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

sample239.0ms

Algorithm

intervals

Results

70.0ms	130×	body	1280	valid
55.0ms	48×	body	1280	nan
22.0ms	31×	body	640	nan
22.0ms	47×	body	640	valid
19.0ms	105×	body	80	overflowed
7.0ms	22×	body	320	valid
6.0ms	10×	body	160	nan
5.0ms	13×	body	320	nan
4.0ms	49×	body	80	valid
4.0ms	6×	body	640	invalid
3.0ms	7×	body	320	invalid
2.0ms	2×	body	1280	invalid
2.0ms	8×	body	160	valid
1.0ms	9×	body	80	invalid
1.0ms	19×	body	80	nan
0.0ms	2×	body	160	invalid

simplify60.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4977	13
1	4977	13

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: 29.6b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow.f64 (+.f64 x 1.0) (/.f64 1.0 n))
0.0b	(pow.f64 x (/.f64 1.0 n))
0.6b	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64`
26×	`pow-unpow_binary64`
19×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
17×	`unpow-prod-down_binary64`
9×	`difference-of-squares_binary64`
8×	`sqr-pow_binary64`
5×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64`
3×	`add-cbrt-cube_binary64` `distribute-lft-out--_binary64`
2×	`pow-to-exp_binary64` `distribute-lft-out_binary64` `pow-pow_binary64` `div-inv_binary64` `pow-exp_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `flip--_binary64`

Counts

3 → 78

Calls

3 calls:

6.0ms	(pow.f64 (+.f64 x 1.0) (/.f64 1.0 n))
4.0ms	(pow.f64 x (/.f64 1.0 n))
11.0ms	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))

series79.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(pow.f64 (+.f64 x 1.0) (/.f64 1.0 n))
12.0ms	(pow.f64 x (/.f64 1.0 n))
48.0ms	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))

simplify47.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5141	1177

prune105.0ms

Filtered

69 candidates to 87 candidates (-26.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	83	4	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	4	88

Merged error: 19.5b

Counts

88 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 n)
0.5b	(cbrt.f64 n)
0.5b	(cbrt.f64 n)
0.8b	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 (pow.f64 x (/.f64 1 (*.f64 (cbrt.f64 n) (cbrt.f64 n)))) (/.f64 1.0 (cbrt.f64 n))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
17×	`unpow-prod-down_binary64`
15×	`difference-of-squares_binary64`
11×	`sqr-pow_binary64`
9×	`*-un-lft-identity_binary64` `cbrt-prod_binary64`
7×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64`
4×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1/3_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

4 → 60

Calls

4 calls:

2.0ms	(cbrt.f64 n)
2.0ms	(cbrt.f64 n)
2.0ms	(cbrt.f64 n)
22.0ms	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 (pow.f64 x (/.f64 1 (*.f64 (cbrt.f64 n) (cbrt.f64 n)))) (/.f64 1.0 (cbrt.f64 n))))

series148.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(cbrt.f64 n)
17.0ms	(cbrt.f64 n)
17.0ms	(cbrt.f64 n)
95.0ms	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 (pow.f64 x (/.f64 1 (*.f64 (cbrt.f64 n) (cbrt.f64 n)))) (/.f64 1.0 (cbrt.f64 n))))

simplify63.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4916	1232
1	4916	1232

prune102.0ms

Filtered

65 candidates to 72 candidates (-10.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	72	4	76

Merged error: 19.5b

Counts

76 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 x (.f64 x n))
0.7b	(/.f64 0.5 (.f64 x (.f64 x n)))
0.8b	(/.f64 (log.f64 x) (*.f64 n n))
4.3b	(.f64 (/.f64 1.0 x) (+.f64 (/.f64 1 n) (/.f64 (log.f64 x) (.f64 n n))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
22×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64` `times-frac_binary64`
16×	`associate-l_binary64`
13×	`pow1_binary64`
9×	`cbrt-unprod_binary64` `prod-exp_binary64`
7×	`associate-/l*_binary64`
6×	`associate-r_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `div-inv_binary64`
3×	`associate-*r/_binary64` `frac-times_binary64`
2×	`flip3-+_binary64` `associate-/r_binary64` `distribute-lft-out_binary64` `frac-add_binary64` `log-pow_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64` `-commutative_binary64`
1×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `associate-*l/_binary64`

Counts

4 → 106

Calls

4 calls:

5.0ms	(.f64 x (.f64 x n))
6.0ms	(/.f64 0.5 (.f64 x (.f64 x n)))
5.0ms	(/.f64 (log.f64 x) (*.f64 n n))
17.0ms	(.f64 (/.f64 1.0 x) (+.f64 (/.f64 1 n) (/.f64 (log.f64 x) (.f64 n n))))

series43.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(.f64 x (.f64 x n))
4.0ms	(/.f64 0.5 (.f64 x (.f64 x n)))
10.0ms	(/.f64 (log.f64 x) (*.f64 n n))
24.0ms	(.f64 (/.f64 1.0 x) (+.f64 (/.f64 1 n) (/.f64 (log.f64 x) (.f64 n n))))

simplify44.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4965	1212
1	4965	1212

prune114.0ms

Filtered

78 candidates to 118 candidates (-51.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	112	6	118
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	113	9	122

Merged error: 19.3b

Counts

122 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 x (.f64 x n))
0.2b	(/.f64 (/.f64 1.0 x) n)
0.3b	(/.f64 (log.f64 x) n)
0.7b	(/.f64 0.5 (.f64 x (.f64 x n)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac_binary64`
58×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
25×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
20×	`associate-/l*_binary64`
13×	`pow1_binary64`
7×	`associate-/r*_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64`
6×	`cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64` `log-pow_binary64`
3×	`pow-prod-down_binary64` `associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`associate-/l/_binary64` `associate-r_binary64` `*-commutative_binary64`

Counts

4 → 142

Calls

4 calls:

5.0ms	(.f64 x (.f64 x n))
6.0ms	(/.f64 (/.f64 1.0 x) n)
4.0ms	(/.f64 (log.f64 x) n)
6.0ms	(/.f64 0.5 (.f64 x (.f64 x n)))

series21.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(.f64 x (.f64 x n))
4.0ms	(/.f64 (/.f64 1.0 x) n)
8.0ms	(/.f64 (log.f64 x) n)
5.0ms	(/.f64 0.5 (.f64 x (.f64 x n)))

simplify64.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4947	1367
1	4947	1367

prune133.0ms

Filtered

110 candidates to 154 candidates (-40.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	151	3	154
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	153	10	163

Merged error: 19.3b

Counts

163 → 10

regimes235.0ms

Accuracy

84.2% (1.7b remaining)

Error of 23.2b against oracle of 21.5b and baseline of 32.5b

bsearch144.0ms

Steps

Iters	Range		Point
11	2.433706907414182e-16	9641786123.138424	35146050.636312656
9	-470993163.7600871	-33.446121995133495	-116924.1052241744

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	73	76
1	73	76

end0.0ms

sample6.7s

Algorithm

intervals

Results

2.1s	3809×	body	1280	valid
1.2s	1068×	body	1280	nan
711.0ms	1558×	body	640	valid
687.0ms	936×	body	640	nan
482.0ms	2687×	body	80	overflowed
232.0ms	739×	body	320	valid
186.0ms	429×	body	320	nan
169.0ms	240×	body	640	invalid
150.0ms	1551×	body	80	valid
117.0ms	90×	body	1280	invalid
85.0ms	201×	body	320	invalid
69.0ms	343×	body	160	valid
60.0ms	235×	body	160	nan
33.0ms	535×	body	80	nan
30.0ms	234×	body	80	invalid
17.0ms	67×	body	160	invalid

Details

analyze1.2s

sample239.0ms

simplify60.0ms

prune3.0ms

localize8.0ms

rewrite24.0ms

series79.0ms

simplify47.0ms

prune105.0ms

localize16.0ms

rewrite32.0ms

series148.0ms

simplify63.0ms

prune102.0ms

localize14.0ms

rewrite36.0ms

series43.0ms

simplify44.0ms

prune114.0ms

localize14.0ms

rewrite27.0ms

series21.0ms

simplify64.0ms

prune133.0ms

regimes235.0ms

bsearch144.0ms

simplify3.0ms

end0.0ms

sample6.7s

Profiling