Details

analyze804.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
3.1%	96.8%	0.1%	6
15.6%	81.2%	3.2%	7
23.4%	72.6%	4%	8
32.4%	56.2%	11.4%	9
36.3%	51.7%	12%	10
40.7%	42.9%	16.4%	11
42.6%	40.3%	17.1%	12
44.5%	36%	19.4%	13
45.5%	34.5%	20%	14

sample229.0ms

Algorithm

intervals

Results

90.0ms	39×	body	2560	valid
87.0ms	96×	body	1280	valid
19.0ms	46×	body	640	valid
5.0ms	9×	body	640	invalid
4.0ms	18×	body	320	valid
3.0ms	44×	body	80	valid
2.0ms	13×	body	160	valid
2.0ms	1×	body	2560	invalid
2.0ms	5×	body	320	invalid
2.0ms	2×	body	1280	invalid
1.0ms	12×	body	80	invalid
1.0ms	4×	body	160	invalid
0.0ms	9×	body	80	nan

simplify44.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5281	15

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: 48.4b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 100.0 (/.f64 (-.f64 (pow.f64 (+.f64 1.0 (/.f64 i n)) n) 1.0) (/.f64 i n)))
2.0b	(-.f64 (pow.f64 (+.f64 1.0 (/.f64 i n)) n) 1.0)
5.2b	(pow.f64 (+.f64 1.0 (/.f64 i n)) n)
13.9b	(/.f64 (-.f64 (pow.f64 (+.f64 1.0 (/.f64 i n)) n) 1.0) (/.f64 i n))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

320×	`times-frac_binary64`
289×	`add-sqr-sqrt_binary64`
198×	`*-un-lft-identity_binary64`
140×	`add-cube-cbrt_binary64`
96×	`associate-r_binary64`
84×	`difference-of-squares_binary64`
32×	`unpow-prod-down_binary64`
29×	`sqr-pow_binary64`
28×	`distribute-lft-out--_binary64`
19×	`add-exp-log_binary64`
18×	`add-cbrt-cube_binary64`
17×	`div-inv_binary64`
13×	`associate-/r*_binary64`
7×	`pow1_binary64` `associate-/l*_binary64`
6×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
3×	`pow-unpow_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `associate-r/_binary64` `pow-pow_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `pow-exp_binary64` `-commutative_binary64`

Counts

4 → 280

Calls

4 calls:

33.0ms	(*.f64 100.0 (/.f64 (-.f64 (pow.f64 (+.f64 1.0 (/.f64 i n)) n) 1.0) (/.f64 i n)))
10.0ms	(-.f64 (pow.f64 (+.f64 1.0 (/.f64 i n)) n) 1.0)
7.0ms	(pow.f64 (+.f64 1.0 (/.f64 i n)) n)
20.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1.0 (/.f64 i n)) n) 1.0) (/.f64 i n))

series251.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(*.f64 100.0 (/.f64 (-.f64 (pow.f64 (+.f64 1.0 (/.f64 i n)) n) 1.0) (/.f64 i n)))
46.0ms	(-.f64 (pow.f64 (+.f64 1.0 (/.f64 i n)) n) 1.0)
38.0ms	(pow.f64 (+.f64 1.0 (/.f64 i n)) n)
80.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1.0 (/.f64 i n)) n) 1.0) (/.f64 i n))

simplify93.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4988	5853
1	4988	5853

prune452.0ms

Filtered

223 candidates to 292 candidates (-30.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	285	7	292
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	286	7	293

Merged error: 23.0b

Counts

293 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 (.f64 i i) 0.5)
0.1b	(.f64 100.0 (/.f64 (-.f64 (+.f64 (.f64 1.0 i) (+.f64 (.f64 n (log.f64 1.0)) (.f64 (.f64 i i) 0.5))) (.f64 (log.f64 1.0) (.f64 (.f64 i i) 0.5))) (/.f64 i n)))
11.1b	(.f64 (log.f64 1.0) (.f64 (*.f64 i i) 0.5))
21.6b	(/.f64 (-.f64 (+.f64 (.f64 1.0 i) (+.f64 (.f64 n (log.f64 1.0)) (.f64 (.f64 i i) 0.5))) (.f64 (log.f64 1.0) (.f64 (*.f64 i i) 0.5))) (/.f64 i n))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac_binary64`
94×	`add-sqr-sqrt_binary64`
84×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
48×	`associate-r_binary64`
32×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
21×	`pow1_binary64`
13×	`associate-/r*_binary64`
12×	`cbrt-unprod_binary64` `prod-exp_binary64`
10×	`pow-prod-down_binary64`
9×	`div-inv_binary64`
8×	`associate-l_binary64`
6×	`cbrt-undiv_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64`
3×	`associate-/l_binary64` `-commutative_binary64`
2×	`associate-/l/_binary64` `associate-/r/_binary64`
1×	`flip3--_binary64` `associate-*r/_binary64` `log-pow_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64`

Counts

4 → 180

Calls

4 calls:

6.0ms	(.f64 (.f64 i i) 0.5)
21.0ms	(.f64 100.0 (/.f64 (-.f64 (+.f64 (.f64 1.0 i) (+.f64 (.f64 n (log.f64 1.0)) (.f64 (.f64 i i) 0.5))) (.f64 (log.f64 1.0) (.f64 (.f64 i i) 0.5))) (/.f64 i n)))
8.0ms	(.f64 (log.f64 1.0) (.f64 (*.f64 i i) 0.5))
17.0ms	(/.f64 (-.f64 (+.f64 (.f64 1.0 i) (+.f64 (.f64 n (log.f64 1.0)) (.f64 (.f64 i i) 0.5))) (.f64 (log.f64 1.0) (.f64 (*.f64 i i) 0.5))) (/.f64 i n))

series75.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(.f64 (.f64 i i) 0.5)
30.0ms	(.f64 100.0 (/.f64 (-.f64 (+.f64 (.f64 1.0 i) (+.f64 (.f64 n (log.f64 1.0)) (.f64 (.f64 i i) 0.5))) (.f64 (log.f64 1.0) (.f64 (.f64 i i) 0.5))) (/.f64 i n)))
16.0ms	(.f64 (log.f64 1.0) (.f64 (*.f64 i i) 0.5))
25.0ms	(/.f64 (-.f64 (+.f64 (.f64 1.0 i) (+.f64 (.f64 n (log.f64 1.0)) (.f64 (.f64 i i) 0.5))) (.f64 (log.f64 1.0) (.f64 (*.f64 i i) 0.5))) (/.f64 i n))

simplify56.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5027	5909

prune608.0ms

Filtered

142 candidates to 192 candidates (-35.2%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	178	14	192
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	179	20	199

Merged error: 8.6b

Counts

199 → 20

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 (/.f64 (-.f64 (+.f64 (.f64 1.0 i) (+.f64 (.f64 n (log.f64 1.0)) (.f64 (.f64 i i) 0.5))) (.f64 (log.f64 1.0) (.f64 (.f64 i i) 0.5))) i) n)
0.1b	(.f64 100.0 (.f64 (/.f64 (-.f64 (+.f64 (.f64 1.0 i) (+.f64 (.f64 n (log.f64 1.0)) (.f64 (.f64 i i) 0.5))) (.f64 (log.f64 1.0) (.f64 (*.f64 i i) 0.5))) i) n))
10.5b	(/.f64 (-.f64 (+.f64 (.f64 1.0 i) (+.f64 (.f64 n (log.f64 1.0)) (.f64 (.f64 i i) 0.5))) (.f64 (log.f64 1.0) (.f64 (*.f64 i i) 0.5))) i)
11.1b	(.f64 (log.f64 1.0) (.f64 (*.f64 i i) 0.5))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
27×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
21×	`pow1_binary64`
20×	`associate-l_binary64`
19×	`times-frac_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64`
10×	`pow-prod-down_binary64`
5×	`associate-r_binary64`
4×	`add-log-exp_binary64`
3×	`associate-/r_binary64` `cbrt-undiv_binary64` `associate-/l_binary64` `div-exp_binary64` `*-commutative_binary64`
2×	`associate-/l/_binary64` `unswap-sqr_binary64` `div-inv_binary64` `associate-*l/_binary64`
1×	`flip3--_binary64` `associate-*r/_binary64` `log-pow_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64`

Counts

4 → 105

Calls

4 calls:

13.0ms	(.f64 (/.f64 (-.f64 (+.f64 (.f64 1.0 i) (+.f64 (.f64 n (log.f64 1.0)) (.f64 (.f64 i i) 0.5))) (.f64 (log.f64 1.0) (.f64 (.f64 i i) 0.5))) i) n)
14.0ms	(.f64 100.0 (.f64 (/.f64 (-.f64 (+.f64 (.f64 1.0 i) (+.f64 (.f64 n (log.f64 1.0)) (.f64 (.f64 i i) 0.5))) (.f64 (log.f64 1.0) (.f64 (*.f64 i i) 0.5))) i) n))
12.0ms	(/.f64 (-.f64 (+.f64 (.f64 1.0 i) (+.f64 (.f64 n (log.f64 1.0)) (.f64 (.f64 i i) 0.5))) (.f64 (log.f64 1.0) (.f64 (*.f64 i i) 0.5))) i)
10.0ms	(.f64 (log.f64 1.0) (.f64 (*.f64 i i) 0.5))

series88.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(.f64 (/.f64 (-.f64 (+.f64 (.f64 1.0 i) (+.f64 (.f64 n (log.f64 1.0)) (.f64 (.f64 i i) 0.5))) (.f64 (log.f64 1.0) (.f64 (.f64 i i) 0.5))) i) n)
29.0ms	(.f64 100.0 (.f64 (/.f64 (-.f64 (+.f64 (.f64 1.0 i) (+.f64 (.f64 n (log.f64 1.0)) (.f64 (.f64 i i) 0.5))) (.f64 (log.f64 1.0) (.f64 (*.f64 i i) 0.5))) i) n))
18.0ms	(/.f64 (-.f64 (+.f64 (.f64 1.0 i) (+.f64 (.f64 n (log.f64 1.0)) (.f64 (.f64 i i) 0.5))) (.f64 (log.f64 1.0) (.f64 (*.f64 i i) 0.5))) i)
16.0ms	(.f64 (log.f64 1.0) (.f64 (*.f64 i i) 0.5))

simplify38.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5039	2564

prune206.0ms

Filtered

82 candidates to 117 candidates (-42.7%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	114	3	117
Fresh	3	16	19
Picked	1	0	1
Done	0	0	0
Total	118	19	137

Merged error: 8.6b

Counts

137 → 19

localize25.0ms

Local error

Found 4 expressions with local error:

11.1b	(.f64 (log.f64 1.0) (-.f64 n (.f64 (*.f64 i i) 0.5)))
11.3b	(cbrt.f64 (+.f64 (.f64 i (+.f64 1.0 (.f64 i 0.5))) (.f64 (log.f64 1.0) (-.f64 n (.f64 (*.f64 i i) 0.5)))))
11.3b	(cbrt.f64 (+.f64 (.f64 i (+.f64 1.0 (.f64 i 0.5))) (.f64 (log.f64 1.0) (-.f64 n (.f64 (*.f64 i i) 0.5)))))
11.3b	(cbrt.f64 (+.f64 (.f64 i (+.f64 1.0 (.f64 i 0.5))) (.f64 (log.f64 1.0) (-.f64 n (.f64 (*.f64 i i) 0.5)))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

26×	`associate-*r/_binary64`
18×	`cbrt-div_binary64`
12×	`frac-add_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`flip3-+_binary64` `*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `flip-+_binary64` `cbrt-prod_binary64`
7×	`pow1_binary64` `flip3--_binary64` `flip--_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `associate-l_binary64`
3×	`associate-r_binary64` `pow1/3_binary64`
2×	`sub-neg_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `log-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 74

Calls

4 calls:

12.0ms	(.f64 (log.f64 1.0) (-.f64 n (.f64 (*.f64 i i) 0.5)))
7.0ms	(cbrt.f64 (+.f64 (.f64 i (+.f64 1.0 (.f64 i 0.5))) (.f64 (log.f64 1.0) (-.f64 n (.f64 (*.f64 i i) 0.5)))))
7.0ms	(cbrt.f64 (+.f64 (.f64 i (+.f64 1.0 (.f64 i 0.5))) (.f64 (log.f64 1.0) (-.f64 n (.f64 (*.f64 i i) 0.5)))))
7.0ms	(cbrt.f64 (+.f64 (.f64 i (+.f64 1.0 (.f64 i 0.5))) (.f64 (log.f64 1.0) (-.f64 n (.f64 (*.f64 i i) 0.5)))))

series254.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(.f64 (log.f64 1.0) (-.f64 n (.f64 (*.f64 i i) 0.5)))
75.0ms	(cbrt.f64 (+.f64 (.f64 i (+.f64 1.0 (.f64 i 0.5))) (.f64 (log.f64 1.0) (-.f64 n (.f64 (*.f64 i i) 0.5)))))
74.0ms	(cbrt.f64 (+.f64 (.f64 i (+.f64 1.0 (.f64 i 0.5))) (.f64 (log.f64 1.0) (-.f64 n (.f64 (*.f64 i i) 0.5)))))
82.0ms	(cbrt.f64 (+.f64 (.f64 i (+.f64 1.0 (.f64 i 0.5))) (.f64 (log.f64 1.0) (-.f64 n (.f64 (*.f64 i i) 0.5)))))

simplify40.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5682	2920

prune309.0ms

Filtered

78 candidates to 86 candidates (-10.3%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	3	15	18
Picked	0	1	1
Done	0	0	0
Total	87	18	105

Merged error: 8.6b

Counts

105 → 18

regimes261.0ms

Accuracy

69.6% (6.0b remaining)

Error of 14.6b against oracle of 8.5b and baseline of 28.4b

bsearch205.0ms

Steps

Iters	Range		Point
8	203.83346152816426	382937.73952731065	206.5505471855869
10	-32745437244888.45	-2.9518020392315095e-06	-0.1758689209773507

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	111	122
1	111	122

end0.0ms

sample6.0s

Algorithm

intervals

Results

2.4s	2925×	body	1280	valid
2.0s	953×	body	2560	valid
591.0ms	1522×	body	640	valid
161.0ms	704×	body	320	valid
112.0ms	226×	body	640	invalid
106.0ms	1574×	body	80	valid
87.0ms	110×	body	1280	invalid
55.0ms	180×	body	320	invalid
47.0ms	322×	body	160	valid
35.0ms	402×	body	80	invalid
18.0ms	10×	body	2560	invalid
15.0ms	85×	body	160	invalid
12.0ms	285×	body	80	nan

Details

analyze804.0ms

sample229.0ms

simplify44.0ms

prune3.0ms

localize8.0ms

rewrite93.0ms

series251.0ms

simplify93.0ms

prune452.0ms

localize14.0ms

rewrite61.0ms

series75.0ms

simplify56.0ms

prune608.0ms

localize14.0ms

rewrite52.0ms

series88.0ms

simplify38.0ms

prune206.0ms

localize25.0ms

rewrite38.0ms

series254.0ms

simplify40.0ms

prune309.0ms

regimes261.0ms

bsearch205.0ms

simplify5.0ms

end0.0ms

sample6.0s

Profiling