Details

sample102.0ms

Algorithm

intervals

Results

43.0ms	556×	body	80	nan
21.0ms	295×	body	80	valid

simplify117.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	14
1	153	14
2	652	14
3	3624	14
4	5002	14

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize19.0ms

Local error

Found 4 expressions with local error:

7.1b	(/ (* l l) Om)
8.1b	(* n (pow (/ l Om) 2.0))
10.8b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.5b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log`
24×	`add-sqr-sqrt`
23×	`pow1`
20×	`associate-r/` `associate-r*` `add-cbrt-cube`
16×	`add-cube-cbrt` `*-un-lft-identity`
15×	`unpow-prod-down`
13×	`times-frac`
12×	`pow-prod-down`
11×	`prod-exp`
10×	`flip3--` `flip--`
8×	`frac-sub` `cbrt-unprod`
6×	`sqrt-div`
4×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-pow1` `associate-l` `associate--l+` `add-log-exp` `unswap-sqr`
3×	`div-exp` `associate-/r*`
2×	`cbrt-undiv` `pow-exp` `*-commutative` `div-inv` `sqr-pow`
1×	`pow-to-exp` `frac-2neg` `pow1/2` `clear-num` `sqrt-prod` `associate-/l*`

Counts

4 → 112

Calls

4 calls:

3.0ms	(/ (* l l) Om)
15.0ms	(* n (pow (/ l Om) 2.0))
48.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
34.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.3s

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ (* l l) Om)
138.0ms	(* n (pow (/ l Om) 2.0))
1.3s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.8s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify130.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	964	1525
1	4793	1370
2	5001	1370

prune512.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 23.3b

localize19.0ms

Local error

Found 4 expressions with local error:

6.5b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.1b	(* n (pow (/ l Om) 2.0))
10.8b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.5b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-exp-log`
25×	`pow1` `add-sqr-sqrt` `associate-r`
22×	`associate-*r/`
20×	`add-cbrt-cube`
19×	`prod-exp`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt` `unpow-prod-down`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`times-frac` `cbrt-unprod`
8×	`frac-sub`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div`
5×	`associate-l`
4×	`sqrt-pow1` `pow-exp` `associate--l+` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`pow-to-exp` `div-exp` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 119

Calls

4 calls:

23.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
15.0ms	(* n (pow (/ l Om) 2.0))
50.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
31.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.7s

Counts

4 → 12

Calls

4 calls:

370.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
149.0ms	(* n (pow (/ l Om) 2.0))
1.3s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.8s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify41.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	987	1664
1	5001	1508

prune516.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 21.2b

localize28.0ms

Local error

Found 4 expressions with local error:

4.4b	(* n (pow (/ l Om) (/ 2.0 2)))
6.5b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
10.8b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
18.5b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-exp-log`
67×	`prod-exp`
25×	`pow1` `add-sqr-sqrt` `associate-r`
24×	`add-cbrt-cube`
22×	`associate-*r/`
20×	`pow-exp`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt` `unpow-prod-down`
13×	`pow-prod-down` `cbrt-unprod`
11×	`flip3--` `flip--`
10×	`pow-to-exp` `times-frac` `div-exp`
8×	`frac-sub`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div`
5×	`associate-l`
4×	`sqrt-pow1` `associate--l+` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 136

Calls

4 calls:

15.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
87.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
64.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
40.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series7.0s

Counts

4 → 12

Calls

4 calls:

166.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
364.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.5s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
4.9s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify50.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1113	2381
1	5002	2030

prune544.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 20.9b

localize21.0ms

Local error

Found 4 expressions with local error:

4.4b	(* n (pow (/ l Om) (/ 2.0 2)))
7.5b	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
10.8b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))
18.5b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
30×	`unpow-prod-down` `associate-*r/`
29×	`add-exp-log`
25×	`-un-lft-identity` `associate-r*`
23×	`pow1` `add-cube-cbrt`
21×	`associate-l`
20×	`times-frac`
17×	`add-cbrt-cube`
14×	`prod-exp`
12×	`pow-prod-down`
11×	`flip3--` `flip--`
8×	`frac-sub` `cbrt-unprod` `unswap-sqr`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div`
4×	`sqrt-pow1` `pow-exp` `associate--l+` `add-log-exp` `sqr-pow`
3×	`*-commutative`
2×	`pow-to-exp` `div-exp` `div-inv`
1×	`pow1/2` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 136

Calls

4 calls:

15.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
23.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
60.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))
41.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))

series6.7s

Counts

4 → 12

Calls

4 calls:

168.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
342.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
1.3s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))
4.8s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))

simplify47.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1078	2175
1	5001	1964

prune613.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 20.2b

regimes457.0ms

Accuracy

11% (8.9b remaining)

Error of 29.9b against oracle of 21.0b and baseline of 31.0b

bsearch520.0ms

Steps

Iters	Range		Point
10	5.761168895017816e+38	6.252508614851994e+54	5.849773459839704e+38
8	5.196301700147731e-22	1.1700142316632325e-17	1.1504183261425661e-17
8	1.43410142141466e-189	6.5416925795497415e-186	5.754288137534979e-186
8	-5.835929371065793e-123	-6.527847966246e-127	-5.852286491090293e-126

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	86	107
1	107	107
2	115	107
3	120	107
4	120	107

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.1s	15073×	body	80	nan
670.0ms	9245×	body	80	valid