Details

sample366.0ms

Algorithm

intervals

Results

40.0ms	306×	body	80	valid
39.0ms	435×	body	80	nan

simplify132.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	49	14
1	155	14
2	684	14
3	3898	14
4	5001	14

prune5.0ms

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: 33.0b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

5.7b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.4b	(/ (* l l) Om)
10.8b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
17.4b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
30×	`prod-diff`
26×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`pow1`
24×	`add-cube-cbrt`
23×	`add-cbrt-cube`
22×	`associate-*r/`
21×	`distribute-rgt-in` `distribute-lft-in`
16×	`prod-exp`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`associate--l+` `cbrt-unprod`
8×	`associate-r` `frac-sub`
6×	`sub-neg` `sqrt-div`
4×	`expm1-log1p-u` `sqrt-pow1` `log1p-expm1-u` `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 → 141

Calls

4 calls:

12.0ms	(* (* 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*))))
15.0ms	(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:

354.0ms	(* (* 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*))))
4.6s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify51.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1176	2339
1	5001	2015

prune531.0ms

Filtered

153 candidates to 93 candidates (60.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	140	13	153
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	141	13	154

Merged error: 22.1b

Counts

154 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

5.4b	(* n (pow (/ l Om) 2.0))
5.7b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.8b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
17.4b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
35×	`add-exp-log`
33×	`*-un-lft-identity`
31×	`add-cube-cbrt`
30×	`prod-diff`
25×	`pow1` `associate-r`
22×	`associate-*r/`
21×	`distribute-rgt-in` `distribute-lft-in`
20×	`add-cbrt-cube`
19×	`prod-exp`
15×	`unpow-prod-down`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`times-frac` `associate--l+` `cbrt-unprod`
8×	`frac-sub`
6×	`sub-neg` `sqrt-div`
5×	`associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `pow-exp` `log1p-expm1-u` `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 → 157

Calls

4 calls:

8.0ms	(* n (pow (/ l Om) 2.0))
12.0ms	(* (* 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*))))
13.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.4s

Counts

4 → 12

Calls

4 calls:

137.0ms	(* n (pow (/ l Om) 2.0))
360.0ms	(* (* 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*))))
4.6s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify51.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1227	2461
1	5002	2136

prune546.0ms

Filtered

169 candidates to 103 candidates (60.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	165	4	169
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	170	12	182

Merged error: 21.6b

Counts

182 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

5.7b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
5.7b	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
5.9b	(* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
17.4b	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

61×	`distribute-rgt-in` `distribute-lft-in`
54×	`prod-diff`
44×	`associate-*r/`
35×	`add-sqr-sqrt`
33×	`pow1` `*-un-lft-identity`
32×	`add-exp-log`
31×	`add-cube-cbrt`
30×	`associate--l+`
23×	`add-cbrt-cube`
18×	`pow-prod-down` `prod-exp`
16×	`flip3--` `flip--`
14×	`sub-neg`
12×	`frac-sub` `cbrt-unprod`
9×	`associate-r`
6×	`sqrt-div`
5×	`sqrt-pow1` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `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 → 186

Calls

4 calls:

12.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
13.0ms	(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
10.0ms	(* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
21.0ms	(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

series7.2s

Counts

4 → 12

Calls

4 calls:

356.0ms	(* (* 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*)))))
839.0ms	(* 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*))))))

simplify60.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1323	3642
1	5001	3181

prune549.0ms

Filtered

198 candidates to 102 candidates (51.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	190	8	198
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	196	14	210

Merged error: 18.7b

Counts

210 → 14

localize29.0ms

Local error

Found 4 expressions with local error:

5.7b	(* (* 2.0 n) (+ (* U (fma (* (cbrt t) (cbrt t)) (cbrt t) (- (* (/ l (/ Om l)) 2.0)))) (* U (- (fma (- (/ l (/ Om l))) 2.0 (* (/ l (/ Om l)) 2.0)) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
8.8b	(* U (- (fma (- (/ l (/ Om l))) 2.0 (* (/ l (/ Om l)) 2.0)) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
9.7b	(fma (- (/ l (/ Om l))) 2.0 (* (/ l (/ Om l)) 2.0))
17.4b	(sqrt (* (* 2.0 n) (+ (* U (fma (* (cbrt t) (cbrt t)) (cbrt t) (- (* (/ l (/ Om l)) 2.0)))) (* U (- (fma (- (/ l (/ Om l))) 2.0 (* (/ l (/ Om l)) 2.0)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1`
11×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `pow-prod-down`
6×	`associate-*r/` `prod-diff`
4×	`expm1-log1p-u` `associate-l` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-pow1` `fma-udef`
2×	`sub-neg` `flip3-+` `sqrt-div` `associate--l+` `*-commutative` `flip-+`
1×	`flip3--` `pow1/2` `sqrt-prod` `flip--` `distribute-lft-out` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

7.0ms	(* (* 2.0 n) (+ (* U (fma (* (cbrt t) (cbrt t)) (cbrt t) (- (* (/ l (/ Om l)) 2.0)))) (* U (- (fma (- (/ l (/ Om l))) 2.0 (* (/ l (/ Om l)) 2.0)) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
6.0ms	(* U (- (fma (- (/ l (/ Om l))) 2.0 (* (/ l (/ Om l)) 2.0)) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
1.0ms	(fma (- (/ l (/ Om l))) 2.0 (* (/ l (/ Om l)) 2.0))
6.0ms	(sqrt (* (* 2.0 n) (+ (* U (fma (* (cbrt t) (cbrt t)) (cbrt t) (- (* (/ l (/ Om l)) 2.0)))) (* U (- (fma (- (/ l (/ Om l))) 2.0 (* (/ l (/ Om l)) 2.0)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))))

series11.9s

Counts

4 → 12

Calls

4 calls:

4.9s	(* (* 2.0 n) (+ (* U (fma (* (cbrt t) (cbrt t)) (cbrt t) (- (* (/ l (/ Om l)) 2.0)))) (* U (- (fma (- (/ l (/ Om l))) 2.0 (* (/ l (/ Om l)) 2.0)) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
497.0ms	(* U (- (fma (- (/ l (/ Om l))) 2.0 (* (/ l (/ Om l)) 2.0)) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
30.0ms	(fma (- (/ l (/ Om l))) 2.0 (* (/ l (/ Om l)) 2.0))
6.4s	(sqrt (* (* 2.0 n) (+ (* U (fma (* (cbrt t) (cbrt t)) (cbrt t) (- (* (/ l (/ Om l)) 2.0)))) (* U (- (fma (- (/ l (/ Om l))) 2.0 (* (/ l (/ Om l)) 2.0)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))))

simplify111.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	676	2305
1	3617	2026
2	5002	1992

prune420.0ms

Filtered

97 candidates to 73 candidates (75.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	97	14	111

Merged error: 18.7b

Counts

111 → 14

regimes699.0ms

Accuracy

21.6% (9.6b remaining)

Error of 27.9b against oracle of 18.3b and baseline of 30.5b

bsearch93.0ms

Steps

Iters	Range		Point
7	2.555595544482059e-295	8.445669096058748e-294	3.442322304142332e-295

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	34
1	46	34

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.3s	15029×	body	80	nan
832.0ms	9245×	body	80	valid