Details

Time bar (total: 1.3m)

sample94.0ms

Algorithm
intervals
Results
37.0ms467×body80nan
22.0ms298×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: 33.0b

Counts
2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

7.3b
(/ (* l l) Om)
7.6b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
11.6b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
16.1b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite220.0ms

Algorithm
rewrite-expression-head
Rules
180×add-sqr-sqrt
142×associate-*l*
114×*-un-lft-identity
82×associate-*r*
64×add-cube-cbrt
61×unswap-sqr
58×times-frac
48×sqrt-prod
32×add-exp-log
31×distribute-lft-out--
28×pow1
23×add-cbrt-cube
22×associate-*r/
21×unpow-prod-down
16×prod-exp
15×pow-prod-down associate-/l*
13×difference-of-squares
12×swap-sqr *-commutative
11×flip3-- flip--
10×cbrt-unprod
8×frac-sub
6×distribute-rgt-in sub-neg distribute-lft-in sqrt-div
5×sqr-pow
4×rem-sqrt-square sqrt-pow1 associate--l+ add-log-exp
3×div-exp associate-/r*
2×cbrt-undiv pow-exp div-inv
1×pow-to-exp frac-2neg pow1/2 clear-num
Counts
4 → 283
Calls
4 calls:
12.0ms
(/ (* l l) Om)
20.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
85.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
88.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.6s

Counts
4 → 12
Calls
4 calls:
20.0ms
(/ (* l l) Om)
383.0ms
(* (* 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*))))
4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify71.0ms

Algorithm
egg-herbie
Counts
295 → 295
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
014743538
150013393

prune1.2s

Filtered
295 candidates to 205 candidates (69.5%)
Pruning

22 alts after pruning (22 fresh and 0 done)

PrunedKeptTotal
New27322295
Fresh000
Picked101
Done000
Total27422296

Merged error: 16.1b

Counts
296 → 22

localize25.0ms

Local error

Found 4 expressions with local error:

7.3b
(/ (* l l) Om)
7.6b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.6b
(* (* (cbrt n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
14.5b
(sqrt (* (* (cbrt n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite220.0ms

Algorithm
rewrite-expression-head
Rules
169×add-sqr-sqrt
112×*-un-lft-identity associate-*l*
76×associate-*r*
62×add-cube-cbrt
58×times-frac
54×unswap-sqr
42×sqrt-prod
31×distribute-lft-out--
28×add-exp-log
22×associate-*r/
21×unpow-prod-down add-cbrt-cube
20×pow1
15×associate-/l*
13×prod-exp difference-of-squares
12×swap-sqr
11×cbrt-prod flip3-- flip--
10×*-commutative
9×pow-prod-down cbrt-unprod
8×frac-sub
6×distribute-rgt-in sub-neg distribute-lft-in sqrt-div
5×sqr-pow
4×rem-sqrt-square associate--l+ add-log-exp
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 → 268
Calls
4 calls:
8.0ms
(/ (* l l) Om)
21.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
86.0ms
(* (* (cbrt n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
90.0ms
(sqrt (* (* (cbrt n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series24.2s

Counts
4 → 12
Calls
4 calls:
19.0ms
(/ (* l l) Om)
386.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
2.1s
(* (* (cbrt n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
21.7s
(sqrt (* (* (cbrt n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify65.0ms

Algorithm
egg-herbie
Counts
280 → 280
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
013683305
150013154

prune1.1s

Filtered
280 candidates to 196 candidates (70.0%)
Pruning

23 alts after pruning (23 fresh and 0 done)

PrunedKeptTotal
New2728280
Fresh61521
Picked101
Done000
Total27923302

Merged error: 14.2b

Counts
302 → 23

localize31.0ms

Local error

Found 4 expressions with local error:

5.3b
(* n (pow (/ l Om) 2.0))
7.3b
(/ (* l l) Om)
7.6b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
12.7b
(sqrt (* (cbrt (* (cbrt n) U)) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
153×add-sqr-sqrt
93×*-un-lft-identity
84×associate-*l*
72×associate-*r*
67×add-cube-cbrt times-frac
46×sqrt-prod
44×unswap-sqr
34×unpow-prod-down
31×add-exp-log
28×cbrt-prod
16×add-cbrt-cube distribute-lft-out--
15×associate-/l*
14×pow1 prod-exp
12×associate-*r/ swap-sqr
9×*-commutative
7×difference-of-squares
6×flip3-- sqrt-div flip-- sqr-pow
5×rem-sqrt-square 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 → 244
Calls
4 calls:
10.0ms
(* n (pow (/ l Om) 2.0))
12.0ms
(/ (* l l) Om)
21.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
92.0ms
(sqrt (* (cbrt (* (cbrt n) U)) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series19.5s

Counts
4 → 12
Calls
4 calls:
146.0ms
(* n (pow (/ l Om) 2.0))
20.0ms
(/ (* l l) Om)
391.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
18.9s
(sqrt (* (cbrt (* (cbrt n) U)) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify69.0ms

Algorithm
egg-herbie
Counts
256 → 256
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
012652583
150022511

prune1.2s

Filtered
256 candidates to 182 candidates (71.1%)
Pruning

23 alts after pruning (23 fresh and 0 done)

PrunedKeptTotal
New2542256
Fresh12122
Picked101
Done000
Total25623279

Merged error: 14.2b

Counts
279 → 23

localize46.0ms

Local error

Found 4 expressions with local error:

5.3b
(* n (pow (/ l Om) 2.0))
7.3b
(/ (* l l) Om)
7.6b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
14.2b
(sqrt (* (cbrt (* (cbrt (cbrt n)) U)) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
162×add-sqr-sqrt
94×*-un-lft-identity
91×associate-*l*
72×associate-*r*
68×add-cube-cbrt
67×times-frac
51×sqrt-prod
49×unswap-sqr
46×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
9×*-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 → 250
Calls
4 calls:
10.0ms
(* n (pow (/ l Om) 2.0))
12.0ms
(/ (* l l) Om)
21.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
88.0ms
(sqrt (* (cbrt (* (cbrt (cbrt n)) U)) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series19.7s

Counts
4 → 12
Calls
4 calls:
150.0ms
(* n (pow (/ l Om) 2.0))
19.0ms
(/ (* l l) Om)
374.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
19.2s
(sqrt (* (cbrt (* (cbrt (cbrt n)) U)) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify64.0ms

Algorithm
egg-herbie
Counts
262 → 262
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
013032792
150012721

prune1.6s

Filtered
262 candidates to 188 candidates (71.8%)
Pruning

25 alts after pruning (25 fresh and 0 done)

PrunedKeptTotal
New2584262
Fresh12122
Picked101
Done000
Total26025285

Merged error: 14.2b

Counts
285 → 25

regimes1.1s

Accuracy

29.3% (6.4b remaining)

Error of 20.0b against oracle of 13.6b and baseline of 22.7b

bsearch342.0ms

Steps
ItersRangePoint
8
6.770499772705243e+94
2.9661045111837723e+99
2.90056484708727e+99
8
-1.40869048741384e+138
-1.8778933842328292e+135
-9.180640496957073e+136

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08974
19474
29474

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.1s14706×body80nan
704.0ms9206×body80valid