Details

sample101.0ms

Algorithm

intervals

Results

41.0ms	526×	body	80	nan
22.0ms	305×	body	80	valid

simplify116.0ms

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

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: 34.1b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

6.5b	(/ (* l l) Om)
8.4b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.5b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.7b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite42.0ms

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:

5.0ms	(/ (* l l) Om)
11.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
12.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
10.0ms	(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:

18.0ms	(/ (* l l) Om)
354.0ms	(* (* 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*))))
4.6s	(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 (22.0ms)

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

prune450.0ms

Filtered

115 candidates to 75 candidates (65.2%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	99	16	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	16	116

Merged error: 24.0b

Counts

116 → 16

localize18.0ms

Local error

Found 4 expressions with local error:

5.6b	(* n (pow (/ l Om) 2.0))
8.4b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.5b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.7b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite45.0ms

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:

9.0ms	(* n (pow (/ l Om) 2.0))
11.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
12.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
10.0ms	(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:

141.0ms	(* n (pow (/ l Om) 2.0))
367.0ms	(* (* 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*))))
4.7s	(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

131 → 131

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	987	1664
1	5001	1508

prune462.0ms

Filtered

131 candidates to 86 candidates (65.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	127	4	131
Fresh	6	9	15
Picked	1	0	1
Done	0	0	0
Total	134	13	147

Merged error: 22.6b

Counts

147 → 13

localize21.0ms

Local error

Found 4 expressions with local error:

5.7b	(* n (pow (/ l Om) (/ 2.0 2)))
8.4b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
10.5b	(* (* (* 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*))))
19.7b	(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*)))))

rewrite61.0ms

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:

9.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
16.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
13.0ms	(* (* (* 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*))))
11.0ms	(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*)))))

series6.8s

Counts

4 → 12

Calls

4 calls:

163.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
362.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
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*)))))

simplify50.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1113	2381
1	5001	2030

prune477.0ms

Filtered

148 candidates to 88 candidates (59.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	148	13	161

Merged error: 22.6b

Counts

161 → 13

localize23.0ms

Local error

Found 4 expressions with local error:

5.6b	(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
6.1b	(* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U)
8.4b	(* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))
19.7b	(sqrt (pow (* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U) 1))

rewrite36.0ms

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:

9.0ms	(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
13.0ms	(* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U)
8.0ms	(* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))
4.0ms	(sqrt (pow (* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U) 1))

series11.3s

Counts

4 → 12

Calls

4 calls:

150.0ms	(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
1.1s	(* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U)
296.0ms	(* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))
9.7s	(sqrt (pow (* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U) 1))

simplify118.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (102.0ms)

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

prune464.0ms

Filtered

118 candidates to 88 candidates (74.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	112	6	118
Fresh	2	9	11
Picked	1	0	1
Done	1	0	1
Total	116	15	131

Merged error: 20.3b

Counts

131 → 15

regimes968.0ms

Accuracy

25.3% (8.5b remaining)

Error of 27.4b against oracle of 18.9b and baseline of 30.3b

bsearch3.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	98
1	87	98
2	88	98
3	88	98

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.1s	14844×	body	80	nan
687.0ms	9160×	body	80	valid