Details

sample414.0ms

Algorithm

intervals

Results

40.0ms	290×	body	80	valid
31.0ms	453×	body	80	nan

simplify120.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.0b

localize21.0ms

Local error

Found 4 expressions with local error:

6.2b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.4b	(/ (* l l) Om)
13.1b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.8b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite279.0ms

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:

46.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.0ms	(/ (* l l) Om)
128.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
88.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.7s

Counts

4 → 12

Calls

4 calls:

374.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
19.0ms	(/ (* l l) Om)
1.3s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
5.0s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify120.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	937	1544
1	4764	1385
2	5001	1385

prune455.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 24.7b

localize18.0ms

Local error

Found 4 expressions with local error:

5.1b	(* n (pow (/ l Om) 2.0))
6.2b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
13.1b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.8b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite287.0ms

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:

26.0ms	(* n (pow (/ l Om) 2.0))
45.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
129.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
82.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.7s

Counts

4 → 12

Calls

4 calls:

146.0ms	(* n (pow (/ l Om) 2.0))
372.0ms	(* (* 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*))))
4.9s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify38.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	987	1668
1	5001	1508

prune477.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 23.2b

localize20.0ms

Local error

Found 4 expressions with local error:

6.2b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
6.8b	(* n (pow (/ l Om) (/ 2.0 2)))
13.1b	(* (* (* 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*))))
19.8b	(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*)))))

rewrite482.0ms

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:

149.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
25.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
183.0ms	(* (* (* 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*))))
119.0ms	(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*)))))

series6.9s

Counts

4 → 12

Calls

4 calls:

375.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
172.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
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*))))
5.0s	(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*)))))

simplify46.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1113	2381
1	5001	2030

prune523.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 22.8b

localize23.0ms

Local error

Found 4 expressions with local error:

5.1b	(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
6.2b	(* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))
6.8b	(* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U)
19.8b	(sqrt (pow (* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U) 1))

rewrite322.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 106

Calls

4 calls:

27.0ms	(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
30.0ms	(* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))
249.0ms	(* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U)
11.0ms	(sqrt (pow (* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U) 1))

series11.6s

Counts

4 → 12

Calls

4 calls:

148.0ms	(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
304.0ms	(* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))
1.1s	(* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U)
10.1s	(sqrt (pow (* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U) 1))

simplify106.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	770	1582
1	4137	1372
2	5002	1364

prune457.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 19.2b

regimes725.0ms

Accuracy

25.1% (9.3b remaining)

Error of 28.2b against oracle of 18.9b and baseline of 31.4b

bsearch289.0ms

Steps

Iters	Range	Point
6	9.655969020719335e-299	8.902876449237102e-298	9.891457184010319e-299
9	-6.135579462598049e-178	-3.735328815158686e-183	-1.9843813902657215e-178
10	-4.595080940101684e-37	-3.0572799811341753e-49	-9.756238003230914e-48

Iters

Range

Point

9.655969020719335e-299

8.902876449237102e-298

9.891457184010319e-299

-6.135579462598049e-178

-3.735328815158686e-183

-1.9843813902657215e-178

-4.595080940101684e-37

-3.0572799811341753e-49

-9.756238003230914e-48

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	100	76
1	115	76
2	117	76
3	117	76

end0.0ms

sample2.6s

Algorithm

intervals

Results

876.0ms	14757×	body	80	nan
545.0ms	9196×	body	80	valid