Details

Time bar (total: 31.4s)

sample112.0ms

Algorithm
intervals
Results
44.0ms473×body80nan
32.0ms294×body80valid

simplify118.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04914
115314
265214
3362414
4500214

prune4.0ms

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: 36.0b

Counts
2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

5.7b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.2b
(/ (* l l) Om)
9.6b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.8b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite43.0ms

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:
11.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
5.0ms
(/ (* l l) Om)
13.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
11.0ms
(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:
366.0ms
(* (* 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*)))))

simplify120.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
09371544
147641385
250011385

prune410.0ms

Filtered
115 candidates to 75 candidates (65.2%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New10411115
Fresh000
Picked101
Done000
Total10511116

Merged error: 21.8b

Counts
116 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

4.8b
(* n (pow (/ l Om) 2.0))
5.7b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
9.6b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.8b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite46.0ms

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:
9.0ms
(* n (pow (/ l Om) 2.0))
11.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
12.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
10.0ms
(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:
142.0ms
(* 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*))))
4.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify50.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
09871664
150011508

prune455.0ms

Filtered
131 candidates to 86 candidates (65.6%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1274131
Fresh1910
Picked101
Done000
Total12913142

Merged error: 20.1b

Counts
142 → 13

localize25.0ms

Local error

Found 4 expressions with local error:

13.5b
(cbrt (/ l Om))
13.5b
(cbrt (/ l Om))
13.5b
(cbrt (/ l Om))
20.8b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U*)))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
39×cbrt-prod
27×times-frac
25×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
14×pow1
10×associate-*r/
6×sqrt-div pow-prod-down
5×flip3-- flip--
4×add-exp-log sqrt-pow1 frac-sub add-cbrt-cube add-log-exp
3×cbrt-div pow1/3 div-inv
1×pow1/2 sqrt-prod
Counts
4 → 85
Calls
4 calls:
3.0ms
(cbrt (/ l Om))
3.0ms
(cbrt (/ l Om))
2.0ms
(cbrt (/ l Om))
12.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U*)))))

series5.2s

Counts
4 → 12
Calls
4 calls:
63.0ms
(cbrt (/ l Om))
63.0ms
(cbrt (/ l Om))
60.0ms
(cbrt (/ l Om))
5.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U*)))))

simplify74.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
05891096
124731054
250021048

prune517.0ms

Filtered
97 candidates to 83 candidates (85.6%)
Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New96197
Fresh01212
Picked011
Done000
Total9614110

Merged error: 20.1b

Counts
110 → 14

localize19.0ms

Local error

Found 4 expressions with local error:

4.8b
(* n (pow (/ l Om) 2.0))
5.7b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.7b
(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
20.8b
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
38×add-exp-log
34×associate-*r/
31×pow1
24×add-sqr-sqrt
23×associate-*r* add-cbrt-cube
21×prod-exp
18×distribute-rgt-in distribute-lft-in
17×pow-prod-down
16×*-un-lft-identity
15×unpow-prod-down
14×add-cube-cbrt
12×cbrt-unprod
11×flip3-- flip--
10×sub-neg times-frac
8×associate--l+ frac-sub
6×sqrt-div
5×sqrt-pow1 associate-*l*
4×pow-exp 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 → 129
Calls
4 calls:
9.0ms
(* n (pow (/ l Om) 2.0))
11.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
15.0ms
(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
11.0ms
(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:
139.0ms
(* n (pow (/ l Om) 2.0))
362.0ms
(* (* 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*))))))

simplify44.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010521826
150011638

prune397.0ms

Filtered
141 candidates to 85 candidates (60.3%)
Pruning

18 alts after pruning (16 fresh and 2 done)

PrunedKeptTotal
New1356141
Fresh21012
Picked011
Done011
Total13718155

Merged error: 15.4b

Counts
155 → 18

regimes971.0ms

Accuracy

27.5% (9.4b remaining)

Error of 27.6b against oracle of 18.2b and baseline of 31.1b

bsearch117.0ms

Steps
ItersRangePoint
8
-1.86472712042006e-306
2.3570956754570394e-308
-6.920675890966e-311

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04737
14737

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.4s14901×body80nan
885.0ms9198×body80valid