Details

sample339.0ms

Algorithm

intervals

Results

31.0ms	487×	body	80	nan
21.0ms	300×	body	80	valid

simplify130.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	49	14
1	155	14
2	684	14
3	3898	14
4	5001	14

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.4b

localize22.0ms

Local error

Found 4 expressions with local error:

7.4b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.2b	(/ (* l l) Om)
10.4b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
21.7b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
30×	`prod-diff`
26×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`pow1`
24×	`add-cube-cbrt`
23×	`add-cbrt-cube`
22×	`associate-*r/`
21×	`distribute-rgt-in` `distribute-lft-in`
16×	`prod-exp`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`associate--l+` `cbrt-unprod`
8×	`associate-r` `frac-sub`
6×	`sub-neg` `sqrt-div`
4×	`expm1-log1p-u` `sqrt-pow1` `log1p-expm1-u` `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 → 141

Calls

4 calls:

24.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
3.0ms	(/ (* l l) Om)
54.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
43.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.2s

Counts

4 → 12

Calls

4 calls:

358.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
24.0ms	(/ (* l l) Om)
1.3s	(* (* (* 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*)))))

simplify48.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1176	2335
1	5001	2011

prune569.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 25.5b

localize19.0ms

Local error

Found 4 expressions with local error:

5.4b	(* n (pow (/ l Om) 2.0))
7.4b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.4b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
21.7b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
35×	`add-exp-log`
33×	`*-un-lft-identity`
31×	`add-cube-cbrt`
30×	`prod-diff`
25×	`pow1` `associate-r`
22×	`associate-*r/`
21×	`distribute-rgt-in` `distribute-lft-in`
20×	`add-cbrt-cube`
19×	`prod-exp`
15×	`unpow-prod-down`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`times-frac` `associate--l+` `cbrt-unprod`
8×	`frac-sub`
6×	`sub-neg` `sqrt-div`
5×	`associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `pow-exp` `log1p-expm1-u` `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 → 157

Calls

4 calls:

14.0ms	(* n (pow (/ l Om) 2.0))
24.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
53.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
40.0ms	(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:

135.0ms	(* n (pow (/ l Om) 2.0))
353.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.3s	(* (* (* 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*)))))

simplify49.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1229	2461
1	5001	2136

prune586.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 24.3b

localize26.0ms

Local error

Found 4 expressions with local error:

5.6b	(* n (pow (/ l Om) (/ 2.0 2)))
7.4b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
10.4b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
21.7b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite218.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-exp-log`
67×	`prod-exp`
41×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
31×	`add-cube-cbrt`
30×	`prod-diff`
25×	`pow1` `associate-r`
24×	`add-cbrt-cube`
22×	`associate-*r/`
21×	`distribute-rgt-in` `distribute-lft-in`
20×	`pow-exp`
15×	`unpow-prod-down`
13×	`pow-prod-down` `cbrt-unprod`
11×	`flip3--` `flip--`
10×	`pow-to-exp` `times-frac` `div-exp` `associate--l+`
8×	`frac-sub`
6×	`sub-neg` `sqrt-div`
5×	`associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `log1p-expm1-u` `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 → 174

Calls

4 calls:

14.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
82.0ms	(* (* (* 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 (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
48.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series6.4s

Counts

4 → 12

Calls

4 calls:

153.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
353.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.3s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
4.7s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1355	3511
1	5002	2841

prune642.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 24.3b

localize23.0ms

Local error

Found 4 expressions with local error:

5.6b	(* n (pow (/ l Om) (/ 2.0 2)))
7.4b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
10.4b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
21.7b	(sqrt (pow (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) 1))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-exp-log`
67×	`prod-exp`
43×	`add-sqr-sqrt`
34×	`*-un-lft-identity`
32×	`add-cube-cbrt`
30×	`prod-diff`
25×	`associate-r`
24×	`add-cbrt-cube`
21×	`distribute-rgt-in` `distribute-lft-in`
20×	`pow-exp`
16×	`unpow-prod-down`
15×	`pow1`
13×	`cbrt-unprod`
12×	`associate-*r/`
10×	`pow-to-exp` `times-frac` `div-exp` `associate--l+`
7×	`pow-prod-down`
6×	`sub-neg` `flip3--` `flip--`
5×	`associate-l` `sqrt-prod`
4×	`expm1-log1p-u` `frac-sub` `log1p-expm1-u` `add-log-exp` `unswap-sqr` `sqr-pow`
3×	`*-commutative`
2×	`rem-sqrt-square`
1×	`sqrt-pow1` `pow1/2` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 171

Calls

4 calls:

14.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
83.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
66.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
18.0ms	(sqrt (pow (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) 1))

series6.5s

Counts

4 → 12

Calls

4 calls:

154.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
368.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.3s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
4.6s	(sqrt (pow (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) 1))

simplify62.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1317	3339
1	5002	2671

prune641.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 24.1b

regimes716.0ms

Accuracy

2.8% (8.9b remaining)

Error of 30.8b against oracle of 21.8b and baseline of 31.0b

bsearch389.0ms

Steps

Iters	Range		Point
7	9.314757112647596e-152	2.0864846078020846e-150	1.8079991333180533e-150
9	-1.604610306938246e-158	-8.879020602459359e-164	-7.523056142154409e-159
8	-2.496332758032299e-132	-6.083988141069605e-137	-2.434834066406249e-133
4	-4.6506962397476484e+170	-2.3994214419064102e+170	-4.5798465738782547e+170

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	82
1	81	82
2	88	82
3	88	82

end0.0ms

sample2.4s

Algorithm

intervals

Results

959.0ms	14633×	body	80	nan
606.0ms	9236×	body	80	valid