Details

Time bar (total: 37.1s)

sample85.0ms

Algorithm
intervals
Results
29.0ms434×body80nan
22.0ms291×body80valid

simplify122.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04914
115514
268414
3389814
4500114

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.8b

localize19.0ms

Local error

Found 4 expressions with local error:

7.8b
(* n (pow (/ l Om) 2.0))
10.3b
(/ (* l l) Om)
13.1b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.7b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite120.0ms

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:
17.0ms
(* n (pow (/ l Om) 2.0))
3.0ms
(/ (* l l) Om)
51.0ms
(* (* (* 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:
135.0ms
(* n (pow (/ l Om) 2.0))
23.0ms
(/ (* l l) Om)
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify45.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
010791952
150011746

prune594.0ms

Filtered
144 candidates to 99 candidates (68.8%)
Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 26.3b

localize18.0ms

Local error

Found 4 expressions with local error:

5.5b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.8b
(* n (pow (/ l Om) 2.0))
13.1b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.7b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite144.0ms

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:
27.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
15.0ms
(* n (pow (/ l Om) 2.0))
51.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
45.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.4s

Counts
4 → 12
Calls
4 calls:
354.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
138.0ms
(* 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*)))))

simplify49.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012292457
150012136

prune597.0ms

Filtered
169 candidates to 103 candidates (60.9%)
Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 24.8b

localize21.0ms

Local error

Found 4 expressions with local error:

5.5b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
6.0b
(* n (pow (/ l Om) (/ 2.0 2)))
13.1b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
20.7b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite232.0ms

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:
87.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
15.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
66.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
55.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series6.7s

Counts
4 → 12
Calls
4 calls:
548.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
169.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
4.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* 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 (29.0ms)

IterNodesCost
013553511
150022841

prune627.0ms

Filtered
186 candidates to 108 candidates (58.1%)
Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 24.3b

localize28.0ms

Local error

Found 4 expressions with local error:

5.5b
(* (- (- U U*)) (* n (pow (/ l Om) (* 2 (/ 2.0 2)))))
6.3b
(* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (- (- U U*)) (* n (pow (/ l Om) (* 2 (/ 2.0 2)))))))) U)
7.8b
(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
20.7b
(sqrt (pow (* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (- (- U U*)) (* n (pow (/ l Om) (* 2 (/ 2.0 2)))))))) U) 1))

rewrite177.0ms

Algorithm
rewrite-expression-head
Rules
35×add-exp-log
31×add-sqr-sqrt
22×*-un-lft-identity
21×associate-*r*
20×add-cbrt-cube
19×prod-exp
18×add-cube-cbrt associate-*l*
16×unpow-prod-down
15×pow1
10×times-frac cbrt-unprod
7×pow-prod-down
5×distribute-lft-neg-in distribute-rgt-neg-in sqrt-prod
4×expm1-log1p-u associate-*l/ pow-exp log1p-expm1-u add-log-exp unswap-sqr sqr-pow
3×*-commutative
2×pow-to-exp rem-sqrt-square flip3-- associate-*r/ div-exp flip-- distribute-neg-frac distribute-lft-out-- difference-of-squares
1×distribute-lft-neg-out neg-mul-1 sqrt-pow1 pow1/2 div-inv
Counts
4 → 118
Calls
4 calls:
33.0ms
(* (- (- U U*)) (* n (pow (/ l Om) (* 2 (/ 2.0 2)))))
120.0ms
(* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (- (- U U*)) (* n (pow (/ l Om) (* 2 (/ 2.0 2)))))))) U)
16.0ms
(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
4.0ms
(sqrt (pow (* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (- (- U U*)) (* n (pow (/ l Om) (* 2 (/ 2.0 2)))))))) U) 1))

series11.0s

Counts
4 → 12
Calls
4 calls:
244.0ms
(* (- (- U U*)) (* n (pow (/ l Om) (* 2 (/ 2.0 2)))))
1.1s
(* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (- (- U U*)) (* n (pow (/ l Om) (* 2 (/ 2.0 2)))))))) U)
147.0ms
(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
9.5s
(sqrt (pow (* (* (* 2.0 n) (- t (- (* 2.0 (* l (/ l Om))) (* (- (- U U*)) (* n (pow (/ l Om) (* 2 (/ 2.0 2)))))))) U) 1))

simplify116.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (95.0ms)

IterNodesCost
07781671
138621446
250031440

prune540.0ms

Filtered
130 candidates to 96 candidates (73.8%)
Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 20.6b

regimes575.0ms

Accuracy

17.3% (10.2b remaining)

Error of 28.8b against oracle of 18.6b and baseline of 30.9b

bsearch109.0ms

Steps
ItersRangePoint
8
9.170912651718186e-258
9.631104734655604e-255
9.333968041762941e-258

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06043
16843
28243
38643
48643

end0.0ms

sample2.5s

Algorithm
intervals
Results
987.0ms14599×body80nan
628.0ms9217×body80valid