Details

Time bar (total: 32.2s)

sample94.0ms

Algorithm
intervals
Results
33.0ms472×body80nan
26.0ms293×body80valid

simplify116.0ms

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: 33.2b

Counts
2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

7.6b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.9b
(/ (* l l) Om)
10.3b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.0b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite44.0ms

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)
12.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
13.0ms
(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:
388.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
21.0ms
(/ (* l l) Om)
1.4s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (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*)))))

simplify123.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
09371544
147641385
250011385

prune478.0ms

Filtered
115 candidates to 75 candidates (65.2%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New10015115
Fresh000
Picked101
Done000
Total10115116

Merged error: 24.7b

Counts
116 → 15

localize18.0ms

Local error

Found 4 expressions with local error:

7.2b
(* n (pow (/ l Om) 2.0))
7.6b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.3b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.0b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite51.0ms

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*))
16.0ms
(* (* (* 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*)))))

series6.9s

Counts
4 → 12
Calls
4 calls:
155.0ms
(* n (pow (/ l Om) 2.0))
390.0ms
(* (* 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*))))
4.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify43.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
09871664
150011508

prune513.0ms

Filtered
131 candidates to 86 candidates (65.6%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New1265131
Fresh41014
Picked101
Done000
Total13115146

Merged error: 23.3b

Counts
146 → 15

localize31.0ms

Local error

Found 4 expressions with local error:

13.7b
(cbrt (/ l Om))
13.7b
(cbrt (/ l Om))
13.7b
(cbrt (/ l Om))
18.0b
(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*)))))

rewrite22.0ms

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:
2.0ms
(cbrt (/ l Om))
2.0ms
(cbrt (/ l Om))
2.0ms
(cbrt (/ l Om))
11.0ms
(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*)))))

series5.1s

Counts
4 → 12
Calls
4 calls:
71.0ms
(cbrt (/ l Om))
70.0ms
(cbrt (/ l Om))
64.0ms
(cbrt (/ l Om))
4.9s
(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*)))))

simplify69.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
05891100
124611054
250031048

prune781.0ms

Filtered
97 candidates to 83 candidates (85.6%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New97097
Fresh01414
Picked011
Done000
Total9715112

Merged error: 23.3b

Counts
112 → 15

localize27.0ms

Local error

Found 4 expressions with local error:

7.2b
(* n (pow (/ l Om) 2.0))
7.6b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.3b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.0b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt 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:
8.0ms
(* 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 (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
10.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.8s

Counts
4 → 12
Calls
4 calls:
146.0ms
(* n (pow (/ l Om) 2.0))
383.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.4s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify52.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
09932129
150021918

prune498.0ms

Filtered
131 candidates to 86 candidates (65.6%)
Pruning

16 alts after pruning (14 fresh and 2 done)

PrunedKeptTotal
New1292131
Fresh11213
Picked011
Done011
Total13016146

Merged error: 23.3b

Counts
146 → 16

regimes834.0ms

Accuracy

16.5% (7.4b remaining)

Error of 29.0b against oracle of 21.6b and baseline of 30.5b

bsearch210.0ms

Steps
ItersRangePoint
6
9.218970226967994e+67
7.2484695024147705e+68
9.844657127410996e+67
8
-4.808974466695775e-09
-7.983923007473122e-12
-1.2817931366245364e-11

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05236
15236

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.1s15071×body80nan
675.0ms9201×body80valid