Details

sample82.0ms

Algorithm

intervals

Results

32.0ms	451×	body	80	nan
17.0ms	275×	body	80	valid

simplify116.0ms

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: 32.4b

localize18.0ms

Local error

Found 4 expressions with local error:

7.6b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.5b	(/ (* l l) Om)
10.9b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
15.9b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
25×	`pow1`
23×	`add-cbrt-cube`
22×	`associate-*r/`
16×	`prod-exp`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`add-sqr-sqrt` `*-un-lft-identity` `cbrt-unprod`
8×	`add-cube-cbrt` `associate-r` `frac-sub`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div`
4×	`sqrt-pow1` `associate--l+` `add-log-exp`
3×	`times-frac` `div-exp` `associate-/r*`
2×	`cbrt-undiv` `associate-l` `pow-exp` `*-commutative`
1×	`pow-to-exp` `frac-2neg` `pow1/2` `clear-num` `sqrt-prod` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 103

Calls

4 calls:

24.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
3.0ms	(/ (* l l) Om)
50.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
32.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.4s

Counts

4 → 12

Calls

4 calls:

349.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
23.0ms	(/ (* l l) Om)
1.4s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.6s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify127.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	937	1548
1	4752	1385
2	5002	1385

prune454.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 18.3b

localize19.0ms

Local error

Found 4 expressions with local error:

6.0b	(* n (pow (/ l Om) 2.0))
7.6b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.5b	(/ (* l l) Om)
15.9b	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log`
26×	`add-sqr-sqrt`
22×	`associate-r`
19×	`pow1`
18×	`-un-lft-identity` `associate-r/`
16×	`add-cube-cbrt` `add-cbrt-cube`
15×	`unpow-prod-down`
14×	`prod-exp`
13×	`times-frac`
9×	`pow-prod-down`
6×	`flip3--` `sqrt-div` `flip--`
5×	`sqrt-pow1` `cbrt-unprod`
4×	`div-exp` `associate-l` `pow-exp` `frac-sub` `add-log-exp` `unswap-sqr`
3×	`associate-/r*`
2×	`cbrt-undiv` `distribute-rgt-in` `pow-to-exp` `sub-neg` `distribute-lft-in` `*-commutative` `div-inv` `sqr-pow`
1×	`frac-2neg` `pow1/2` `clear-num` `sqrt-prod` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 106

Calls

4 calls:

15.0ms	(* n (pow (/ l Om) 2.0))
26.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
3.0ms	(/ (* l l) Om)
38.0ms	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

series5.2s

Counts

4 → 12

Calls

4 calls:

138.0ms	(* n (pow (/ l Om) 2.0))
367.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
18.0ms	(/ (* l l) Om)
4.7s	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify103.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	874	1017
1	4205	957
2	5002	957

prune494.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.0b

localize22.0ms

Local error

Found 4 expressions with local error:

5.4b	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
6.0b	(* n (pow (/ l Om) 2.0))
7.6b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
15.9b	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-exp-log`
34×	`associate-*r/`
31×	`pow1`
24×	`add-sqr-sqrt`
23×	`associate-r` `add-cbrt-cube`
21×	`prod-exp`
18×	`distribute-rgt-in` `distribute-lft-in`
17×	`pow-prod-down`
16×	`*-un-lft-identity`
15×	`unpow-prod-down`
14×	`add-cube-cbrt`
12×	`cbrt-unprod`
11×	`flip3--` `flip--`
10×	`sub-neg` `times-frac`
8×	`associate--l+` `frac-sub`
6×	`sqrt-div`
5×	`sqrt-pow1` `associate-l`
4×	`pow-exp` `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 → 129

Calls

4 calls:

50.0ms	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
18.0ms	(* n (pow (/ l Om) 2.0))
24.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
39.0ms	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

series6.6s

Counts

4 → 12

Calls

4 calls:

1.3s	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
141.0ms	(* n (pow (/ l Om) 2.0))
365.0ms	(* (* 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*))))))

simplify49.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1052	1821
1	5001	1638

prune522.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.8b

localize21.0ms

Local error

Found 4 expressions with local error:

5.2b	(* n (pow (/ l Om) (/ 2.0 2)))
5.4b	(* (* 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*)))))
7.6b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
15.9b	(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*))))))

rewrite249.0ms

Algorithm

rewrite-expression-head

Rules

102×	`add-exp-log`
69×	`prod-exp`
34×	`associate-*r/`
31×	`pow1`
27×	`add-cbrt-cube`
24×	`add-sqr-sqrt`
23×	`associate-r`
20×	`pow-exp`
18×	`distribute-rgt-in` `distribute-lft-in`
17×	`pow-prod-down`
16×	`*-un-lft-identity`
15×	`unpow-prod-down` `cbrt-unprod`
14×	`add-cube-cbrt`
11×	`flip3--` `flip--`
10×	`pow-to-exp` `sub-neg` `times-frac` `div-exp`
8×	`associate--l+` `frac-sub`
6×	`sqrt-div`
5×	`sqrt-pow1` `associate-l`
4×	`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 → 146

Calls

4 calls:

16.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
78.0ms	(* (* 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*)))))
89.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
59.0ms	(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:

162.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
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*)))))
358.0ms	(* (* (* 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*))))))

simplify49.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1178	2593
1	5001	2182

prune497.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 13.5b

regimes845.0ms

Accuracy

34.9% (8.1b remaining)

Error of 26.8b against oracle of 18.7b and baseline of 31.1b

bsearch210.0ms

Steps

Iters	Range		Point
8	-1.640344397674756e-308	2.3284295378993804e-306	1.5370107522182492e-307
8	-2.715559418712464e-135	-2.0908746616514593e-138	-1.7917712095234028e-135

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	56
1	77	56
2	78	56
3	78	56

end0.0ms

sample2.4s

Algorithm

intervals

Results

966.0ms	14806×	body	80	nan
587.0ms	9075×	body	80	valid