+.f64 (.f64 a x) (.f64 1/2 (.f64 (.f64 a a) (*.f64 x x))))
9.0ms	(.f64 (.f64 a a) (*.f64 x x))

series31.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(.f64 1/2 (.f64 (.f64 a a) (.f64 x x)))
14.0ms	(+.f64 (.f64 a x) (.f64 1/2 (.f64 (.f64 a a) (*.f64 x x))))
8.0ms	(.f64 (.f64 a a) (*.f64 x x))

simplify64.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4962	572
1	4962	572

prune52.0ms

Filtered

40 candidates to 76 candidates (-90.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	2	1	3
Picked	1	0	1
Done	1	0	1
Total	79	2	81

Merged error: 0.1b

Counts

81 → 2

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(.f64 1/2 (pow.f64 (.f64 a x) 2))
0.2b	(pow.f64 (*.f64 a x) 2)
4.2b	(+.f64 (.f64 a x) (.f64 1/2 (pow.f64 (*.f64 a x) 2)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log_binary64`
10×	`add-sqr-sqrt_binary64`
6×	`-un-lft-identity_binary64` `pow1_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64` `prod-exp_binary64`
5×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
4×	`pow-exp_binary64`
3×	`pow-unpow_binary64` `unpow2_binary64` `sqr-pow_binary64` `associate-l_binary64` `unswap-sqr_binary64`
2×	`pow-to-exp_binary64` `pow-pow_binary64` `unpow-prod-down_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

3 → 54

Calls

3 calls:

5.0ms	(.f64 1/2 (pow.f64 (.f64 a x) 2))
4.0ms	(pow.f64 (*.f64 a x) 2)
5.0ms	(+.f64 (.f64 a x) (.f64 1/2 (pow.f64 (*.f64 a x) 2)))

series31.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(.f64 1/2 (pow.f64 (.f64 a x) 2))
6.0ms	(pow.f64 (*.f64 a x) 2)
14.0ms	(+.f64 (.f64 a x) (.f64 1/2 (pow.f64 (*.f64 a x) 2)))

simplify29.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5115	523

prune41.0ms

Filtered

39 candidates to 63 candidates (-61.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	63	2	65

Merged error: 0.1b

Counts

65 → 2

regimes143.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 22.2b

bsearch13.0ms

Steps

Iters	Range		Point
10	-7.62739742382033	-1.1098068008089188e-11	-1.2065385524619287e-05

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	36
1	31	36

end0.0ms

sample949.0ms

Algorithm

intervals

Results

495.0ms	2718×	body	1280	valid
154.0ms	1306×	body	640	valid
71.0ms	2865×	body	80	valid
56.0ms	708×	body	320	valid
22.0ms	403×	body	160	valid
3.0ms	131×	body	80	invalid

Details

analyze46.0ms

sample36.0ms

simplify67.0ms

prune3.0ms

localize4.0ms

rewrite7.0ms

series13.0ms

simplify75.0ms

prune44.0ms

localize12.0ms

rewrite33.0ms

series81.0ms

simplify33.0ms

prune84.0ms

localize8.0ms

rewrite31.0ms

series31.0ms

simplify64.0ms

prune52.0ms

localize6.0ms

rewrite15.0ms

series31.0ms

simplify29.0ms

prune41.0ms

regimes143.0ms

bsearch13.0ms

simplify2.0ms

end0.0ms

sample949.0ms

Profiling