Details

Time bar (total: 35.5s)

sample357.0ms

Algorithm
intervals
Results
38.0ms544×body80nan
19.0ms292×body80valid

simplify127.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
04914
115314
265214
3362414
4500214

prune6.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize22.0ms

Local error

Found 4 expressions with local error:

7.1b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.0b
(/ (* l l) Om)
10.6b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.3b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
25×pow1
23×add-cbrt-cube
22×associate-*r/
16×prod-exp
13×pow-prod-down
11×flip3-- flip--
10×add-sqr-sqrt *-un-lft-identity cbrt-unprod
8×add-cube-cbrt associate-*r* frac-sub
6×distribute-rgt-in sub-neg distribute-lft-in sqrt-div
4×sqrt-pow1 associate--l+ 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 → 103
Calls
4 calls:
24.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
4.0ms
(/ (* l l) Om)
56.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
34.0ms
(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:
364.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
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*))))
4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify133.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
09371548
147521385
250021385

prune489.0ms

Filtered
115 candidates to 75 candidates (65.2%)
Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 22.6b

localize19.0ms

Local error

Found 4 expressions with local error:

5.8b
(* n (pow (/ l Om) 2.0))
7.1b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.6b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.3b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
35×add-exp-log
25×pow1 add-sqr-sqrt associate-*r*
22×associate-*r/
20×add-cbrt-cube
19×prod-exp
17×*-un-lft-identity
15×add-cube-cbrt unpow-prod-down
13×pow-prod-down
11×flip3-- flip--
10×times-frac cbrt-unprod
8×frac-sub
6×distribute-rgt-in sub-neg distribute-lft-in sqrt-div
5×associate-*l*
4×sqrt-pow1 pow-exp associate--l+ 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 → 119
Calls
4 calls:
16.0ms
(* n (pow (/ l Om) 2.0))
24.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
53.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
32.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.7s

Counts
4 → 12
Calls
4 calls:
148.0ms
(* n (pow (/ l Om) 2.0))
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*)))))

simplify40.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09871668
150011508

prune520.0ms

Filtered
131 candidates to 86 candidates (65.6%)
Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 20.8b

localize25.0ms

Local error

Found 4 expressions with local error:

5.9b
(* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
6.2b
(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
7.1b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
18.3b
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
44×associate-*r/
33×pow1
32×add-exp-log
23×add-cbrt-cube
22×distribute-rgt-in distribute-lft-in
18×pow-prod-down prod-exp
16×flip3-- flip--
14×sub-neg
12×associate--l+ frac-sub cbrt-unprod
11×add-sqr-sqrt
9×*-un-lft-identity associate-*r*
7×add-cube-cbrt
6×sqrt-div
5×sqrt-pow1 associate-*l*
4×add-log-exp
3×*-commutative
2×pow-exp
1×pow-to-exp pow1/2 div-exp sqrt-prod distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 124
Calls
4 calls:
34.0ms
(* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
54.0ms
(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
24.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
38.0ms
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

series7.7s

Counts
4 → 12
Calls
4 calls:
899.0ms
(* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* 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*)))))
384.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
5.1s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify132.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
09722173
148911949
250021949

prune516.0ms

Filtered
136 candidates to 79 candidates (58.1%)
Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 17.5b

localize19.0ms

Local error

Found 4 expressions with local error:

5.9b
(* U (- (- t (* 2.0 (* l (/ l Om)))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))
6.2b
(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))
6.4b
(* (pow (/ l Om) 2.0) (- U U*))
18.3b
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))))

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
56×associate-*r/
31×pow1
27×add-sqr-sqrt
26×add-exp-log
22×distribute-rgt-in distribute-lft-in
21×associate-*l*
20×add-cbrt-cube
17×*-un-lft-identity pow-prod-down
16×flip3-- flip--
15×add-cube-cbrt unpow-prod-down
14×sub-neg
13×prod-exp
12×associate--l+ frac-sub
10×times-frac cbrt-unprod
9×associate-*r*
6×sqrt-div
5×sqrt-pow1 unswap-sqr
4×add-log-exp
3×*-commutative
2×pow-exp sqr-pow
1×pow-to-exp pow1/2 div-exp sqrt-prod div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 141
Calls
4 calls:
38.0ms
(* U (- (- t (* 2.0 (* l (/ l Om)))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))
60.0ms
(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))
24.0ms
(* (pow (/ l Om) 2.0) (- U U*))
48.0ms
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))))

series7.5s

Counts
4 → 12
Calls
4 calls:
883.0ms
(* U (- (- t (* 2.0 (* l (/ l Om)))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))
1.4s
(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* n (* (pow (/ l Om) 2.0) (- U U*))))))
348.0ms
(* (pow (/ l Om) 2.0) (- U U*))
4.9s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* n (* (pow (/ l Om) 2.0) (- U U*)))))))

simplify129.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
010252269
148642040
250012040

prune595.0ms

Filtered
153 candidates to 98 candidates (64.1%)
Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 17.5b

regimes710.0ms

Accuracy

27.1% (10.0b remaining)

Error of 29.3b against oracle of 19.3b and baseline of 33.1b

bsearch114.0ms

Steps
ItersRangePoint
9
-7.610013761419582e-308
1.0598526293452503e-300
1.096720098972556e-309

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04129
14129

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.1s15208×body80nan
632.0ms9258×body80valid