Details

Time bar (total: 33.5s)

sample331.0ms

Algorithm
intervals
Results
31.0ms456×body80nan
19.0ms292×body80valid

simplify137.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (12.0ms)

IterNodesCost
04914
115514
268414
3389814
4500114

prune5.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize21.0ms

Local error

Found 4 expressions with local error:

6.0b
(* n (pow (/ l Om) 2.0))
8.2b
(/ (* l l) Om)
10.2b
(* (* (* 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*)))))

rewrite125.0ms

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:
15.0ms
(* n (pow (/ l Om) 2.0))
3.0ms
(/ (* l l) Om)
56.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
44.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.2s

Counts
4 → 12
Calls
4 calls:
145.0ms
(* n (pow (/ l Om) 2.0))
19.0ms
(/ (* 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*)))))

simplify46.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
010791948
150011746

prune615.0ms

Filtered
144 candidates to 99 candidates (68.8%)
Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 22.1b

localize23.0ms

Local error

Found 4 expressions with local error:

5.9b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.0b
(* n (pow (/ l Om) 2.0))
10.2b
(* (* (* 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*)))))

rewrite142.0ms

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:
25.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
15.0ms
(* n (pow (/ l Om) 2.0))
54.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
42.0ms
(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:
366.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
140.0ms
(* n (pow (/ l Om) 2.0))
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*)))))

simplify48.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012272461
150022136

prune625.0ms

Filtered
169 candidates to 103 candidates (60.9%)
Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 20.2b

localize26.0ms

Local error

Found 4 expressions with local error:

4.6b
(* n (pow (/ l Om) (/ 2.0 2)))
5.9b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
10.2b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
17.4b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite228.0ms

Algorithm
rewrite-expression-head
Rules
99×add-exp-log
67×prod-exp
41×add-sqr-sqrt
33×*-un-lft-identity
31×add-cube-cbrt
30×prod-diff
25×pow1 associate-*r*
24×add-cbrt-cube
22×associate-*r/
21×distribute-rgt-in distribute-lft-in
20×pow-exp
15×unpow-prod-down
13×pow-prod-down cbrt-unprod
11×flip3-- flip--
10×pow-to-exp times-frac div-exp associate--l+
8×frac-sub
6×sub-neg sqrt-div
5×associate-*l*
4×expm1-log1p-u sqrt-pow1 log1p-expm1-u add-log-exp unswap-sqr
3×*-commutative
2×sqr-pow
1×pow1/2 sqrt-prod div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 174
Calls
4 calls:
15.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
85.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
66.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
51.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series6.7s

Counts
4 → 12
Calls
4 calls:
157.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
363.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
4.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify62.0ms

Algorithm
egg-herbie
Counts
186 → 186
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
013533511
150012841

prune693.0ms

Filtered
186 candidates to 108 candidates (58.1%)
Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 19.7b

localize21.0ms

Local error

Found 4 expressions with local error:

4.6b
(* n (pow (/ l Om) (/ 2.0 2)))
7.3b
(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
10.2b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))
17.4b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
57×add-sqr-sqrt
41×*-un-lft-identity
39×add-cube-cbrt
30×unpow-prod-down associate-*r/ prod-diff
29×add-exp-log
25×associate-*r*
23×pow1
21×distribute-rgt-in distribute-lft-in associate-*l*
20×times-frac
17×add-cbrt-cube
14×prod-exp
12×pow-prod-down
11×flip3-- flip--
10×associate--l+
8×frac-sub cbrt-unprod unswap-sqr
6×sub-neg sqrt-div
4×expm1-log1p-u sqrt-pow1 pow-exp log1p-expm1-u add-log-exp sqr-pow
3×*-commutative
2×pow-to-exp div-exp div-inv
1×pow1/2 sqrt-prod distribute-lft-out-- difference-of-squares
Counts
4 → 174
Calls
4 calls:
15.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
24.0ms
(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
63.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))
51.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))

series6.6s

Counts
4 → 12
Calls
4 calls:
168.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
349.0ms
(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))
4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))

simplify57.0ms

Algorithm
egg-herbie
Counts
186 → 186
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012793113
150012722

prune747.0ms

Filtered
186 candidates to 122 candidates (65.6%)
Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 19.1b

regimes594.0ms

Accuracy

25.5% (6.8b remaining)

Error of 28.3b against oracle of 21.5b and baseline of 30.6b

bsearch236.0ms

Steps
ItersRangePoint
8
2.191288679581832e+102
5.76647855236344e+105
2.216005498822668e+102
7
-4.0312812855289493e-51
-3.7503760186388468e-53
-3.8210451181189894e-51

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05643
15643

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.0s15165×body80nan
607.0ms9237×body80valid