Details

sample259.0ms

Algorithm

intervals

Results

72.0ms	129×	body	1280	valid
47.0ms	45×	body	1280	nan
27.0ms	59×	body	640	valid
23.0ms	124×	body	80	overflowed
17.0ms	25×	body	640	nan
12.0ms	118×	body	80	valid
10.0ms	221×	body	80	nan
7.0ms	13×	body	160	valid
6.0ms	20×	body	320	valid
5.0ms	12×	body	320	nan
2.0ms	10×	body	160	nan

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

prune4.0ms

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: 29.6b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(pow x (/ 1.0 n))
1.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite15.0ms

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:

4.0ms	(pow x (/ 1.0 n))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series421.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(pow x (/ 1.0 n))
348.0ms	(- (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

prune254.0ms

Filtered

57 candidates to 46 candidates (19.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	53	4	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	4	58

Merged error: 19.6b

Counts

58 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.0b	(log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
0.0b	(exp (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
1.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 106

Calls

4 calls:

4.0ms	(pow x (/ 1.0 n))
10.0ms	(log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
11.0ms	(exp (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
10.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.4s

Counts

4 → 12

Calls

4 calls:

76.0ms	(pow x (/ 1.0 n))
599.0ms	(log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
360.0ms	(exp (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
356.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify51.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	529	1271
1	1700	1217
2	5001	1181

prune774.0ms

Filtered

118 candidates to 90 candidates (23.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	117	5	122

Merged error: 19.6b

Counts

122 → 5

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (* (log x) 1.0) (* x (pow n 2)))
3.5b	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
7.7b	(/ (/ 0.5 n) (pow x 2))
8.5b	(* x (pow n 2))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

189×	`times-frac`
113×	`add-sqr-sqrt`
103×	`*-un-lft-identity`
98×	`add-cube-cbrt`
46×	`add-exp-log` `unpow-prod-down`
23×	`add-cbrt-cube`
17×	`div-exp`
16×	`unpow2` `sqr-pow`
14×	`associate-/l*`
13×	`prod-exp`
11×	`div-inv`
9×	`associate-/r*` `add-log-exp`
8×	`associate-r`
7×	`cbrt-undiv`
5×	`pow-to-exp` `pow-exp` `cbrt-unprod`
4×	`pow1` `frac-sub` `unswap-sqr`
3×	`diff-log` `associate-l` `distribute-lft-out--` `difference-of-squares`
2×	`sub-neg` `flip3--` `frac-2neg` `clear-num` `flip--` `associate--r+`
1×	`*-commutative` `associate-/l/` `associate--r-`

Counts

4 → 220

Calls

4 calls:

7.0ms	(/ (* (log x) 1.0) (* x (pow n 2)))
67.0ms	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
9.0ms	(/ (/ 0.5 n) (pow x 2))
6.0ms	(* x (pow n 2))

series277.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ (* (log x) 1.0) (* x (pow n 2)))
88.0ms	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
33.0ms	(/ (/ 0.5 n) (pow x 2))
43.0ms	(* x (pow n 2))

simplify48.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1112	2049
1	5001	1857

prune2.2s

Filtered

232 candidates to 140 candidates (39.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	228	4	232
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	229	8	237

Merged error: 19.4b

Counts

237 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (* (log x) 1.0) (* x (pow n 2)))
3.5b	(- (/ (/ 1.0 n) x) (- (log (exp (/ 0.5 (* (pow x 2) n)))) (/ (* (log x) 1.0) (* x (pow n 2)))))
7.8b	(* (pow x 2) n)
8.5b	(* x (pow n 2))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-exp-log`
32×	`add-sqr-sqrt`
20×	`add-cbrt-cube`
18×	`*-un-lft-identity`
16×	`prod-exp`
11×	`add-cube-cbrt` `associate-r` `associate-l`
8×	`unpow-prod-down` `div-exp` `add-log-exp` `unswap-sqr`
6×	`cbrt-unprod`
5×	`pow1` `associate--r+` `distribute-lft-out--`
4×	`cbrt-undiv` `pow-to-exp` `times-frac` `pow-exp` `unpow2` `sqr-pow`
3×	`log-prod` `diff-log` `associate--l+` `difference-of-squares`
2×	`sub-neg` `flip3--` `*-commutative` `frac-sub` `flip--`
1×	`frac-2neg` `clear-num` `associate-/r` `log-pow` `div-inv` `associate-/l` `associate--r-`

Counts

4 → 106

Calls

4 calls:

7.0ms	(/ (* (log x) 1.0) (* x (pow n 2)))
28.0ms	(- (/ (/ 1.0 n) x) (- (log (exp (/ 0.5 (* (pow x 2) n)))) (/ (* (log x) 1.0) (* x (pow n 2)))))
5.0ms	(* (pow x 2) n)
6.0ms	(* x (pow n 2))

series250.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (* (log x) 1.0) (* x (pow n 2)))
84.0ms	(- (/ (/ 1.0 n) x) (- (log (exp (/ 0.5 (* (pow x 2) n)))) (/ (* (log x) 1.0) (* x (pow n 2)))))
22.0ms	(* (pow x 2) n)
41.0ms	(* x (pow n 2))

simplify98.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	617	1072
1	3099	948
2	5001	936

prune741.0ms

Filtered

118 candidates to 75 candidates (36.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	113	5	118
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	115	11	126

Merged error: 19.4b

Counts

126 → 11

regimes501.0ms

Accuracy

81.8% (2.1b remaining)

Error of 23.9b against oracle of 21.8b and baseline of 33.5b

bsearch179.0ms

Steps

Iters	Range		Point
4	7916476625122.62	14502975650822.773	8033134678603.644
11	-2621393.439199732	-3.9048216217793476e-19	-85.39147387860265

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	37
1	53	37

end0.0ms

sample7.1s

Algorithm

intervals

Results

2.1s	4038×	body	1280	valid
1.2s	1086×	body	1280	nan
774.0ms	1751×	body	640	valid
623.0ms	914×	body	640	nan
581.0ms	4120×	body	80	overflowed
295.0ms	3074×	body	80	valid
285.0ms	6262×	body	80	nan
257.0ms	846×	body	320	valid
185.0ms	462×	body	320	nan
84.0ms	458×	body	160	valid
45.0ms	217×	body	160	nan

Details

sample259.0ms

simplify34.0ms

prune4.0ms

localize9.0ms

rewrite15.0ms

series421.0ms

simplify38.0ms

prune254.0ms

localize11.0ms

rewrite39.0ms

series1.4s

simplify51.0ms

prune774.0ms

localize18.0ms

rewrite100.0ms

series277.0ms

simplify48.0ms

prune2.2s

localize22.0ms

rewrite50.0ms

series250.0ms

simplify98.0ms

prune741.0ms

regimes501.0ms

bsearch179.0ms

simplify2.0ms

end0.0ms

sample7.1s

Profiling