Details

sample218.0ms

Algorithm

intervals

Results

64.0ms	119×	body	1280	valid
31.0ms	64×	body	640	valid
22.0ms	18×	body	1280	nan
18.0ms	115×	body	80	overflowed
17.0ms	18×	body	640	nan
10.0ms	184×	body	80	nan
9.0ms	91×	body	80	valid
9.0ms	27×	body	320	valid
8.0ms	18×	body	320	nan
3.0ms	14×	body	160	valid
2.0ms	7×	body	160	nan

simplify32.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	6
1	34	6
2	80	6
3	236	6
4	868	6
5	5001	6

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 35.1b

Counts

2 → 1

localize8.0ms

Local error

Found 1 expressions with local error:

3.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`unpow-prod-down`
9×	`difference-of-squares`
8×	`*-un-lft-identity`
6×	`sqr-pow`
3×	`distribute-lft-out--` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out`

Counts

1 → 24

Calls

1 calls:

9.0ms

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

series44.0ms

Counts

1 → 3

Calls

1 calls:

44.0ms

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

simplify93.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	280	352
1	785	337
2	3548	329
3	5001	329

prune75.0ms

Filtered

27 candidates to 23 candidates (14.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	24	3	27
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	25	3	28

Merged error: 27.4b

Counts

28 → 3

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
3.6b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
3.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
30×	`unpow-prod-down` `exp-prod`
27×	`*-un-lft-identity` `difference-of-squares`
18×	`sqr-pow`
16×	`log-pow`
9×	`distribute-lft-out--`
8×	`add-log-exp`
6×	`add-cube-cbrt`
5×	`log-prod`
4×	`pow1` `exp-sum`
3×	`add-exp-log` `sub-neg` `add-cbrt-cube` `distribute-lft-out`
2×	`exp-diff` `diff-log` `rem-exp-log`
1×	`log-div` `flip3--` `rem-log-exp` `flip--`

Counts

3 → 81

Calls

3 calls:

10.0ms	(exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
12.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series144.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
40.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
38.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify125.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	373	899
1	1095	844
2	4481	813
3	5002	813

prune209.0ms

Filtered

90 candidates to 70 candidates (22.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	87	3	90
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	88	5	93

Merged error: 27.2b

Counts

93 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (pow (+ x 1.0) (/ 1.0 n)))
0.0b	(* (exp (pow (+ x 1.0) (/ 1.0 n))) (exp (neg (pow x (/ 1.0 n)))))
0.0b	(exp (neg (pow x (/ 1.0 n))))
3.6b	(log (* (exp (pow (+ x 1.0) (/ 1.0 n))) (exp (neg (pow x (/ 1.0 n))))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

42×	`exp-prod`
33×	`*-un-lft-identity`
18×	`unpow-prod-down`
15×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `distribute-rgt-neg-in`
9×	`pow1`
8×	`pow-prod-up`
7×	`distribute-lft-neg-in` `add-log-exp`
6×	`log-pow` `add-cbrt-cube`
5×	`add-exp-log` `exp-neg`
4×	`associate-*r/`
3×	`neg-sub0` `log-div` `exp-diff` `associate-r` `associate-l` `rem-exp-log` `distribute-lft-out` `sqr-pow`
2×	`rem-log-exp` `pow-prod-down` `prod-exp` `un-div-inv`
1×	`neg-mul-1` `log-prod` `neg-log` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

5.0ms	(exp (pow (+ x 1.0) (/ 1.0 n)))
20.0ms	(* (exp (pow (+ x 1.0) (/ 1.0 n))) (exp (neg (pow x (/ 1.0 n)))))
4.0ms	(exp (neg (pow x (/ 1.0 n))))
19.0ms	(log (* (exp (pow (+ x 1.0) (/ 1.0 n))) (exp (neg (pow x (/ 1.0 n))))))

series273.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(exp (pow (+ x 1.0) (/ 1.0 n)))
125.0ms	(* (exp (pow (+ x 1.0) (/ 1.0 n))) (exp (neg (pow x (/ 1.0 n)))))
19.0ms	(exp (neg (pow x (/ 1.0 n))))
85.0ms	(log (* (exp (pow (+ x 1.0) (/ 1.0 n))) (exp (neg (pow x (/ 1.0 n))))))

simplify43.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	455	756
1	1544	660
2	5001	618

prune234.0ms

Filtered

101 candidates to 73 candidates (27.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	94	7	101
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	97	9	106

Merged error: 26.6b

Counts

106 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (cbrt (log (* (exp (pow (+ x 1.0) (/ 1.0 n))) (exp (neg (pow x (/ 1.0 n))))))) (cbrt (log (* (exp (pow (+ x 1.0) (/ 1.0 n))) (exp (neg (pow x (/ 1.0 n))))))))
3.6b	(log (* (exp (pow (+ x 1.0) (/ 1.0 n))) (exp (neg (pow x (/ 1.0 n))))))
3.6b	(log (* (exp (pow (+ x 1.0) (/ 1.0 n))) (exp (neg (pow x (/ 1.0 n))))))
3.6b	(log (* (exp (pow (+ x 1.0) (/ 1.0 n))) (exp (neg (pow x (/ 1.0 n))))))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

97×	`*-un-lft-identity`
72×	`exp-prod`
60×	`cbrt-prod`
58×	`log-pow`
44×	`pow1`
38×	`pow-prod-up`
36×	`unpow-prod-down`
27×	`distribute-rgt-neg-in`
22×	`swap-sqr`
20×	`add-sqr-sqrt`
13×	`pow-prod-down`
12×	`add-cube-cbrt` `associate-r` `associate-l`
9×	`add-exp-log` `log-div` `distribute-lft-out`
6×	`exp-neg` `pow1/3` `associate-*r/` `rem-log-exp`
4×	`prod-exp` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
3×	`neg-sub0` `log-prod` `exp-diff` `un-div-inv`
2×	`pow-sqr`
1×	`pow2` `pow-plus` `*-commutative` `cbrt-unprod`

Counts

4 → 125

Calls

4 calls:

40.0ms	(* (cbrt (log (* (exp (pow (+ x 1.0) (/ 1.0 n))) (exp (neg (pow x (/ 1.0 n))))))) (cbrt (log (* (exp (pow (+ x 1.0) (/ 1.0 n))) (exp (neg (pow x (/ 1.0 n))))))))
21.0ms	(log (* (exp (pow (+ x 1.0) (/ 1.0 n))) (exp (neg (pow x (/ 1.0 n))))))
18.0ms	(log (* (exp (pow (+ x 1.0) (/ 1.0 n))) (exp (neg (pow x (/ 1.0 n))))))
18.0ms	(log (* (exp (pow (+ x 1.0) (/ 1.0 n))) (exp (neg (pow x (/ 1.0 n))))))

series600.0ms

Counts

4 → 12

Calls

4 calls:

348.0ms	(* (cbrt (log (* (exp (pow (+ x 1.0) (/ 1.0 n))) (exp (neg (pow x (/ 1.0 n))))))) (cbrt (log (* (exp (pow (+ x 1.0) (/ 1.0 n))) (exp (neg (pow x (/ 1.0 n))))))))
83.0ms	(log (* (exp (pow (+ x 1.0) (/ 1.0 n))) (exp (neg (pow x (/ 1.0 n))))))
84.0ms	(log (* (exp (pow (+ x 1.0) (/ 1.0 n))) (exp (neg (pow x (/ 1.0 n))))))
84.0ms	(log (* (exp (pow (+ x 1.0) (/ 1.0 n))) (exp (neg (pow x (/ 1.0 n))))))

simplify47.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	299	2065
1	1114	1784
2	5001	1478

prune458.0ms

Filtered

137 candidates to 74 candidates (46.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	135	2	137
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	136	10	146

Merged error: 26.6b

Counts

146 → 10

regimes311.0ms

Accuracy

86.6% (1.5b remaining)

Error of 22.6b against oracle of 21.2b and baseline of 32.3b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	106
1	40	106

end0.0ms

sample7.4s

Algorithm

intervals

Results

2.2s	3958×	body	1280	valid
1.2s	1075×	body	1280	nan
815.0ms	1727×	body	640	valid
610.0ms	4056×	body	80	overflowed
603.0ms	848×	body	640	nan
328.0ms	3129×	body	80	valid
325.0ms	6197×	body	80	nan
303.0ms	924×	body	320	valid
196.0ms	470×	body	320	nan
85.0ms	417×	body	160	valid
54.0ms	231×	body	160	nan

Details

sample218.0ms

simplify32.0ms

prune3.0ms

localize8.0ms

rewrite10.0ms

series44.0ms

simplify93.0ms

prune75.0ms

localize10.0ms

rewrite35.0ms

series144.0ms

simplify125.0ms

prune209.0ms

localize13.0ms

rewrite51.0ms

series273.0ms

simplify43.0ms

prune234.0ms

localize20.0ms

rewrite104.0ms

series600.0ms

simplify47.0ms

prune458.0ms

regimes311.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample7.4s

Profiling