Details

Time bar (total: 1.8m)

sample345.0ms

Algorithm
intervals
Results
34.0ms455×body80nan
22.0ms305×body80valid

simplify123.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04914
115314
265214
3362414
4500214

prune6.0ms

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: 30.8b

Counts
2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

6.0b
(* n (pow (/ l Om) 2.0))
7.7b
(/ (* l l) Om)
10.6b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
14.3b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite215.0ms

Algorithm
rewrite-expression-head
Rules
162×add-sqr-sqrt
113×associate-*l*
110×*-un-lft-identity
77×associate-*r*
62×add-cube-cbrt
57×times-frac
52×unswap-sqr
48×sqrt-prod
30×distribute-lft-out--
26×add-exp-log
25×pow1
20×associate-*r/ add-cbrt-cube
19×unpow-prod-down
15×associate-/l*
13×pow-prod-down
12×swap-sqr difference-of-squares
11×prod-exp *-commutative
10×flip3-- flip--
8×frac-sub cbrt-unprod
6×sqrt-div
4×distribute-rgt-in sub-neg rem-sqrt-square distribute-lft-in sqrt-pow1 associate--l+ add-log-exp sqr-pow
3×div-exp associate-/r*
2×cbrt-undiv pow-exp div-inv
1×pow-to-exp frac-2neg pow1/2 clear-num
Counts
4 → 259
Calls
4 calls:
11.0ms
(* n (pow (/ l Om) 2.0))
12.0ms
(/ (* l l) Om)
85.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
94.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.0s

Counts
4 → 12
Calls
4 calls:
143.0ms
(* n (pow (/ l Om) 2.0))
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*))))
4.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify60.0ms

Algorithm
egg-herbie
Counts
271 → 271
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013813287
150013136

prune1.0s

Filtered
271 candidates to 184 candidates (67.9%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New25417271
Fresh000
Picked101
Done000
Total25517272

Merged error: 14.8b

Counts
272 → 17

localize28.0ms

Local error

Found 4 expressions with local error:

6.0b
(* n (pow (/ l Om) 2.0))
7.7b
(/ (* l l) Om)
8.0b
(* (* (cbrt (* 2.0 n)) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
12.7b
(sqrt (* (* (cbrt (* 2.0 n)) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite212.0ms

Algorithm
rewrite-expression-head
Rules
177×add-sqr-sqrt
127×associate-*l*
112×*-un-lft-identity
77×associate-*r*
64×add-cube-cbrt
60×unswap-sqr
57×times-frac
53×sqrt-prod
34×cbrt-prod
30×distribute-lft-out--
22×add-exp-log
20×associate-*r/
19×unpow-prod-down
18×add-cbrt-cube
17×pow1
15×associate-/l*
12×swap-sqr difference-of-squares
11×*-commutative
10×flip3-- flip--
8×prod-exp frac-sub
7×pow-prod-down cbrt-unprod
6×sqrt-div
5×rem-sqrt-square
4×distribute-rgt-in sub-neg distribute-lft-in associate--l+ add-log-exp sqr-pow
3×sqrt-pow1 div-exp associate-/r*
2×cbrt-undiv pow-exp div-inv
1×pow-to-exp frac-2neg pow1/2 clear-num
Counts
4 → 267
Calls
4 calls:
14.0ms
(* n (pow (/ l Om) 2.0))
8.0ms
(/ (* l l) Om)
85.0ms
(* (* (cbrt (* 2.0 n)) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
91.0ms
(sqrt (* (* (cbrt (* 2.0 n)) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series31.1s

Counts
4 → 12
Calls
4 calls:
126.0ms
(* n (pow (/ l Om) 2.0))
22.0ms
(/ (* l l) Om)
2.0s
(* (* (cbrt (* 2.0 n)) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
29.0s
(sqrt (* (* (cbrt (* 2.0 n)) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify61.0ms

Algorithm
egg-herbie
Counts
279 → 279
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
013873623
150023468

prune1.1s

Filtered
279 candidates to 195 candidates (69.9%)
Pruning

22 alts after pruning (22 fresh and 0 done)

PrunedKeptTotal
New2709279
Fresh31316
Picked101
Done000
Total27422296

Merged error: 14.0b

Counts
296 → 22

localize30.0ms

Local error

Found 4 expressions with local error:

6.0b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.0b
(* n (pow (/ l Om) 2.0))
7.7b
(/ (* l l) Om)
11.4b
(sqrt (* (cbrt (* (cbrt (* 2.0 n)) U)) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
168×add-sqr-sqrt
106×associate-*l*
95×*-un-lft-identity
75×associate-*r*
69×add-cube-cbrt
67×times-frac
57×sqrt-prod
53×unswap-sqr
52×cbrt-prod
34×unpow-prod-down
31×add-exp-log
16×add-cbrt-cube distribute-lft-out--
15×associate-/l*
14×pow1 prod-exp
12×associate-*r/ swap-sqr
10×*-commutative
7×difference-of-squares
6×rem-sqrt-square flip3-- sqrt-div flip-- sqr-pow
5×pow-prod-down cbrt-unprod
4×div-exp pow-exp frac-sub add-log-exp
3×associate-/r* div-inv
2×cbrt-undiv distribute-rgt-in pow-to-exp sub-neg distribute-lft-in sqrt-pow1
1×frac-2neg pow1/2 clear-num
Counts
4 → 256
Calls
4 calls:
19.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
11.0ms
(* n (pow (/ l Om) 2.0))
8.0ms
(/ (* l l) Om)
85.0ms
(sqrt (* (cbrt (* (cbrt (* 2.0 n)) U)) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series30.6s

Counts
4 → 12
Calls
4 calls:
334.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
127.0ms
(* n (pow (/ l Om) 2.0))
17.0ms
(/ (* l l) Om)
30.2s
(sqrt (* (cbrt (* (cbrt (* 2.0 n)) U)) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify59.0ms

Algorithm
egg-herbie
Counts
268 → 268
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
014182938
150012868

prune1.3s

Filtered
268 candidates to 192 candidates (71.6%)
Pruning

24 alts after pruning (24 fresh and 0 done)

PrunedKeptTotal
New2617268
Fresh41721
Picked101
Done000
Total26624290

Merged error: 12.7b

Counts
290 → 24

localize26.0ms

Local error

Found 4 expressions with local error:

3.7b
(cbrt (* (cbrt (* 2.0 n)) U))
6.0b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.0b
(* n (pow (/ l Om) 2.0))
11.4b
(sqrt (* (cbrt (* (cbrt (* 2.0 n)) U)) (- (- t (* 2.0 (/ (* l 1) (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite187.0ms

Algorithm
rewrite-expression-head
Rules
139×add-sqr-sqrt
112×associate-*l*
92×cbrt-prod
69×associate-*r*
65×*-un-lft-identity
57×sqrt-prod
54×unswap-sqr
39×add-cube-cbrt
34×unpow-prod-down
26×add-exp-log
22×times-frac
16×distribute-lft-out--
14×pow1
13×prod-exp
12×associate-*r/
11×add-cbrt-cube
8×*-commutative
7×difference-of-squares
6×rem-sqrt-square flip3-- sqrt-div flip-- sqr-pow
5×pow-prod-down
4×pow-exp frac-sub cbrt-unprod add-log-exp
2×distribute-rgt-in pow-to-exp sub-neg distribute-lft-in sqrt-pow1 div-exp div-inv
1×pow1/2 pow1/3
Counts
4 → 213
Calls
4 calls:
8.0ms
(cbrt (* (cbrt (* 2.0 n)) U))
22.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
11.0ms
(* n (pow (/ l Om) 2.0))
136.0ms
(sqrt (* (cbrt (* (cbrt (* 2.0 n)) U)) (- (- t (* 2.0 (/ (* l 1) (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series30.8s

Counts
4 → 12
Calls
4 calls:
182.0ms
(cbrt (* (cbrt (* 2.0 n)) U))
330.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
127.0ms
(* n (pow (/ l Om) 2.0))
30.1s
(sqrt (* (cbrt (* (cbrt (* 2.0 n)) U)) (- (- t (* 2.0 (/ (* l 1) (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify56.0ms

Algorithm
egg-herbie
Counts
225 → 225
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
012512958
150022896

prune1.2s

Filtered
225 candidates to 174 candidates (77.3%)
Pruning

24 alts after pruning (24 fresh and 0 done)

PrunedKeptTotal
New2187225
Fresh61723
Picked101
Done000
Total22524249

Merged error: 12.5b

Counts
249 → 24

regimes1.1s

Accuracy

-3% (6.2b remaining)

Error of 19.5b against oracle of 13.3b and baseline of 19.3b

bsearch199.0ms

Steps
ItersRangePoint
8
7.944861243753147e-283
1.3297804240946638e-278
3.1279589487835526e-279
7
-1.2766748097608943e-302
-3.0056790197676315e-304
-3.0444517088294223e-304

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07454
17754
27754

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.0s15061×body80nan
623.0ms9208×body80valid