Details

sample395.0ms

Algorithm

intervals

Results

48.0ms	435×	body	80	nan
39.0ms	290×	body	80	valid

simplify123.0ms

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

prune9.0ms

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: 35.4b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

6.8b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.7b	(/ (* l l) Om)
9.6b	(* (* (* 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*)))))

rewrite52.0ms

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:

11.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
12.0ms	(/ (* l l) Om)
12.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
12.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.1s

Counts

4 → 12

Calls

4 calls:

349.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
19.0ms	(/ (* l l) Om)
1.2s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.5s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify119.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 1 (22.0ms)

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

prune758.0ms

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: 22.8b

Counts

116 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

5.5b	(* n (pow (/ l Om) 2.0))
6.8b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.6b	(* (* (* 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*)))))

rewrite44.0ms

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

series6.2s

Counts

4 → 12

Calls

4 calls:

131.0ms	(* n (pow (/ l Om) 2.0))
345.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.2s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.5s	(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 (24.0ms)

Iter	Nodes	Cost
0	987	1668
1	5001	1508

prune808.0ms

Filtered

131 candidates to 86 candidates (65.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	126	5	131
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	132	12	144

Merged error: 21.6b

Counts

144 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

5.6b	(* n (pow (/ l Om) (/ 2.0 2)))
6.8b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
9.6b	(* (* (* 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*)))))

rewrite56.0ms

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:

8.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
16.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
16.0ms	(* (* (* 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*))))
10.0ms	(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*)))))

series6.3s

Counts

4 → 12

Calls

4 calls:

152.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
341.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.2s	(* (* (* 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*))))
4.6s	(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*)))))

simplify46.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1113	2381
1	5001	2030

prune843.0ms

Filtered

148 candidates to 88 candidates (59.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	145	3	148
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	147	13	160

Merged error: 21.2b

Counts

160 → 13

localize22.0ms

Local error

Found 4 expressions with local error:

5.6b	(* n (pow (/ l Om) (/ 2.0 2)))
8.1b	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
9.6b	(* (* (* 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*))))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
30×	`unpow-prod-down` `associate-*r/`
29×	`add-exp-log`
25×	`-un-lft-identity` `associate-r*`
23×	`pow1` `add-cube-cbrt`
21×	`associate-l`
20×	`times-frac`
17×	`add-cbrt-cube`
14×	`prod-exp`
12×	`pow-prod-down`
11×	`flip3--` `flip--`
8×	`frac-sub` `cbrt-unprod` `unswap-sqr`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div`
4×	`sqrt-pow1` `pow-exp` `associate--l+` `add-log-exp` `sqr-pow`
3×	`*-commutative`
2×	`pow-to-exp` `div-exp` `div-inv`
1×	`pow1/2` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 136

Calls

4 calls:

11.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
10.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
12.0ms	(* (* (* 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*)))))
10.0ms	(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*))))))

series6.2s

Counts

4 → 12

Calls

4 calls:

157.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
317.0ms	(* (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*)))))
4.4s	(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*))))))

simplify45.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1079	2175
1	5001	1964

prune925.0ms

Filtered

148 candidates to 105 candidates (70.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

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

Merged error: 21.2b

Counts

161 → 13

regimes1.3s

Accuracy

31.7% (6.5b remaining)

Error of 27.8b against oracle of 21.4b and baseline of 30.8b

bsearch4.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	79
1	65	79

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.5s	14620×	body	80	nan
971.0ms	9221×	body	80	valid

Details

sample395.0ms

simplify123.0ms

prune9.0ms

localize23.0ms

rewrite52.0ms

series6.1s

simplify119.0ms

prune758.0ms

localize19.0ms

rewrite44.0ms

series6.2s

simplify45.0ms

prune808.0ms

localize21.0ms

rewrite56.0ms

series6.3s

simplify46.0ms

prune843.0ms

localize22.0ms

rewrite49.0ms

series6.2s

simplify45.0ms

prune925.0ms

regimes1.3s

bsearch4.0ms

simplify2.0ms

end0.0ms

sample4.1s

Profiling