Details

sample212.0ms

Algorithm

intervals

Results

65.0ms	130×	body	1280	valid
43.0ms	76×	body	1280	nan
20.0ms	57×	body	640	nan
19.0ms	35×	body	10240	exit
18.0ms	55×	body	640	valid
7.0ms	164×	body	80	nan
6.0ms	27×	body	320	valid
6.0ms	23×	body	320	nan
5.0ms	105×	body	80	valid
3.0ms	19×	body	160	nan
2.0ms	12×	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.5b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(pow x (/ 1.0 n))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
13×	`unpow-prod-down` `pow-unpow`
10×	`add-cube-cbrt`
9×	`times-frac` `difference-of-squares`
7×	`sqr-pow`
4×	`add-log-exp`
3×	`pow1` `add-exp-log` `distribute-lft-out--`
2×	`add-cbrt-cube`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `pow-exp` `flip--` `div-inv` `distribute-lft-out`

Counts

2 → 51

Calls

2 calls:

2.0ms	(pow x (/ 1.0 n))
42.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series322.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(pow x (/ 1.0 n))
267.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify38.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	404	475
1	1391	461
2	5001	449

prune158.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 19.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.0b	(pow x (/ 1.0 n))
0.0b	(* (sqrt (pow x (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
4.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (* (sqrt (pow x (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
54×	`sqrt-prod`
32×	`add-cube-cbrt` `*-un-lft-identity`
27×	`unpow-prod-down`
26×	`pow-unpow`
18×	`times-frac`
16×	`unswap-sqr`
15×	`sqr-pow`
13×	`pow1`
12×	`swap-sqr`
10×	`associate-r` `associate-l`
8×	`add-exp-log`
6×	`sqrt-pow1` `pow1/2` `add-cbrt-cube` `add-log-exp`
3×	`pow-prod-down` `pow-sqr` `pow-prod-up` `difference-of-squares`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 140

Calls

4 calls:

2.0ms	(pow x (/ 1.0 n))
4.0ms	(pow x (/ 1.0 n))
14.0ms	(* (sqrt (pow x (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
38.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (sqrt (pow x (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))))

series436.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(pow x (/ 1.0 n))
55.0ms	(pow x (/ 1.0 n))
59.0ms	(* (sqrt (pow x (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
263.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (sqrt (pow x (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))))

simplify65.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	486	1132
1	2190	1063
2	5002	1043

prune383.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 18.9b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1.0 n))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.3b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 81

Calls

3 calls:

2.0ms	(pow x (/ 1.0 n))
42.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
96.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

series606.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(pow x (/ 1.0 n))
273.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
273.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

simplify43.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	469	758
1	1551	722
2	5001	703

prune280.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 18.9b

localize12.0ms

Local error

Found 4 expressions with local error:

2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.3b	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
2.3b	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

rewrite291.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
40×	`unpow-prod-down`
38×	`*-un-lft-identity`
36×	`log-pow` `difference-of-squares`
32×	`sqrt-pow1`
30×	`exp-prod`
24×	`sqr-pow`
16×	`log-prod`
12×	`distribute-lft-out--`
10×	`add-cube-cbrt` `sqrt-prod`
8×	`pow1` `add-log-exp`
6×	`add-exp-log`
4×	`sub-neg` `exp-sum` `add-cbrt-cube` `distribute-lft-out`
2×	`log-div` `flip3--` `pow1/2` `exp-diff` `sqrt-div` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 118

Calls

4 calls:

43.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
41.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
100.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
101.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

series1.5s

Counts

4 → 12

Calls

4 calls:

275.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
285.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
455.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
454.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

simplify117.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	349	1482
1	940	1394
2	4101	1370
3	5001	1370

prune529.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 18.9b

regimes224.0ms

Accuracy

81.8% (1.9b remaining)

Error of 23.4b against oracle of 21.5b and baseline of 32.2b

bsearch164.0ms

Steps

Iters	Range		Point
10	0.11513722063736925	8521518135.486671	104178.38706182929
7	-127575.43791052715	-3188.0865089400295	-71002.37754098696

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	20
1	34	20

end0.0ms

sample6.5s

Algorithm

intervals

Results

1.8s	3972×	body	1280	valid
1.3s	2194×	body	1280	nan
744.0ms	1885×	body	640	nan
601.0ms	1775×	body	640	valid
544.0ms	1381×	body	10240	exit
262.0ms	6213×	body	80	nan
217.0ms	916×	body	320	nan
194.0ms	869×	body	320	valid
148.0ms	3156×	body	80	valid
69.0ms	484×	body	160	nan
64.0ms	439×	body	160	valid