Details

Time bar (total: 1.5m)

sample349.0ms

Algorithm
intervals
Results
35.0ms467×body80nan
21.0ms298×body80valid

simplify142.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (13.0ms)

IterNodesCost
04914
115514
268414
3389814
4500114

prune6.0ms

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: 33.0b

Counts
2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

7.3b
(/ (* l l) Om)
7.6b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
11.6b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
16.1b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite789.0ms

Algorithm
rewrite-expression-head
Rules
3806×add-sqr-sqrt
1452×prod-diff
1226×*-un-lft-identity
1070×associate-*l*
1062×times-frac
1049×unswap-sqr
958×associate-*r*
776×add-cube-cbrt
732×distribute-rgt-in distribute-lft-in
653×difference-of-squares
429×unpow-prod-down
382×associate--l+
231×distribute-lft-out--
178×*-commutative
160×swap-sqr
77×sqr-pow
48×sqrt-prod
32×add-exp-log div-inv
28×pow1
23×add-cbrt-cube
22×associate-*r/
16×prod-exp
15×pow-prod-down associate-/l*
11×flip3-- flip--
10×cbrt-unprod
8×frac-sub
6×sub-neg sqrt-div
4×expm1-log1p-u 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 → 1743
Calls
4 calls:
8.0ms
(/ (* l l) Om)
21.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
164.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
315.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.5s

Counts
4 → 12
Calls
4 calls:
19.0ms
(/ (* l l) Om)
371.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify648.0ms

Algorithm
egg-herbie
Counts
1755 → 1755
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
0500173925

prune5.5s

Filtered
1755 candidates to 944 candidates (53.8%)
Pruning

21 alts after pruning (21 fresh and 0 done)

PrunedKeptTotal
New1734211755
Fresh000
Picked101
Done000
Total1735211756

Merged error: 16.1b

Counts
1756 → 21

localize24.0ms

Local error

Found 4 expressions with local error:

7.3b
(/ (* l l) Om)
7.6b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.6b
(* (* (cbrt n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
14.5b
(sqrt (* (* (cbrt n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite751.0ms

Algorithm
rewrite-expression-head
Rules
3795×add-sqr-sqrt
1452×prod-diff
1224×*-un-lft-identity
1062×times-frac
1042×unswap-sqr
1040×associate-*l*
952×associate-*r*
774×add-cube-cbrt
732×distribute-rgt-in distribute-lft-in
653×difference-of-squares
429×unpow-prod-down
382×associate--l+
231×distribute-lft-out--
176×*-commutative
160×swap-sqr
77×sqr-pow
42×sqrt-prod
32×div-inv
28×add-exp-log
22×associate-*r/
21×add-cbrt-cube
20×pow1
15×associate-/l*
13×prod-exp
11×cbrt-prod flip3-- flip--
9×pow-prod-down cbrt-unprod
8×frac-sub
6×sub-neg sqrt-div
4×expm1-log1p-u rem-sqrt-square 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 → 1728
Calls
4 calls:
8.0ms
(/ (* l l) Om)
21.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
153.0ms
(* (* (cbrt n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
297.0ms
(sqrt (* (* (cbrt n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series23.7s

Counts
4 → 12
Calls
4 calls:
19.0ms
(/ (* l l) Om)
367.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
2.0s
(* (* (cbrt n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
21.2s
(sqrt (* (* (cbrt n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify620.0ms

Algorithm
egg-herbie
Counts
1740 → 1740
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
0500173696

prune6.5s

Filtered
1740 candidates to 936 candidates (53.8%)
Pruning

24 alts after pruning (24 fresh and 0 done)

PrunedKeptTotal
New173191740
Fresh51520
Picked101
Done000
Total1737241761

Merged error: 14.2b

Counts
1761 → 24

localize28.0ms

Local error

Found 4 expressions with local error:

5.3b
(* n (pow (/ l Om) 2.0))
7.3b
(/ (* l l) Om)
7.6b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
12.7b
(sqrt (* (cbrt (* (cbrt n) U)) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite354.0ms

Algorithm
rewrite-expression-head
Rules
165×add-sqr-sqrt
105×*-un-lft-identity
84×associate-*l*
79×add-cube-cbrt
72×associate-*r*
67×times-frac
46×sqrt-prod
44×unswap-sqr
34×unpow-prod-down
31×add-exp-log
28×cbrt-prod
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
9×*-commutative
7×difference-of-squares
6×flip3-- sqrt-div flip-- sqr-pow
5×rem-sqrt-square 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 → 270
Calls
4 calls:
10.0ms
(* n (pow (/ l Om) 2.0))
8.0ms
(/ (* l l) Om)
20.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
300.0ms
(sqrt (* (cbrt (* (cbrt n) U)) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series18.2s

Counts
4 → 12
Calls
4 calls:
145.0ms
(* n (pow (/ l Om) 2.0))
19.0ms
(/ (* l l) Om)
365.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
17.7s
(sqrt (* (cbrt (* (cbrt n) U)) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify61.0ms

Algorithm
egg-herbie
Counts
282 → 282
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
014102999
150012812

prune1.2s

Filtered
282 candidates to 195 candidates (69.1%)
Pruning

24 alts after pruning (24 fresh and 0 done)

PrunedKeptTotal
New2802282
Fresh12223
Picked101
Done000
Total28224306

Merged error: 14.2b

Counts
306 → 24

localize42.0ms

Local error

Found 4 expressions with local error:

5.3b
(* n (pow (/ l Om) 2.0))
7.3b
(/ (* l l) Om)
7.6b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
14.2b
(sqrt (* (cbrt (* (cbrt (cbrt n)) U)) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite355.0ms

Algorithm
rewrite-expression-head
Rules
174×add-sqr-sqrt
106×*-un-lft-identity
91×associate-*l*
80×add-cube-cbrt
72×associate-*r*
67×times-frac
51×sqrt-prod
49×unswap-sqr
46×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
9×*-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 → 276
Calls
4 calls:
10.0ms
(* n (pow (/ l Om) 2.0))
8.0ms
(/ (* l l) Om)
24.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
297.0ms
(sqrt (* (cbrt (* (cbrt (cbrt n)) U)) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series18.9s

Counts
4 → 12
Calls
4 calls:
145.0ms
(* n (pow (/ l Om) 2.0))
19.0ms
(/ (* l l) Om)
357.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
18.4s
(sqrt (* (cbrt (* (cbrt (cbrt n)) U)) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify61.0ms

Algorithm
egg-herbie
Counts
288 → 288
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
014483212
150013024

prune1.5s

Filtered
288 candidates to 201 candidates (69.8%)
Pruning

25 alts after pruning (25 fresh and 0 done)

PrunedKeptTotal
New2844288
Fresh22123
Picked101
Done000
Total28725312

Merged error: 14.2b

Counts
312 → 25

regimes1.0s

Accuracy

29.3% (6.4b remaining)

Error of 20.0b against oracle of 13.7b and baseline of 22.7b

bsearch301.0ms

Steps
ItersRangePoint
8
6.770499772705243e+94
2.9661045111837723e+99
2.90056484708727e+99
8
-1.40869048741384e+138
-1.8778933842328292e+135
-9.180640496957073e+136

simplify4.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
010289
112489
213789
313789

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.0s14706×body80nan
660.0ms9206×body80valid