Details

sample431.0ms

Algorithm

intervals

Results

42.0ms	288×	body	80	valid
31.0ms	484×	body	80	nan

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.4b

localize22.0ms

Local error

Found 4 expressions with local error:

6.3b	(* n (pow (/ l Om) 2.0))
9.5b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
10.3b	(/ (* l l) Om)
22.3b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite273.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
26×	`add-exp-log`
23×	`pow1`
20×	`add-cube-cbrt` `-un-lft-identity` `associate-r/` `associate-r` `add-cbrt-cube`
15×	`unpow-prod-down`
13×	`times-frac`
12×	`prod-diff` `pow-prod-down`
11×	`prod-exp`
10×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `associate--l+` `flip--`
8×	`frac-sub` `cbrt-unprod`
6×	`sqrt-div`
4×	`expm1-log1p-u` `sub-neg` `sqrt-pow1` `associate-l` `log1p-expm1-u` `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 → 132

Calls

4 calls:

24.0ms	(* n (pow (/ l Om) 2.0))
126.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
10.0ms	(/ (* l l) Om)
107.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series5.8s

Counts

4 → 12

Calls

4 calls:

138.0ms	(* n (pow (/ l Om) 2.0))
1.2s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
17.0ms	(/ (* l l) Om)
4.5s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify47.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1079	1948
1	5001	1746

prune593.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 25.1b

localize22.0ms

Local error

Found 4 expressions with local error:

5.4b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.3b	(* n (pow (/ l Om) 2.0))
9.5b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
22.3b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite303.0ms

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:

45.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
25.0ms	(* n (pow (/ l Om) 2.0))
129.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
96.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.1s

Counts

4 → 12

Calls

4 calls:

342.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
131.0ms	(* n (pow (/ l Om) 2.0))
1.2s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.4s	(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

prune575.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 22.8b

localize30.0ms

Local error

Found 4 expressions with local error:

5.3b	(* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0))
5.4b	(* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0)) (pow (/ (cbrt l) (cbrt Om)) 2.0)) (- U U*))
9.5b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0)) (pow (/ (cbrt l) (cbrt Om)) 2.0)) (- U U*))))
22.3b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0)) (pow (/ (cbrt l) (cbrt Om)) 2.0)) (- U U*)))))

rewrite495.0ms

Algorithm

rewrite-expression-head

Rules

188×	`add-exp-log`
126×	`prod-exp`
41×	`pow-exp`
33×	`add-sqr-sqrt`
30×	`prod-diff`
28×	`div-exp`
27×	`*-un-lft-identity`
25×	`pow1` `add-cube-cbrt`
24×	`add-cbrt-cube`
22×	`associate-*r/`
21×	`distribute-rgt-in` `distribute-lft-in`
17×	`associate-r`
13×	`pow-to-exp` `pow-prod-down` `cbrt-unprod`
11×	`flip3--` `flip--`
10×	`associate--l+`
8×	`frac-sub`
7×	`unpow-prod-down`
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×	`times-frac` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 181

Calls

4 calls:

27.0ms	(* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0))
173.0ms	(* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0)) (pow (/ (cbrt l) (cbrt Om)) 2.0)) (- U U*))
162.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0)) (pow (/ (cbrt l) (cbrt Om)) 2.0)) (- U U*))))
123.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0)) (pow (/ (cbrt l) (cbrt Om)) 2.0)) (- U U*)))))

series6.2s

Counts

4 → 12

Calls

4 calls:

164.0ms	(* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0))
327.0ms	(* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0)) (pow (/ (cbrt l) (cbrt Om)) 2.0)) (- U U*))
1.2s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0)) (pow (/ (cbrt l) (cbrt Om)) 2.0)) (- U U*))))
4.5s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0)) (pow (/ (cbrt l) (cbrt Om)) 2.0)) (- U U*)))))

simplify68.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1396	4996
1	5002	4416

prune707.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 22.5b

localize44.0ms

Local error

Found 4 expressions with local error:

22.3b	(sqrt (* (* (cbrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0)) (pow (/ (cbrt l) (cbrt Om)) 2.0)) (- U U))))) (cbrt ( (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0)) (pow (/ (cbrt l) (cbrt Om)) 2.0)) (- U U)))))) (cbrt ( (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0)) (pow (/ (cbrt l) (cbrt Om)) 2.0)) (- U U*)))))))
23.5b	(cbrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0)) (pow (/ (cbrt l) (cbrt Om)) 2.0)) (- U U*)))))
23.5b	(cbrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0)) (pow (/ (cbrt l) (cbrt Om)) 2.0)) (- U U*)))))
23.5b	(cbrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0)) (pow (/ (cbrt l) (cbrt Om)) 2.0)) (- U U*)))))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

1548×	`associate-*r/`
900×	`cbrt-div`
750×	`flip3--` `flip--`
600×	`frac-sub`
540×	`frac-times`
342×	`sqrt-div`
90×	`associate-*l/`
24×	`pow1`
15×	`sqrt-pow1`
12×	`pow1/3`
9×	`pow-prod-up`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 419

Calls

4 calls:

756.0ms	(sqrt (* (* (cbrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0)) (pow (/ (cbrt l) (cbrt Om)) 2.0)) (- U U))))) (cbrt ( (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0)) (pow (/ (cbrt l) (cbrt Om)) 2.0)) (- U U)))))) (cbrt ( (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0)) (pow (/ (cbrt l) (cbrt Om)) 2.0)) (- U U*)))))))
100.0ms	(cbrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0)) (pow (/ (cbrt l) (cbrt Om)) 2.0)) (- U U*)))))
102.0ms	(cbrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0)) (pow (/ (cbrt l) (cbrt Om)) 2.0)) (- U U*)))))
104.0ms	(cbrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0)) (pow (/ (cbrt l) (cbrt Om)) 2.0)) (- U U*)))))

series7.0s

Counts

4 → 12

Calls

4 calls:

4.3s	(sqrt (* (* (cbrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0)) (pow (/ (cbrt l) (cbrt Om)) 2.0)) (- U U))))) (cbrt ( (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0)) (pow (/ (cbrt l) (cbrt Om)) 2.0)) (- U U)))))) (cbrt ( (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0)) (pow (/ (cbrt l) (cbrt Om)) 2.0)) (- U U*)))))))
904.0ms	(cbrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0)) (pow (/ (cbrt l) (cbrt Om)) 2.0)) (- U U*)))))
887.0ms	(cbrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0)) (pow (/ (cbrt l) (cbrt Om)) 2.0)) (- U U*)))))
891.0ms	(cbrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0)) (pow (/ (cbrt l) (cbrt Om)) 2.0)) (- U U*)))))

simplify579.0ms

Algorithm

egg-herbie

Counts

431 → 431

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	2468	66641
1	4738	66404
2	5001	66404

prune2.1s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 22.5b

regimes768.0ms

Accuracy

10.6% (8.2b remaining)

Error of 30.2b against oracle of 22.1b and baseline of 31.2b

bsearch81.0ms

Steps

Iters	Range		Point
5	1.0011276807577403e-148	2.3890075056810385e-148	1.0468514204986157e-148

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	51
1	43	51

end0.0ms

sample2.7s

Algorithm

intervals

Results

916.0ms	14793×	body	80	nan
578.0ms	9236×	body	80	valid