Details

sample6.8s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 4.956055%

Guaranteed chance to sample good point: 21.448754%

Results

42.0ms	441×	body	80	nan
31.0ms	296×	body	80	valid

simplify120.0ms

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

prune5.0ms

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: 36.7b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

7.9b	(* n (pow (/ l Om) 2.0))
9.5b	(/ (* l l) Om)
10.3b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.3b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite40.0ms

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:

9.0ms	(* n (pow (/ l Om) 2.0))
5.0ms	(/ (* l l) Om)
13.0ms	(* (* (* 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*)))))

series2.2s

Counts

4 → 12

Calls

4 calls:

40.0ms	(* n (pow (/ l Om) 2.0))
3.0ms	(/ (* l l) Om)
344.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
1.9s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify128.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1026	1602
1	4925	1447
2	5001	1447

prune336.0ms

Filtered

88 candidates to 124 candidates (-40.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	108	16	124
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	16	125

Merged error: 24.2b

Counts

125 → 16

localize18.0ms

Local error

Found 4 expressions with local error:

6.8b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.9b	(* n (pow (/ l Om) 2.0))
10.3b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.3b	(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:

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

series2.6s

Counts

4 → 12

Calls

4 calls:

125.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
43.0ms	(* n (pow (/ l Om) 2.0))
551.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
1.8s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify44.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1071	1765
1	5001	1602

prune304.0ms

Filtered

86 candidates to 131 candidates (-52.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	126	5	131
Fresh	5	10	15
Picked	1	0	1
Done	0	0	0
Total	132	15	147

Merged error: 22.3b

Counts

147 → 15

localize18.0ms

Local error

Found 4 expressions with local error:

4.7b	(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
6.8b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.9b	(* n (pow (/ l Om) 2.0))
20.3b	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite46.0ms

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:

12.0ms	(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
10.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.0ms	(* n (pow (/ l Om) 2.0))
10.0ms	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

series2.4s

Counts

4 → 12

Calls

4 calls:

347.0ms	(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
126.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
44.0ms	(* n (pow (/ l Om) 2.0))
1.9s	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify46.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1136	1922
1	5001	1732

prune313.0ms

Filtered

85 candidates to 141 candidates (-65.9%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	135	6	141
Fresh	3	11	14
Picked	1	0	1
Done	0	0	0
Total	139	17	156

Merged error: 19.1b

Counts

156 → 17

localize20.0ms

Local error

Found 4 expressions with local error:

4.7b	(* (* 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*)))))
6.0b	(* n (pow (/ l Om) (/ 2.0 2)))
6.8b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
20.3b	(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*))))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

102×	`add-exp-log`
69×	`prod-exp`
34×	`associate-*r/`
31×	`pow1`
27×	`add-cbrt-cube`
24×	`add-sqr-sqrt`
23×	`associate-r`
20×	`pow-exp`
18×	`distribute-rgt-in` `distribute-lft-in`
17×	`pow-prod-down`
16×	`*-un-lft-identity`
15×	`unpow-prod-down` `cbrt-unprod`
14×	`add-cube-cbrt`
11×	`flip3--` `flip--`
10×	`pow-to-exp` `sub-neg` `times-frac` `div-exp`
8×	`associate--l+` `frac-sub`
6×	`sqrt-div`
5×	`sqrt-pow1` `associate-l`
4×	`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 → 146

Calls

4 calls:

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

series2.4s

Counts

4 → 12

Calls

4 calls:

346.0ms	(* (* 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*)))))
46.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
126.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.9s	(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*))))))

simplify55.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1308	2694
1	5001	2292

prune288.0ms

Filtered

91 candidates to 158 candidates (-73.6%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	155	3	158
Fresh	2	14	16
Picked	1	0	1
Done	0	0	0
Total	158	17	175

Merged error: 18.9b

Counts

175 → 17

regimes974.0ms

Accuracy

20.7% (9.6b remaining)

Error of 28.0b against oracle of 18.3b and baseline of 30.5b

bsearch56.0ms

Steps

Iters	Range		Point
7	4.810989671753871e-276	1.2034705764342798e-273	4.92338489550887e-276

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	34
1	46	34

end0.0ms

sample10.2s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 4.956055%

Guaranteed chance to sample good point: 21.448754%

Results

1.3s	13866×	body	80	nan
888.0ms	9211×	body	80	valid

Details

sample6.8s

simplify120.0ms

prune5.0ms

localize19.0ms

rewrite40.0ms

series2.2s

simplify128.0ms

prune336.0ms

localize18.0ms

rewrite44.0ms

series2.6s

simplify44.0ms

prune304.0ms

localize18.0ms

rewrite46.0ms

series2.4s

simplify46.0ms

prune313.0ms

localize20.0ms

rewrite57.0ms

series2.4s

simplify55.0ms

prune288.0ms

regimes974.0ms

bsearch56.0ms

simplify1.0ms

end0.0ms

sample10.2s

Profiling