Details

sample374.0ms

Algorithm

intervals

Results

55.0ms	479×	body	80	nan
29.0ms	296×	body	80	valid

simplify131.0ms

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

prune7.0ms

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: 34.8b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

5.7b	(* n (pow (/ l Om) 2.0))
9.6b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
9.6b	(/ (* l l) Om)
20.0b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
26×	`add-exp-log`
23×	`pow1`
20×	`add-cube-cbrt` `-un-lft-identity` `associate-r/` `associate-r` `add-cbrt-cube`
15×	`unpow-prod-down`
13×	`times-frac`
12×	`prod-diff` `pow-prod-down`
11×	`prod-exp`
10×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `associate--l+` `flip--`
8×	`frac-sub` `cbrt-unprod`
6×	`sqrt-div`
4×	`expm1-log1p-u` `sub-neg` `sqrt-pow1` `associate-l` `log1p-expm1-u` `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 → 132

Calls

4 calls:

9.0ms	(* n (pow (/ l Om) 2.0))
13.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
5.0ms	(/ (* l l) Om)
15.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.0s

Counts

4 → 12

Calls

4 calls:

139.0ms	(* n (pow (/ l Om) 2.0))
1.3s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
23.0ms	(/ (* l l) Om)
4.5s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify53.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1079	1948
1	5001	1746

prune558.0ms

Filtered

144 candidates to 99 candidates (68.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	131	13	144
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	132	13	145

Merged error: 25.2b

Counts

145 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

5.4b	(- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))
5.7b	(* n (pow (/ l Om) 2.0))
9.6b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.0b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
36×	`prod-diff`
33×	`add-cube-cbrt` `*-un-lft-identity`
24×	`associate-*r/`
23×	`pow1`
22×	`associate--r+`
21×	`add-exp-log` `distribute-rgt-in` `distribute-lft-in`
20×	`associate-r`
15×	`unpow-prod-down` `flip3--` `associate--l+` `add-cbrt-cube` `flip--`
12×	`pow-prod-down` `frac-sub`
10×	`times-frac` `prod-exp`
9×	`add-log-exp`
8×	`sub-neg`
7×	`cbrt-unprod`
6×	`sqrt-div`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-l` `log1p-expm1-u` `unswap-sqr`
3×	`fma-neg` `diff-log`
2×	`pow-exp` `*-commutative` `sqr-pow`
1×	`associate--l-` `pow-to-exp` `pow1/2` `div-exp` `sqrt-prod` `div-inv`

Counts

4 → 162

Calls

4 calls:

9.0ms	(- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))
8.0ms	(* n (pow (/ l Om) 2.0))
13.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
13.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.7s

Counts

4 → 12

Calls

4 calls:

643.0ms	(- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))
136.0ms	(* n (pow (/ l Om) 2.0))
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*)))))

simplify52.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1246	2749
1	5001	2446

prune656.0ms

Filtered

174 candidates to 126 candidates (72.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	168	6	174
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	174	13	187

Merged error: 23.5b

Counts

187 → 13

localize24.0ms

Local error

Found 4 expressions with local error:

5.4b	(- (- t (* 2.0 (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))
5.7b	(* n (pow (/ l Om) 2.0))
9.6b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.0b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
36×	`prod-diff`
33×	`add-cube-cbrt` `*-un-lft-identity`
24×	`associate-*r/`
23×	`pow1`
22×	`associate--r+`
21×	`add-exp-log` `distribute-rgt-in` `distribute-lft-in`
20×	`associate-r`
15×	`unpow-prod-down` `flip3--` `associate--l+` `add-cbrt-cube` `flip--`
12×	`pow-prod-down` `frac-sub`
10×	`times-frac` `prod-exp`
9×	`add-log-exp`
8×	`sub-neg`
7×	`cbrt-unprod`
6×	`sqrt-div`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-l` `log1p-expm1-u` `unswap-sqr`
3×	`fma-neg` `diff-log`
2×	`pow-exp` `*-commutative` `sqr-pow`
1×	`associate--l-` `pow-to-exp` `pow1/2` `div-exp` `sqrt-prod` `div-inv`

Counts

4 → 162

Calls

4 calls:

9.0ms	(- (- t (* 2.0 (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))
9.0ms	(* n (pow (/ l Om) 2.0))
17.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
13.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.9s

Counts

4 → 12

Calls

4 calls:

680.0ms	(- (- t (* 2.0 (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))
134.0ms	(* n (pow (/ l Om) 2.0))
1.3s	(* (* (* 2.0 n) U) (- (- t (* 2.0 (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.7s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify58.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1253	3770
1	5002	3391

prune713.0ms

Filtered

174 candidates to 125 candidates (71.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	173	1	174
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	175	12	187

Merged error: 23.5b

Counts

187 → 12

localize23.0ms

Local error

Found 4 expressions with local error:

9.8b	(cbrt (- t (* 2.0 (* l (/ l Om)))))
9.8b	(cbrt (- t (* 2.0 (* l (/ l Om)))))
9.8b	(cbrt (- t (* 2.0 (* l (/ l Om)))))
20.0b	(sqrt (* (* (* 2.0 n) U) (fma (* (cbrt (- t (* 2.0 (* l (/ l Om))))) (cbrt (- t (* 2.0 (* l (/ l Om)))))) (cbrt (- t (* 2.0 (* l (/ l Om))))) (- (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1`
9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div` `pow-prod-down`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--`
1×	`pow1/2` `sqrt-prod`

Counts

4 → 60

Calls

4 calls:

2.0ms	(cbrt (- t (* 2.0 (* l (/ l Om)))))
2.0ms	(cbrt (- t (* 2.0 (* l (/ l Om)))))
2.0ms	(cbrt (- t (* 2.0 (* l (/ l Om)))))
5.0ms	(sqrt (* (* (* 2.0 n) U) (fma (* (cbrt (- t (* 2.0 (* l (/ l Om))))) (cbrt (- t (* 2.0 (* l (/ l Om)))))) (cbrt (- t (* 2.0 (* l (/ l Om))))) (- (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

series2.6s

Counts

4 → 12

Calls

4 calls:

269.0ms	(cbrt (- t (* 2.0 (* l (/ l Om)))))
267.0ms	(cbrt (- t (* 2.0 (* l (/ l Om)))))
266.0ms	(cbrt (- t (* 2.0 (* l (/ l Om)))))
1.8s	(sqrt (* (* (* 2.0 n) U) (fma (* (cbrt (- t (* 2.0 (* l (/ l Om))))) (cbrt (- t (* 2.0 (* l (/ l Om)))))) (cbrt (- t (* 2.0 (* l (/ l Om))))) (- (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify48.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	366	931
1	1264	870
2	5001	858

prune345.0ms

Filtered

72 candidates to 64 candidates (88.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	71	13	84

Merged error: 23.5b

Counts

84 → 13

regimes791.0ms

Accuracy

37% (6.0b remaining)

Error of 28.5b against oracle of 22.5b and baseline of 32.0b

bsearch5.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	81
1	68	81

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.4s	14657×	body	80	nan
846.0ms	9171×	body	80	valid