Details

sample108.0ms

Algorithm

intervals

Results

46.0ms	458×	body	80	nan
27.0ms	289×	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: 34.0b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

7.1b	(* n (pow (/ l Om) 2.0))
8.8b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
9.8b	(/ (* l l) Om)
19.3b	(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

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:

9.0ms	(* n (pow (/ l Om) 2.0))
13.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
5.0ms	(/ (* l l) Om)
17.0ms	(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:

146.0ms	(* n (pow (/ l Om) 2.0))
1.4s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.0ms	(/ (* l l) Om)
4.9s	(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

144 → 144

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1079	1948
1	5001	1746

prune605.0ms

Filtered

144 candidates to 99 candidates (68.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	128	16	144
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	129	16	145

Merged error: 22.4b

Counts

145 → 16

localize19.0ms

Local error

Found 4 expressions with local error:

5.8b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.1b	(* n (pow (/ l Om) 2.0))
8.8b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.3b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite59.0ms

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:

12.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.0ms	(* n (pow (/ l Om) 2.0))
17.0ms	(* (* (* 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*)))))

series6.8s

Counts

4 → 12

Calls

4 calls:

383.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
146.0ms	(* n (pow (/ l Om) 2.0))
1.4s	(* (* (* 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*)))))

simplify54.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1229	2457
1	5001	2136

prune592.0ms

Filtered

169 candidates to 103 candidates (60.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	163	6	169
Fresh	7	8	15
Picked	1	0	1
Done	0	0	0
Total	171	14	185

Merged error: 21.1b

Counts

185 → 14

localize24.0ms

Local error

Found 4 expressions with local error:

8.8b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
8.8b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.3b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
19.3b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

42×	`pow1`
40×	`associate-*r/`
24×	`prod-diff` `pow-prod-down`
22×	`add-exp-log` `add-cbrt-cube`
20×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `associate--l+` `flip--`
16×	`frac-sub`
14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`sqrt-div` `prod-exp` `cbrt-unprod`
8×	`sub-neg` `sqrt-pow1`
6×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow1/2` `associate-l` `sqrt-prod` `*-commutative`

Counts

4 → 140

Calls

4 calls:

18.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
14.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
16.0ms	(sqrt (* (* (* 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*)))))

series12.5s

Counts

4 → 12

Calls

4 calls:

1.3s	(* (* (* 2.0 n) 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*))))
4.8s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
5.1s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify129.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (100.0ms)

Iter	Nodes	Cost
0	819	3288
1	4176	2936
2	5001	2934

prune712.0ms

Filtered

152 candidates to 96 candidates (63.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	152	14	166

Merged error: 21.1b

Counts

166 → 14

localize24.0ms

Local error

Found 4 expressions with local error:

7.6b	(* n (* (pow (/ l Om) 2.0) (- U U*)))
8.3b	(* (pow (/ l Om) 2.0) (- U U*))
8.8b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))
19.3b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

66×	`prod-diff`
65×	`distribute-rgt-in` `add-sqr-sqrt` `distribute-lft-in`
57×	`*-un-lft-identity`
55×	`add-cube-cbrt`
35×	`add-exp-log`
34×	`associate-*r/`
25×	`pow1`
21×	`associate-l`
20×	`add-cbrt-cube`
19×	`prod-exp`
15×	`unpow-prod-down`
13×	`pow-prod-down`
12×	`flip3--` `flip--`
10×	`sub-neg` `times-frac` `associate--l+` `cbrt-unprod`
9×	`associate-r`
8×	`frac-sub`
6×	`sqrt-div`
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 → 203

Calls

4 calls:

13.0ms	(* n (* (pow (/ l Om) 2.0) (- U U*)))
12.0ms	(* (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*)))))
15.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))

series6.9s

Counts

4 → 12

Calls

4 calls:

367.0ms	(* n (* (pow (/ l Om) 2.0) (- U U*)))
352.0ms	(* (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*))))))

simplify59.0ms

Algorithm

egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1311	3285
1	5001	2698

prune552.0ms

Filtered

215 candidates to 111 candidates (51.6%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	214	1	215
Fresh	1	11	12
Picked	0	1	1
Done	0	1	1
Total	215	14	229

Merged error: 20.2b

Counts

229 → 14

regimes708.0ms

Accuracy

13.2% (9.3b remaining)

Error of 30.9b against oracle of 21.6b and baseline of 32.3b

bsearch92.0ms

Steps

Iters	Range		Point
6	-1.9677041583951972e-293	-4.6457074396350103e-294	-4.6967744637083e-294

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	46
1	36	46

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.4s	14964×	body	80	nan
855.0ms	9174×	body	80	valid