Details

sample110.0ms

Algorithm

intervals

Results

47.0ms	479×	body	80	nan
27.0ms	299×	body	80	valid

simplify124.0ms

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: 34.5b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

6.1b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.8b	(/ (* l l) Om)
10.7b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.1b	(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

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:

15.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
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*))))
10.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.4s

Counts

4 → 12

Calls

4 calls:

358.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
18.0ms	(/ (* l l) Om)
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*)))))

simplify130.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	937	1544
1	4764	1385
2	5001	1385

prune432.0ms

Filtered

115 candidates to 75 candidates (65.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	103	12	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	104	12	116

Merged error: 21.8b

Counts

116 → 12

localize23.0ms

Local error

Found 4 expressions with local error:

4.0b	(* n (pow (/ l Om) 2.0))
6.1b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.7b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.1b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite47.0ms

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

series6.5s

Counts

4 → 12

Calls

4 calls:

150.0ms	(* n (pow (/ l Om) 2.0))
363.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.3s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.7s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* 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	987	1664
1	5001	1508

prune469.0ms

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	5	6	11
Picked	1	0	1
Done	0	0	0
Total	132	11	143

Merged error: 20.4b

Counts

143 → 11

localize24.0ms

Local error

Found 4 expressions with local error:

5.4b	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
6.1b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.4b	(* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.1b	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

44×	`associate-*r/`
33×	`pow1`
32×	`add-exp-log`
23×	`add-cbrt-cube`
22×	`distribute-rgt-in` `distribute-lft-in`
18×	`pow-prod-down` `prod-exp`
16×	`flip3--` `flip--`
14×	`sub-neg`
12×	`associate--l+` `frac-sub` `cbrt-unprod`
11×	`add-sqr-sqrt`
9×	`-un-lft-identity` `associate-r*`
7×	`add-cube-cbrt`
6×	`sqrt-div`
5×	`sqrt-pow1` `associate-l`
4×	`add-log-exp`
3×	`*-commutative`
2×	`pow-exp`
1×	`pow-to-exp` `pow1/2` `div-exp` `sqrt-prod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 124

Calls

4 calls:

13.0ms	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
11.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.0ms	(* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
10.0ms	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

series7.4s

Counts

4 → 12

Calls

4 calls:

1.2s	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
555.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
872.0ms	(* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.8s	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify130.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	972	2178
1	4853	1949
2	5001	1949

prune430.0ms

Filtered

136 candidates to 80 candidates (58.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	129	7	136
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	133	14	147

Merged error: 18.2b

Counts

147 → 14

localize23.0ms

Local error

Found 4 expressions with local error:

4.2b	(* (* (cbrt U) (cbrt U)) (* (cbrt U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
5.4b	(* (* 2.0 n) (* (* (cbrt U) (cbrt U)) (* (cbrt U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
6.1b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
19.1b	(sqrt (* (* 2.0 n) (* (* (cbrt U) (cbrt U)) (* (cbrt U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

101×	`pow1`
71×	`add-exp-log` `pow-prod-down`
66×	`distribute-rgt-in` `distribute-lft-in`
62×	`associate-*r/`
48×	`prod-exp`
44×	`add-cbrt-cube`
42×	`cbrt-unprod`
26×	`sub-neg`
24×	`associate--l+`
16×	`flip3--` `flip--`
12×	`frac-sub`
11×	`sqrt-pow1`
7×	`add-sqr-sqrt` `-un-lft-identity` `associate-r*`
6×	`sqrt-div`
5×	`add-cube-cbrt`
4×	`add-log-exp`
3×	`associate-l` `*-commutative`
2×	`pow-exp`
1×	`pow-to-exp` `pow1/2` `div-exp` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 176

Calls

4 calls:

15.0ms	(* (* (cbrt U) (cbrt U)) (* (cbrt U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
22.0ms	(* (* 2.0 n) (* (* (cbrt U) (cbrt U)) (* (cbrt U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
14.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
17.0ms	(sqrt (* (* 2.0 n) (* (* (cbrt U) (cbrt U)) (* (cbrt U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))))

series7.1s

Counts

4 → 12

Calls

4 calls:

896.0ms	(* (* (cbrt U) (cbrt U)) (* (cbrt U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
1.3s	(* (* 2.0 n) (* (* (cbrt U) (cbrt U)) (* (cbrt U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
359.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
4.5s	(sqrt (* (* 2.0 n) (* (* (cbrt U) (cbrt U)) (* (cbrt U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))))

simplify67.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1259	4017
1	5002	3105

prune462.0ms

Filtered

188 candidates to 84 candidates (44.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	187	1	188
Fresh	0	13	13
Picked	1	0	1
Done	0	0	0
Total	188	14	202

Merged error: 18.2b

Counts

202 → 14

regimes535.0ms

Accuracy

10% (11.9b remaining)

Error of 31.1b against oracle of 19.2b and baseline of 32.4b

bsearch520.0ms

Steps

Iters	Range		Point
9	3.477364271574161e+249	1.8663818275530302e+258	3.528054756084284e+249
7	1.631206338118161e+217	7.399010727242409e+218	2.730311664834788e+218
7	1.4699936350102353e-51	3.1952359561246404e-49	3.1433311514194662e-49
8	-2.032480306732497e-261	-8.809482150592798e-265	-1.4222335564411585e-262

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	131
1	71	131

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.4s	14712×	body	80	nan
838.0ms	9205×	body	80	valid

Details

sample110.0ms

simplify124.0ms

prune4.0ms

localize19.0ms

rewrite46.0ms

series6.4s

simplify130.0ms

prune432.0ms

localize23.0ms

rewrite47.0ms

series6.5s

simplify44.0ms

prune469.0ms

localize24.0ms

rewrite48.0ms

series7.4s

simplify130.0ms

prune430.0ms

localize23.0ms

rewrite77.0ms

series7.1s

simplify67.0ms

prune462.0ms

regimes535.0ms

bsearch520.0ms

simplify2.0ms

end0.0ms

sample3.1s

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