Details

Time bar (total: 33.4s)

sample352.0ms

Algorithm
intervals
Results
33.0ms487×body80nan
22.0ms300×body80valid

simplify139.0ms

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: 37.4b

localize21.0ms

Local error

Found 4 expressions with local error:

7.4b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.2b
(/ (* l l) Om)
10.4b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
21.7b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
30×prod-diff
26×add-sqr-sqrt *-un-lft-identity
25×pow1
24×add-cube-cbrt
23×add-cbrt-cube
22×associate-*r/
21×distribute-rgt-in distribute-lft-in
16×prod-exp
13×pow-prod-down
11×flip3-- flip--
10×associate--l+ cbrt-unprod
8×associate-*r* frac-sub
6×sub-neg sqrt-div
4×expm1-log1p-u sqrt-pow1 log1p-expm1-u add-log-exp
3×times-frac div-exp associate-/r*
2×cbrt-undiv associate-*l* pow-exp *-commutative
1×pow-to-exp frac-2neg pow1/2 clear-num sqrt-prod div-inv associate-/l* distribute-lft-out-- difference-of-squares
Counts
4 → 141
Calls
4 calls:
24.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
3.0ms
(/ (* l l) Om)
55.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
42.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.3s

Counts
4 → 12
Calls
4 calls:
353.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
25.0ms
(/ (* 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*)))))

simplify54.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
011762335
150012011

prune577.0ms

Filtered
153 candidates to 92 candidates (60.1%)
Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 25.5b

localize18.0ms

Local error

Found 4 expressions with local error:

5.4b
(* n (pow (/ l Om) 2.0))
7.4b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.4b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
21.7b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite136.0ms

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:
14.0ms
(* n (pow (/ l Om) 2.0))
24.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
51.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
40.0ms
(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:
143.0ms
(* n (pow (/ l Om) 2.0))
349.0ms
(* (* 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*))))
4.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify48.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012292461
150012136

prune589.0ms

Filtered
169 candidates to 103 candidates (60.9%)
Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 24.3b

localize19.0ms

Local error

Found 4 expressions with local error:

5.6b
(* n (pow (/ l Om) (/ 2.0 2)))
7.4b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
10.4b
(* (* (* 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*))))
21.7b
(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*)))))

rewrite220.0ms

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:
14.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
80.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
64.0ms
(* (* (* 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*))))
53.0ms
(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*)))))

series6.5s

Counts
4 → 12
Calls
4 calls:
160.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
356.0ms
(* (* (* 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 (/ 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*)))))

simplify58.0ms

Algorithm
egg-herbie
Counts
186 → 186
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013553511
150022841

prune658.0ms

Filtered
186 candidates to 107 candidates (57.5%)
Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 24.3b

localize26.0ms

Local error

Found 4 expressions with local error:

5.6b
(* n (pow (/ l Om) (/ 2.0 2)))
7.4b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
10.4b
(* (* (* 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*))))
21.7b
(sqrt (pow (* (* (* 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*)))) 1))

rewrite186.0ms

Algorithm
rewrite-expression-head
Rules
99×add-exp-log
67×prod-exp
43×add-sqr-sqrt
34×*-un-lft-identity
32×add-cube-cbrt
30×prod-diff
25×associate-*r*
24×add-cbrt-cube
21×distribute-rgt-in distribute-lft-in
20×pow-exp
16×unpow-prod-down
15×pow1
13×cbrt-unprod
12×associate-*r/
10×pow-to-exp times-frac div-exp associate--l+
7×pow-prod-down
6×sub-neg flip3-- flip--
5×associate-*l* sqrt-prod
4×expm1-log1p-u frac-sub log1p-expm1-u add-log-exp unswap-sqr sqr-pow
3×*-commutative
2×rem-sqrt-square
1×sqrt-pow1 pow1/2 div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 171
Calls
4 calls:
14.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
81.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
64.0ms
(* (* (* 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*))))
19.0ms
(sqrt (pow (* (* (* 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*)))) 1))

series6.5s

Counts
4 → 12
Calls
4 calls:
161.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
366.0ms
(* (* (* 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 (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
4.7s
(sqrt (pow (* (* (* 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*)))) 1))

simplify57.0ms

Algorithm
egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013173339
150022671

prune653.0ms

Filtered
183 candidates to 109 candidates (59.6%)
Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 24.1b

regimes758.0ms

Accuracy

3.1% (8.9b remaining)

Error of 30.7b against oracle of 21.8b and baseline of 31.0b

bsearch419.0ms

Steps
ItersRangePoint
7
9.314757112647596e-152
2.0864846078020846e-150
1.8079991333180533e-150
9
-1.604610306938246e-158
-8.879020602459359e-164
-3.378837726859911e-162
8
-2.496332758032299e-132
-6.083988141069605e-137
-9.173018010933093e-133
4
-4.6506962397476484e+170
-2.3994214419064102e+170
-4.5798465738782547e+170

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
088102
194102
2101102
3101102

end0.0ms

sample2.5s

Algorithm
intervals
Results
985.0ms14633×body80nan
632.0ms9236×body80valid