Details

sample91.0ms

Algorithm

intervals

Results

34.0ms	432×	body	80	nan
22.0ms	305×	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

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: 36.3b

Counts

2 → 1

localize19.0ms

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*))))
9.3b	(* n (pow (/ l Om) 2.0))
11.3b	(/ (* l l) Om)
18.9b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log`
24×	`add-sqr-sqrt`
23×	`pow1`
20×	`associate-r/` `associate-r*` `add-cbrt-cube`
16×	`add-cube-cbrt` `*-un-lft-identity`
15×	`unpow-prod-down`
13×	`times-frac`
12×	`pow-prod-down`
11×	`prod-exp`
10×	`flip3--` `flip--`
8×	`frac-sub` `cbrt-unprod`
6×	`sqrt-div`
4×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-pow1` `associate-l` `associate--l+` `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 → 112

Calls

4 calls:

12.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
9.0ms	(* n (pow (/ l Om) 2.0))
5.0ms	(/ (* l l) Om)
13.0ms	(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:

1.4s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
142.0ms	(* n (pow (/ l Om) 2.0))
20.0ms	(/ (* l l) Om)
4.9s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify131.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	964	1525
1	4793	1370
2	5002	1370

prune572.0ms

Filtered

124 candidates to 87 candidates (70.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	109	15	124
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	15	125

Merged error: 22.8b

Counts

125 → 15

localize19.0ms

Local error

Found 4 expressions with local error:

5.0b	(* (* 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*))))
9.3b	(* n (pow (/ l Om) 2.0))
18.9b	(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

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:

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*))))
13.0ms	(* n (pow (/ l Om) 2.0))
11.0ms	(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:

384.0ms	(* (* 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*))))
143.0ms	(* n (pow (/ l Om) 2.0))
4.9s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify45.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	987	1664
1	5001	1508

prune555.0ms

Filtered

131 candidates to 86 candidates (65.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	118	13	131
Fresh	12	2	14
Picked	1	0	1
Done	0	0	0
Total	131	15	146

Merged error: 21.7b

Counts

146 → 15

localize21.0ms

Local error

Found 4 expressions with local error:

3.3b	(* n (pow (/ l Om) (/ 2.0 2)))
5.0b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
8.8b	(* (* (* 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*))))
18.9b	(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)))
21.0ms	(* (* (* 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*)))))

series7.0s

Counts

4 → 12

Calls

4 calls:

169.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
376.0ms	(* (* (* 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*))))
5.1s	(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*)))))

simplify51.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1113	2381
1	5001	2030

prune589.0ms

Filtered

148 candidates to 89 candidates (60.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	136	12	148
Fresh	11	3	14
Picked	1	0	1
Done	0	0	0
Total	148	15	163

Merged error: 21.6b

Counts

163 → 15

localize25.0ms

Local error

Found 4 expressions with local error:

3.3b	(* n (pow (/ l Om) (/ 2.0 2)))
3.4b	(* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))
8.8b	(* (* (* 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*)))))
18.9b	(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*))))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

111×	`add-exp-log`
75×	`prod-exp`
32×	`associate-*r/`
27×	`add-cbrt-cube`
25×	`pow1`
22×	`add-sqr-sqrt` `pow-exp`
21×	`associate-r`
15×	`unpow-prod-down` `cbrt-unprod`
14×	`add-cube-cbrt` `*-un-lft-identity`
13×	`pow-prod-down`
12×	`distribute-rgt-in` `distribute-lft-in`
11×	`pow-to-exp` `flip3--` `div-exp` `flip--`
10×	`times-frac`
8×	`sub-neg` `frac-sub`
6×	`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`

Counts

4 → 141

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*)))
14.0ms	(* (* (* 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:

167.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
374.0ms	(* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))
1.4s	(* (* (* 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*)))))
4.8s	(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

153 → 153

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1122	2510
1	5001	2103

prune515.0ms

Filtered

153 candidates to 84 candidates (54.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	149	4	153
Fresh	3	11	14
Picked	1	0	1
Done	0	0	0
Total	153	15	168

Merged error: 21.5b

Counts

168 → 15

regimes591.0ms

Accuracy

17.9% (7.3b remaining)

Error of 29.3b against oracle of 22.0b and baseline of 30.9b

bsearch264.0ms

Steps

Iters	Range		Point
8	3.8869880032397244e-101	2.6326129653409476e-98	1.06333856989431e-98
9	-3.11395884928631e-28	-3.5951055523924267e-34	-6.340019414053634e-31

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	59
1	73	59
2	74	59
3	74	59

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.1s	14907×	body	80	nan
663.0ms	9228×	body	80	valid