Details

sample90.0ms

Algorithm

intervals

Results

33.0ms	490×	body	80	nan
22.0ms	289×	body	80	valid

simplify115.0ms

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: 31.9b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

5.3b	(/ (* l l) Om)
5.6b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.7b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
17.9b	(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

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*))
15.0ms	(* (* (* 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:

19.0ms	(/ (* l l) Om)
358.0ms	(* (* 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*)))))

simplify118.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 1 (22.0ms)

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

prune407.0ms

Filtered

115 candidates to 75 candidates (65.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	102	13	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	13	116

Merged error: 22.0b

Counts

116 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

5.1b	(* n (pow (/ l Om) 2.0))
5.6b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.7b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
17.9b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite50.0ms

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:

8.0ms	(* n (pow (/ l Om) 2.0))
15.0ms	(* (* 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:

142.0ms	(* n (pow (/ l Om) 2.0))
369.0ms	(* (* 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*)))))

simplify42.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	987	1664
1	5001	1508

prune444.0ms

Filtered

131 candidates to 86 candidates (65.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	126	5	131
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	133	11	144

Merged error: 21.4b

Counts

144 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

3.8b	(* n (pow (/ l Om) (/ 2.0 2)))
5.6b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
9.7b	(* (* (* 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*))))
17.9b	(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*)))))

rewrite60.0ms

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)))
17.0ms	(* (* (* 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*))))
15.0ms	(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:

165.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
367.0ms	(* (* (* 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*))))
4.9s	(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*)))))

simplify49.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1113	2385
1	5002	2030

prune463.0ms

Filtered

148 candidates to 88 candidates (59.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	149	10	159

Merged error: 21.4b

Counts

159 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

5.1b	(* n (pow (/ l Om) 2.0))
5.6b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.1b	(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
17.9b	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-exp-log`
34×	`associate-*r/`
31×	`pow1`
24×	`add-sqr-sqrt`
23×	`associate-r` `add-cbrt-cube`
21×	`prod-exp`
18×	`distribute-rgt-in` `distribute-lft-in`
17×	`pow-prod-down`
16×	`*-un-lft-identity`
15×	`unpow-prod-down`
14×	`add-cube-cbrt`
12×	`cbrt-unprod`
11×	`flip3--` `flip--`
10×	`sub-neg` `times-frac`
8×	`associate--l+` `frac-sub`
6×	`sqrt-div`
5×	`sqrt-pow1` `associate-l`
4×	`pow-exp` `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 → 129

Calls

4 calls:

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

140.0ms	(* n (pow (/ l Om) 2.0))
368.0ms	(* (* 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*))))))

simplify43.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1052	1821
1	5001	1638

prune403.0ms

Filtered

141 candidates to 85 candidates (60.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	137	4	141
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	139	12	151

Merged error: 18.9b

Counts

151 → 12

regimes676.0ms

Accuracy

20.6% (9.8b remaining)

Error of 28.5b against oracle of 18.8b and baseline of 31.1b

bsearch193.0ms

Steps

Iters	Range	Point
7	1.2101053720005742e-135	2.54095932775131e-133	5.2010062722959627e-135
4	1.416237487246357e-187	2.7048464604048396e-187	2.637013642721778e-187
5	-1.6443605818716367e-308	1.126154342143043e-308	-4.2656641425651e-310

Iters

Range

Point

1.2101053720005742e-135

2.54095932775131e-133

5.2010062722959627e-135

1.416237487246357e-187

2.7048464604048396e-187

2.637013642721778e-187

-1.6443605818716367e-308

1.126154342143043e-308

-4.2656641425651e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	58
1	60	58

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.0s	14993×	body	80	nan
643.0ms	9224×	body	80	valid