Details

analyze3.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	0%	50%	4

sample43.0ms

Algorithm

intervals

Results

18.0ms	75×	body	1024	valid
7.0ms	117×	body	128	valid
6.0ms	42×	body	512	valid
6.0ms	15×	body	2048	valid
1.0ms	7×	body	256	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune1.0ms

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: 33.1b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

1.0b	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
1.4b	(log.f64 (+.f64 N 1))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
11×	`log-prod_binary64`
7×	`pow1_binary64` `add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64` `log-pow_binary64`
4×	`distribute-lft-out--_binary64` `log-div_binary64` `associate--l+_binary64`
3×	`associate--r+_binary64` `add-exp-log_binary64`
2×	`flip3-+_binary64` `add-log-exp_binary64` `associate--l-_binary64` `distribute-lft-out_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `rem-log-exp_binary64` `difference-of-squares_binary64` `flip--_binary64`

Counts

2 → 40

Calls

2 calls:

7.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
3.0ms	(log.f64 (+.f64 N 1))

series78.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
25.0ms	(log.f64 (+.f64 N 1))

simplify74.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4882	648
1	4882	648

prune41.0ms

Filtered

33 candidates to 46 candidates (-39.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	44	2	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	2	47

Merged error: 0.0b

Counts

47 → 2

localize11.0ms

Local error

Found 3 expressions with local error:

0.4b	(/.f64 1/3 (pow.f64 N 3))
0.8b	(/.f64 1/2 (*.f64 N N))
12.6b	(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (/.f64 1/2 (*.f64 N N)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

40×	`times-frac_binary64`
37×	`*-un-lft-identity_binary64`
34×	`add-sqr-sqrt_binary64`
30×	`add-cube-cbrt_binary64`
13×	`associate-/r*_binary64` `add-exp-log_binary64`
12×	`unpow-prod-down_binary64` `cube-prod_binary64`
10×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
6×	`associate-/l*_binary64`
5×	`div-exp_binary64`
4×	`sqr-pow_binary64` `unpow3_binary64` `cube-mult_binary64`
3×	`pow1_binary64` `cbrt-undiv_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `frac-sub_binary64`
2×	`diff-log_binary64` `distribute-lft-out_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `frac-add_binary64` `prod-exp_binary64` `flip--_binary64` `flip-+_binary64` `pow-exp_binary64` `associate--l+_binary64` `sum-log_binary64`

Counts

3 → 107

Calls

3 calls:

6.0ms	(/.f64 1/3 (pow.f64 N 3))
5.0ms	(/.f64 1/2 (*.f64 N N))
38.0ms	(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (/.f64 1/2 (*.f64 N N)))

series116.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(/.f64 1/3 (pow.f64 N 3))
30.0ms	(/.f64 1/2 (*.f64 N N))
28.0ms	(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (/.f64 1/2 (*.f64 N N)))

simplify44.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5206	1847

prune81.0ms

Filtered

68 candidates to 116 candidates (-70.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	115	3	118

Merged error: 0.0b

Counts

118 → 3

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (+.f64 N 1) N)
1.0b	(log.f64 (/.f64 (+.f64 N 1) N))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64`
24×	`times-frac_binary64`
19×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
16×	`log-prod_binary64`
7×	`distribute-lft-out_binary64` `add-exp-log_binary64`
4×	`add-cbrt-cube_binary64` `associate-/l*_binary64`
3×	`associate-/r*_binary64` `pow1_binary64`
2×	`associate-/l/_binary64` `add-log-exp_binary64` `rem-log-exp_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`flip3-+_binary64` `cbrt-undiv_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `log-div_binary64` `flip-+_binary64`

Counts

2 → 60

Calls

2 calls:

6.0ms	(/.f64 (+.f64 N 1) N)
5.0ms	(log.f64 (/.f64 (+.f64 N 1) N))

series99.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(/.f64 (+.f64 N 1) N)
42.0ms	(log.f64 (/.f64 (+.f64 N 1) N))

simplify57.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5276	940

prune38.0ms

Filtered

45 candidates to 66 candidates (-46.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	65	4	69

Merged error: 0b

Counts

69 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (/.f64 (sqrt.f64 (+.f64 N 1)) N))
0.1b	(/.f64 (sqrt.f64 (+.f64 N 1)) N)
1.0b	(+.f64 (log.f64 (sqrt.f64 (+.f64 N 1))) (log.f64 (/.f64 (sqrt.f64 (+.f64 N 1)) N)))
1.4b	(log.f64 (sqrt.f64 (+.f64 N 1)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

80×	`*-un-lft-identity_binary64`
64×	`log-prod_binary64`
63×	`times-frac_binary64`
52×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
48×	`sqrt-prod_binary64`
25×	`associate-+r+_binary64`
16×	`distribute-lft-out_binary64`
11×	`pow1_binary64`
10×	`add-exp-log_binary64`
8×	`log-pow_binary64`
7×	`associate-+l+_binary64` `associate-/l*_binary64`
6×	`add-cbrt-cube_binary64` `log-div_binary64` `sqrt-div_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `flip-+_binary64`
3×	`associate-/r*_binary64` `rem-log-exp_binary64` `div-inv_binary64`
2×	`associate-/l/_binary64` `associate-+l-_binary64` `div-exp_binary64`
1×	`associate-+r-_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 151

Calls

4 calls:

6.0ms	(log.f64 (/.f64 (sqrt.f64 (+.f64 N 1)) N))
7.0ms	(/.f64 (sqrt.f64 (+.f64 N 1)) N)
16.0ms	(+.f64 (log.f64 (sqrt.f64 (+.f64 N 1))) (log.f64 (/.f64 (sqrt.f64 (+.f64 N 1)) N)))
4.0ms	(log.f64 (sqrt.f64 (+.f64 N 1)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(log.f64 (/.f64 (sqrt.f64 (+.f64 N 1)) N))
56.0ms	(/.f64 (sqrt.f64 (+.f64 N 1)) N)
110.0ms	(+.f64 (log.f64 (sqrt.f64 (+.f64 N 1))) (log.f64 (/.f64 (sqrt.f64 (+.f64 N 1)) N)))
45.0ms	(log.f64 (sqrt.f64 (+.f64 N 1)))

simplify54.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5046	3210

prune131.0ms

Filtered

110 candidates to 163 candidates (-48.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	163	4	167

Merged error: 0b

Counts

167 → 4

regimes18.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.0b

bsearch17.0ms

Steps

Iters	Range		Point
9	0.8118807294673237	251290.20220650133	10276.954470906452

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	37
1	39	37

end0.0ms

sample1.2s

Algorithm

intervals

Results

496.0ms	2016×	body	1024	valid
240.0ms	4185×	body	128	valid
160.0ms	1024×	body	512	valid
121.0ms	303×	body	2048	valid
44.0ms	472×	body	256	valid

Details

analyze3.0ms

sample43.0ms

simplify10.0ms

prune1.0ms

localize7.0ms

rewrite13.0ms

series78.0ms

simplify74.0ms

prune41.0ms

localize11.0ms

rewrite58.0ms

series116.0ms

simplify44.0ms

prune81.0ms

localize5.0ms

rewrite17.0ms

series99.0ms

simplify57.0ms

prune38.0ms

localize10.0ms

rewrite48.0ms

series286.0ms

simplify54.0ms

prune131.0ms

regimes18.0ms

bsearch17.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling