Details

Time bar (total: 2.6m)

sample340.0ms

Algorithm
intervals
Results
33.0ms455×body80nan
22.0ms305×body80valid

simplify138.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (13.0ms)

IterNodesCost
04914
115514
268414
3389814
4500114

prune5.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 30.8b

Counts
2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

6.0b
(* n (pow (/ l Om) 2.0))
7.7b
(/ (* l l) Om)
10.6b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
14.3b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite694.0ms

Algorithm
rewrite-expression-head
Rules
3776×add-sqr-sqrt
1434×prod-diff
1210×*-un-lft-identity
1061×times-frac
1041×associate-*l*
1040×unswap-sqr
953×associate-*r*
762×add-cube-cbrt
721×distribute-rgt-in distribute-lft-in
652×difference-of-squares
427×unpow-prod-down
382×associate--l+
230×distribute-lft-out--
177×*-commutative
160×swap-sqr
76×sqr-pow
48×sqrt-prod
32×div-inv
26×add-exp-log
25×pow1
20×associate-*r/ add-cbrt-cube
15×associate-/l*
13×pow-prod-down
11×prod-exp
10×flip3-- flip--
8×frac-sub cbrt-unprod
6×sqrt-div
4×expm1-log1p-u sub-neg rem-sqrt-square sqrt-pow1 log1p-expm1-u add-log-exp
3×div-exp associate-/r*
2×cbrt-undiv pow-exp
1×pow-to-exp frac-2neg pow1/2 clear-num
Counts
4 → 1701
Calls
4 calls:
11.0ms
(* n (pow (/ l Om) 2.0))
8.0ms
(/ (* l l) Om)
151.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
289.0ms
(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))
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*)))))

simplify603.0ms

Algorithm
egg-herbie
Counts
1713 → 1713
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
0500273307

prune6.3s

Filtered
1713 candidates to 912 candidates (53.2%)
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New1695181713
Fresh000
Picked101
Done000
Total1696181714

Merged error: 14.6b

Counts
1714 → 18

localize22.0ms

Local error

Found 4 expressions with local error:

6.0b
(* n (pow (/ l Om) 2.0))
7.7b
(/ (* l l) Om)
8.0b
(* (* (cbrt (* 2.0 n)) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
12.7b
(sqrt (* (* (cbrt (* 2.0 n)) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite679.0ms

Algorithm
rewrite-expression-head
Rules
3791×add-sqr-sqrt
1434×prod-diff
1212×*-un-lft-identity
1061×times-frac
1055×associate-*l*
1048×unswap-sqr
953×associate-*r*
764×add-cube-cbrt
721×distribute-rgt-in distribute-lft-in
652×difference-of-squares
427×unpow-prod-down
382×associate--l+
230×distribute-lft-out--
177×*-commutative
160×swap-sqr
76×sqr-pow
53×sqrt-prod
34×cbrt-prod
32×div-inv
22×add-exp-log
20×associate-*r/
18×add-cbrt-cube
17×pow1
15×associate-/l*
10×flip3-- flip--
8×prod-exp frac-sub
7×pow-prod-down cbrt-unprod
6×sqrt-div
5×rem-sqrt-square
4×expm1-log1p-u sub-neg log1p-expm1-u add-log-exp
3×sqrt-pow1 div-exp associate-/r*
2×cbrt-undiv pow-exp
1×pow-to-exp frac-2neg pow1/2 clear-num
Counts
4 → 1709
Calls
4 calls:
16.0ms
(* n (pow (/ l Om) 2.0))
8.0ms
(/ (* l l) Om)
147.0ms
(* (* (cbrt (* 2.0 n)) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
281.0ms
(sqrt (* (* (cbrt (* 2.0 n)) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series31.7s

Counts
4 → 12
Calls
4 calls:
132.0ms
(* n (pow (/ l Om) 2.0))
17.0ms
(/ (* l l) Om)
2.0s
(* (* (cbrt (* 2.0 n)) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
29.6s
(sqrt (* (* (cbrt (* 2.0 n)) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify580.0ms

Algorithm
egg-herbie
Counts
1721 → 1721
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
0500276517

prune6.3s

Filtered
1721 candidates to 923 candidates (53.6%)
Pruning

22 alts after pruning (22 fresh and 0 done)

PrunedKeptTotal
New171381721
Fresh31417
Picked101
Done000
Total1717221739

Merged error: 13.6b

Counts
1739 → 22

localize30.0ms

Local error

Found 4 expressions with local error:

6.0b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.0b
(* n (pow (/ l Om) 2.0))
7.7b
(/ (* l l) Om)
11.4b
(sqrt (* (cbrt (* (cbrt (* 2.0 n)) U)) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite318.0ms

Algorithm
rewrite-expression-head
Rules
180×add-sqr-sqrt
107×*-un-lft-identity
106×associate-*l*
81×add-cube-cbrt
75×associate-*r*
67×times-frac
57×sqrt-prod
53×unswap-sqr
52×cbrt-prod
34×unpow-prod-down
31×add-exp-log
18×prod-diff
16×add-cbrt-cube distribute-lft-out--
15×associate-/l*
14×pow1 prod-exp
12×associate-*r/ swap-sqr
11×distribute-rgt-in distribute-lft-in
10×*-commutative
7×difference-of-squares
6×rem-sqrt-square flip3-- sqrt-div flip-- sqr-pow
5×pow-prod-down cbrt-unprod
4×expm1-log1p-u div-exp pow-exp frac-sub log1p-expm1-u add-log-exp
3×associate-/r* div-inv
2×cbrt-undiv pow-to-exp sub-neg sqrt-pow1
1×frac-2neg pow1/2 clear-num
Counts
4 → 282
Calls
4 calls:
22.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.0ms
(* n (pow (/ l Om) 2.0))
7.0ms
(/ (* l l) Om)
265.0ms
(sqrt (* (cbrt (* (cbrt (* 2.0 n)) U)) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series31.1s

Counts
4 → 12
Calls
4 calls:
331.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
133.0ms
(* n (pow (/ l Om) 2.0))
17.0ms
(/ (* l l) Om)
30.7s
(sqrt (* (cbrt (* (cbrt (* 2.0 n)) U)) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify57.0ms

Algorithm
egg-herbie
Counts
294 → 294
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
015633358
150023162

prune1.5s

Filtered
294 candidates to 202 candidates (68.7%)
Pruning

22 alts after pruning (22 fresh and 0 done)

PrunedKeptTotal
New2895294
Fresh41721
Picked101
Done000
Total29422316

Merged error: 12.7b

Counts
316 → 22

localize30.0ms

Local error

Found 4 expressions with local error:

3.7b
(cbrt (* (cbrt (* 2.0 n)) U))
6.0b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.0b
(* n (pow (/ l Om) 2.0))
11.4b
(sqrt (* (cbrt (* (cbrt (* 2.0 n)) U)) (- (- t (* 2.0 (/ (* (* (cbrt l) (cbrt l)) (* (cbrt l) (cbrt l))) (/ Om (* (cbrt l) (cbrt l)))))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite31.1s

Algorithm
rewrite-expression-head
Rules
151×add-sqr-sqrt
112×associate-*l*
92×cbrt-prod
77×*-un-lft-identity
69×associate-*r*
57×sqrt-prod
54×unswap-sqr
51×add-cube-cbrt
34×unpow-prod-down
26×add-exp-log
22×times-frac
18×prod-diff
16×distribute-lft-out--
14×pow1
13×prod-exp
12×associate-*r/
11×distribute-rgt-in distribute-lft-in add-cbrt-cube
8×*-commutative
7×difference-of-squares
6×rem-sqrt-square flip3-- sqrt-div flip-- sqr-pow
5×pow-prod-down
4×expm1-log1p-u pow-exp frac-sub cbrt-unprod log1p-expm1-u add-log-exp
2×pow-to-exp sub-neg sqrt-pow1 div-exp div-inv
1×pow1/2 pow1/3
Counts
4 → 239
Calls
4 calls:
7.0ms
(cbrt (* (cbrt (* 2.0 n)) U))
22.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.0ms
(* n (pow (/ l Om) 2.0))
31.1s
(sqrt (* (cbrt (* (cbrt (* 2.0 n)) U)) (- (- t (* 2.0 (/ (* (* (cbrt l) (cbrt l)) (* (cbrt l) (cbrt l))) (/ Om (* (cbrt l) (cbrt l)))))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series33.0s

Counts
4 → 12
Calls
4 calls:
185.0ms
(cbrt (* (cbrt (* 2.0 n)) U))
334.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
134.0ms
(* n (pow (/ l Om) 2.0))
32.3s
(sqrt (* (cbrt (* (cbrt (* 2.0 n)) U)) (- (- t (* 2.0 (/ (* (* (cbrt l) (cbrt l)) (* (cbrt l) (cbrt l))) (/ Om (* (cbrt l) (cbrt l)))))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify59.0ms

Algorithm
egg-herbie
Counts
251 → 251
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
014024401
150014204

prune1.5s

Filtered
251 candidates to 184 candidates (73.3%)
Pruning

22 alts after pruning (22 fresh and 0 done)

PrunedKeptTotal
New2465251
Fresh41721
Picked101
Done000
Total25122273

Merged error: 12.5b

Counts
273 → 22

regimes881.0ms

Accuracy

4.5% (6.1b remaining)

Error of 19.8b against oracle of 13.8b and baseline of 20.1b

bsearch5.0ms

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
093120
1102120
2102120

end0.0ms

sample2.4s

Algorithm
intervals
Results
989.0ms15061×body80nan
620.0ms9208×body80valid