Details

sample98.0ms

Algorithm

intervals

Results

40.0ms	544×	body	80	nan
20.0ms	292×	body	80	valid

simplify118.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize19.0ms

Local error

Found 4 expressions with local error:

7.1b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.0b	(/ (* l l) Om)
10.6b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.3b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite112.0ms

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:

25.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
3.0ms	(/ (* l l) Om)
47.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
33.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.5s

Counts

4 → 12

Calls

4 calls:

373.0ms	(* (* 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*))))
4.8s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify119.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 1 (21.0ms)

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

prune465.0ms

Filtered

115 candidates to 75 candidates (65.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 22.6b

localize18.0ms

Local error

Found 4 expressions with local error:

5.8b	(* n (pow (/ l Om) 2.0))
7.1b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.6b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.3b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* 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:

17.0ms	(* n (pow (/ l Om) 2.0))
23.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
50.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
30.0ms	(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:

148.0ms	(* n (pow (/ l Om) 2.0))
370.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.4s	(* (* (* 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*)))))

simplify40.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	987	1664
1	5001	1508

prune524.0ms

Filtered

131 candidates to 86 candidates (65.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 20.8b

localize24.0ms

Local error

Found 4 expressions with local error:

5.9b	(* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
6.2b	(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
7.1b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
18.3b	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

44×	`associate-*r/`
33×	`pow1`
32×	`add-exp-log`
23×	`add-cbrt-cube`
22×	`distribute-rgt-in` `distribute-lft-in`
18×	`pow-prod-down` `prod-exp`
16×	`flip3--` `flip--`
14×	`sub-neg`
12×	`associate--l+` `frac-sub` `cbrt-unprod`
11×	`add-sqr-sqrt`
9×	`-un-lft-identity` `associate-r*`
7×	`add-cube-cbrt`
6×	`sqrt-div`
5×	`sqrt-pow1` `associate-l`
4×	`add-log-exp`
3×	`*-commutative`
2×	`pow-exp`
1×	`pow-to-exp` `pow1/2` `div-exp` `sqrt-prod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 124

Calls

4 calls:

33.0ms	(* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* 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*)))))
23.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
37.0ms	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

series7.6s

Counts

4 → 12

Calls

4 calls:

875.0ms	(* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* 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*)))))
372.0ms	(* (* 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*))))))

simplify138.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	972	2173
1	4891	1949
2	5002	1949

prune483.0ms

Filtered

136 candidates to 79 candidates (58.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 17.5b

localize19.0ms

Local error

Found 4 expressions with local error:

5.9b	(* U (- (- t (* 2.0 (* l (/ l Om)))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))
6.2b	(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))
6.4b	(* (pow (/ l Om) 2.0) (- U U*))
18.3b	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 141

Calls

4 calls:

38.0ms	(* U (- (- t (* 2.0 (* l (/ l Om)))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))
55.0ms	(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))
25.0ms	(* (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*)))))))

series7.4s

Counts

4 → 12

Calls

4 calls:

892.0ms	(* U (- (- t (* 2.0 (* l (/ l Om)))) (* 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*))))))
348.0ms	(* (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

153 → 153

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1025	2264
1	4876	2040
2	5002	2040

prune537.0ms

Filtered

153 candidates to 98 candidates (64.1%)

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 17.5b

regimes620.0ms

Accuracy

27.1% (10.0b remaining)

Error of 29.3b against oracle of 19.3b and baseline of 33.1b

bsearch123.0ms

Steps

Iters	Range		Point
9	-7.610013761419582e-308	1.0598526293452503e-300	1.096720098972556e-309

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	29
1	41	29

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.0s	15208×	body	80	nan
626.0ms	9258×	body	80	valid