Details

sample221.0ms

Algorithm

intervals

Results

77.0ms	132×	body	1280	valid
37.0ms	23×	body	1280	nan
19.0ms	42×	body	640	valid
16.0ms	20×	body	640	nan
13.0ms	126×	body	80	valid
13.0ms	81×	body	80	overflowed
6.0ms	21×	body	320	valid
5.0ms	98×	body	80	nan
4.0ms	9×	body	320	nan
2.0ms	10×	body	160	nan
1.0ms	7×	body	160	valid

simplify34.0ms

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: 29.8b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.0b	(pow (+ x 1.0) (/ 1.0 n))
1.8b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite23.0ms

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 → 79

Calls

3 calls:

6.0ms	(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)))

series68.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(pow x (/ 1.0 n))
17.0ms	(pow (+ x 1.0) (/ 1.0 n))
40.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify48.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	552	688
1	1885	669
2	5002	641

prune170.0ms

Filtered

88 candidates to 71 candidates (19.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	84	4	88
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	84	5	89

Merged error: 19.7b

Counts

89 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.0b	(exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
1.8b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.9b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
34×	`unpow-prod-down`
30×	`exp-prod`
27×	`difference-of-squares`
19×	`sqr-pow`
16×	`log-pow`
15×	`add-cube-cbrt`
13×	`pow-unpow`
9×	`times-frac` `distribute-lft-out--` `add-log-exp`
6×	`pow1`
5×	`add-exp-log` `log-prod`
4×	`exp-sum` `add-cbrt-cube` `distribute-lft-out`
3×	`sub-neg`
2×	`exp-diff` `diff-log` `rem-exp-log`
1×	`pow-to-exp` `log-div` `flip3--` `pow-pow` `rem-log-exp` `pow-exp` `flip--` `div-inv`

Counts

4 → 109

Calls

4 calls:

6.0ms	(pow (+ x 1.0) (/ 1.0 n))
11.0ms	(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)))
10.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

series164.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (+ x 1.0) (/ 1.0 n))
67.0ms	(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)))
40.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

simplify49.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	506	1067
1	1604	1010
2	5001	981

prune277.0ms

Filtered

121 candidates to 94 candidates (22.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	117	4	121
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	118	8	126

Merged error: 19.7b

Counts

126 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
1.9b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
1.9b	(log (exp (* (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))) (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
28×	`unpow-prod-down`
26×	`*-un-lft-identity`
20×	`sqrt-prod`
16×	`difference-of-squares`
11×	`add-log-exp`
8×	`sqr-pow`
7×	`log-prod` `distribute-lft-out`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `exp-sum` `log-pow` `add-cbrt-cube` `distribute-lft-out--`
3×	`sub-neg`
2×	`distribute-rgt-in` `exp-to-pow` `distribute-lft-in` `flip3-+` `sqrt-div` `sum-log` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `exp-prod` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 82

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
12.0ms	(+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
15.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
8.0ms	(log (exp (* (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))) (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))))

series383.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
61.0ms	(+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
108.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
211.0ms	(log (exp (* (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))) (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))))

simplify59.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	586	1452
1	2096	1341
2	5001	1341

prune308.0ms

Filtered

94 candidates to 72 candidates (23.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	93	9	102

Merged error: 19.7b

Counts

102 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

1.9b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
1.9b	(log (exp (* (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))) (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))))
1.9b	(log (exp (* (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))) (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))))
1.9b	(log (exp (* (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))) (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
22×	`unpow-prod-down`
21×	`log-prod`
16×	`*-un-lft-identity` `difference-of-squares`
15×	`add-log-exp`
12×	`exp-sum` `sqrt-prod` `log-pow`
8×	`sqr-pow`
7×	`pow1` `add-cube-cbrt` `sub-neg`
6×	`distribute-rgt-in` `exp-to-pow` `distribute-lft-in`
4×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--`
3×	`exp-prod` `rem-log-exp` `sum-log`
1×	`flip3--` `diff-log` `flip--` `distribute-lft-out`

Counts

4 → 89

Calls

4 calls:

13.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
9.0ms	(log (exp (* (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))) (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))))
9.0ms	(log (exp (* (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))) (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))))
9.0ms	(log (exp (* (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))) (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))))

series687.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
196.0ms	(log (exp (* (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))) (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))))
194.0ms	(log (exp (* (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))) (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))))
196.0ms	(log (exp (* (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))) (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))))

simplify53.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	417	2241
1	1508	2002
2	5001	1961

prune847.0ms

Filtered

101 candidates to 75 candidates (25.7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	97	4	101
Fresh	0	6	6
Picked	1	0	1
Done	0	2	2
Total	98	12	110

Merged error: 19.7b

Counts

110 → 12

regimes597.0ms

Accuracy

84% (1.7b remaining)

Error of 23.0b against oracle of 21.3b and baseline of 31.8b

bsearch1.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	38
1	53	38
2	56	38
3	56	38

end0.0ms

sample6.4s

Algorithm

intervals

Results

2.1s	3676×	body	1280	valid
940.0ms	687×	body	1280	nan
721.0ms	1605×	body	640	valid
492.0ms	589×	body	640	nan
450.0ms	2660×	body	80	overflowed
450.0ms	4081×	body	80	valid
239.0ms	763×	body	320	valid
220.0ms	4086×	body	80	nan
147.0ms	309×	body	320	nan
67.0ms	344×	body	160	valid
38.0ms	155×	body	160	nan

Details

sample221.0ms

simplify34.0ms

prune3.0ms

localize9.0ms

rewrite23.0ms

series68.0ms

simplify48.0ms

prune170.0ms

localize11.0ms

rewrite40.0ms

series164.0ms

simplify49.0ms

prune277.0ms

localize15.0ms

rewrite40.0ms

series383.0ms

simplify59.0ms

prune308.0ms

localize23.0ms

rewrite42.0ms

series687.0ms

simplify53.0ms

prune847.0ms

regimes597.0ms

bsearch1.0ms

simplify3.0ms

end0.0ms

sample6.4s

Profiling