Details

sample91.0ms

Algorithm

intervals

Results

34.0ms	472×	body	80	nan
22.0ms	293×	body	80	valid

simplify120.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 33.2b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

7.6b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.9b	(/ (* l l) Om)
10.3b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.0b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite49.0ms

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:

12.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
5.0ms	(/ (* l l) Om)
13.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
13.0ms	(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:

351.0ms	(* (* 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*)))))

simplify51.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1176	2335
1	5001	2011

prune538.0ms

Filtered

153 candidates to 92 candidates (60.1%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	137	16	153
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	138	16	154

Merged error: 24.7b

Counts

154 → 16

localize22.0ms

Local error

Found 4 expressions with local error:

7.2b	(* n (pow (/ l Om) 2.0))
7.6b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.3b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.0b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite54.0ms

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:

9.0ms	(* n (pow (/ l Om) 2.0))
12.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
13.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
14.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.6s

Counts

4 → 12

Calls

4 calls:

145.0ms	(* n (pow (/ l Om) 2.0))
380.0ms	(* (* 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*)))))

simplify59.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1229	2457
1	5001	2136

prune570.0ms

Filtered

169 candidates to 103 candidates (60.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	164	5	169
Fresh	4	11	15
Picked	1	0	1
Done	0	0	0
Total	169	16	185

Merged error: 23.3b

Counts

185 → 16

localize30.0ms

Local error

Found 4 expressions with local error:

13.7b	(cbrt (/ l Om))
13.7b	(cbrt (/ l Om))
13.7b	(cbrt (/ l Om))
18.0b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U*)))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

39×	`cbrt-prod`
27×	`times-frac`
25×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
14×	`pow1`
10×	`associate-*r/`
6×	`sqrt-div` `pow-prod-down`
5×	`flip3--` `flip--`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `frac-sub` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `pow1/3` `div-inv`
1×	`pow1/2` `sqrt-prod`

Counts

4 → 93

Calls

4 calls:

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

series5.1s

Counts

4 → 12

Calls

4 calls:

64.0ms	(cbrt (/ l Om))
59.0ms	(cbrt (/ l Om))
64.0ms	(cbrt (/ l Om))
4.9s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U*)))))

simplify76.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	609	1159
1	2564	1115
2	5001	1109

prune582.0ms

Filtered

105 candidates to 91 candidates (86.7%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	15	15
Picked	0	1	1
Done	0	0	0
Total	105	16	121

Merged error: 23.3b

Counts

121 → 16

localize29.0ms

Local error

Found 4 expressions with local error:

7.2b	(* n (pow (/ l Om) 2.0))
7.6b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.3b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.0b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite54.0ms

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:

9.0ms	(* n (pow (/ l Om) 2.0))
12.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
13.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
13.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.5s

Counts

4 → 12

Calls

4 calls:

145.0ms	(* n (pow (/ l Om) 2.0))
362.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.3s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.7s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify55.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1235	3092
1	5001	2706

prune563.0ms

Filtered

169 candidates to 103 candidates (60.9%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	167	2	169
Fresh	1	13	14
Picked	0	1	1
Done	0	1	1
Total	168	17	185

Merged error: 23.3b

Counts

185 → 17

regimes869.0ms

Accuracy

16.5% (7.4b remaining)

Error of 29.0b against oracle of 21.6b and baseline of 30.5b

bsearch200.0ms

Steps

Iters	Range		Point
6	9.218970226967994e+67	7.2484695024147705e+68	9.844657127410996e+67
8	-4.808974466695775e-09	-7.983923007473122e-12	-1.2817931366245364e-11

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	36
1	52	36

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.1s	15071×	body	80	nan
697.0ms	9201×	body	80	valid