Details

analyze1.1s

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

sample228.0ms

Algorithm

intervals

Results

82.0ms	148×	body	1280	valid
41.0ms	37×	body	1280	nan
19.0ms	43×	body	640	valid
19.0ms	27×	body	640	nan
15.0ms	87×	body	80	overflowed
8.0ms	5×	body	1280	invalid
7.0ms	6×	body	640	invalid
6.0ms	15×	body	320	nan
4.0ms	14×	body	320	valid
4.0ms	44×	body	80	valid
3.0ms	8×	body	320	invalid
2.0ms	8×	body	160	nan
1.0ms	7×	body	160	valid
1.0ms	19×	body	80	nan
1.0ms	5×	body	80	invalid
0.0ms	2×	body	160	invalid

simplify46.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

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: 31.6b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.0b	(pow (+ x 1.0) (/ 1.0 n))
1.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`pow-unpow`
19×	`add-cube-cbrt`
18×	`times-frac`
17×	`unpow-prod-down`
9×	`difference-of-squares`
8×	`sqr-pow`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`add-cbrt-cube` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 78

Calls

3 calls:

3.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series75.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(pow x (/ 1.0 n))
18.0ms	(pow (+ x 1.0) (/ 1.0 n))
44.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify53.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4985	1250
1	4985	1250

prune185.0ms

Filtered

71 candidates to 87 candidates (-22.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	3	88

Merged error: 21.3b

Counts

88 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))
1.5b	(- (* (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 53

Calls

4 calls:

3.0ms	(cbrt (+ x 1.0))
3.0ms	(cbrt (+ x 1.0))
3.0ms	(cbrt (+ x 1.0))
13.0ms	(- (* (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))

series118.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(cbrt (+ x 1.0))
6.0ms	(cbrt (+ x 1.0))
6.0ms	(cbrt (+ x 1.0))
99.0ms	(- (* (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))

simplify51.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4946	1055
1	4946	1055

prune233.0ms

Filtered

55 candidates to 65 candidates (-18.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	62	3	65
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	63	5	68

Merged error: 21.1b

Counts

68 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
1.5b	(- (* (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))
1.5b	(- (* (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))
1.5b	(- (* (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
7×	`*-un-lft-identity`
5×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `cbrt-prod` `add-cbrt-cube`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
2×	`cbrt-div`
1×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`

Counts

4 → 47

Calls

4 calls:

3.0ms	(cbrt (+ x 1.0))
13.0ms	(- (* (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))
11.0ms	(- (* (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))
12.0ms	(- (* (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))

series307.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(cbrt (+ x 1.0))
100.0ms	(- (* (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))
100.0ms	(- (* (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))
101.0ms	(- (* (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))

simplify55.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4946	1901
1	4946	1901

prune722.0ms

Filtered

53 candidates to 59 candidates (-11.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	59	0	59
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	59	5	64

Merged error: 21.1b

Counts

64 → 5

localize23.0ms

Local error

Found 3 expressions with local error:

0.3b	(/ (neg (log x)) n)
0.6b	(/ 1.0 (* x n))
8.4b	(/ (pow (log 1) 2) (* n n))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
34×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
24×	`associate-/l*`
23×	`add-exp-log`
16×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
15×	`add-cbrt-cube`
13×	`pow1`
10×	`log-pow`
9×	`div-exp`
8×	`unpow-prod-down`
5×	`cbrt-undiv` `associate-/r*`
4×	`neg-mul-1` `prod-exp`
3×	`frac-2neg` `clear-num` `div-inv` `add-log-exp`
2×	`pow-to-exp` `pow-exp` `cbrt-unprod` `unpow2` `sqr-pow`
1×	`neg-sub0` `div-sub` `distribute-frac-neg`

Counts

3 → 123

Calls

3 calls:

5.0ms	(/ (neg (log x)) n)
4.0ms	(/ 1.0 (* x n))
6.0ms	(/ (pow (log 1) 2) (* n n))

series29.0ms

Counts

3 → 9

Calls

3 calls:

10.0ms	(/ (neg (log x)) n)
4.0ms	(/ 1.0 (* x n))
15.0ms	(/ (pow (log 1) 2) (* n n))

simplify43.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5666	1108

prune243.0ms

Filtered

86 candidates to 132 candidates (-53.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	127	5	132
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	127	10	137

Merged error: 20.7b

Counts

137 → 10

regimes343.0ms

Accuracy

87% (1.4b remaining)

Error of 23.3b against oracle of 21.9b and baseline of 32.6b

bsearch138.0ms

Steps

Iters	Range		Point
9	125.72319852033803	241712044735.4793	18206649765.93102
10	-253.3258898344875	-9.667303938317425e-11	-250.7434974379807

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	167	165
1	167	165

end0.0ms

sample6.4s

Algorithm

intervals

Results

2.0s	3747×	body	1280	valid
1.2s	1108×	body	1280	nan
710.0ms	1583×	body	640	valid
581.0ms	833×	body	640	nan
465.0ms	2700×	body	80	overflowed
217.0ms	723×	body	320	valid
181.0ms	444×	body	320	nan
161.0ms	230×	body	640	invalid
143.0ms	108×	body	1280	invalid
139.0ms	1580×	body	80	valid
70.0ms	367×	body	160	valid
69.0ms	177×	body	320	invalid
48.0ms	218×	body	160	nan
33.0ms	498×	body	80	nan
26.0ms	214×	body	80	invalid
25.0ms	90×	body	160	invalid

Details

analyze1.1s

sample228.0ms

simplify46.0ms

prune3.0ms

localize8.0ms

rewrite20.0ms

series75.0ms

simplify53.0ms

prune185.0ms

localize14.0ms

rewrite23.0ms

series118.0ms

simplify51.0ms

prune233.0ms

localize20.0ms

rewrite40.0ms

series307.0ms

simplify55.0ms

prune722.0ms

localize23.0ms

rewrite20.0ms

series29.0ms

simplify43.0ms

prune243.0ms

regimes343.0ms

bsearch138.0ms

simplify3.0ms

end0.0ms

sample6.4s

Profiling