Details

Time bar (total: 19.2s)

sample124.0ms

Algorithm
intervals
Results
42.0ms446×body80nan
31.0ms290×body80valid

simplify118.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04914
115314
265214
3362414
4500214

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 36.4b

Counts
2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

8.4b
(* n (pow (/ l Om) 2.0))
11.9b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
12.3b
(/ (* l l) Om)
17.4b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
26×add-exp-log
24×add-sqr-sqrt
23×pow1
20×associate-*r/ associate-*r* add-cbrt-cube
16×add-cube-cbrt *-un-lft-identity
15×unpow-prod-down
13×times-frac
12×pow-prod-down
11×prod-exp
10×flip3-- flip--
8×frac-sub cbrt-unprod
6×sqrt-div
4×distribute-rgt-in sub-neg distribute-lft-in sqrt-pow1 associate-*l* associate--l+ add-log-exp unswap-sqr
3×div-exp associate-/r*
2×cbrt-undiv pow-exp *-commutative div-inv sqr-pow
1×pow-to-exp frac-2neg pow1/2 clear-num sqrt-prod associate-/l*
Counts
4 → 112
Calls
4 calls:
8.0ms
(* n (pow (/ l Om) 2.0))
11.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.0ms
(/ (* l l) Om)
11.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series2.3s

Counts
4 → 12
Calls
4 calls:
41.0ms
(* n (pow (/ l Om) 2.0))
351.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
3.0ms
(/ (* l l) Om)
1.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify125.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
010261598
149371447
250011447

prune328.0ms

Filtered
88 candidates to 124 candidates (-40.9%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New11113124
Fresh000
Picked101
Done000
Total11213125

Merged error: 22.6b

Counts
125 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

7.2b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.4b
(* n (pow (/ l Om) 2.0))
11.9b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
17.4b
(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
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:
10.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.0ms
(* n (pow (/ l Om) 2.0))
11.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
9.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series2.4s

Counts
4 → 12
Calls
4 calls:
129.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
41.0ms
(* n (pow (/ l Om) 2.0))
363.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
1.9s
(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 (26.0ms)

IterNodesCost
010711765
150011602

prune302.0ms

Filtered
86 candidates to 131 candidates (-52.3%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New1256131
Fresh4812
Picked101
Done000
Total13014144

Merged error: 20.8b

Counts
144 → 14

localize24.0ms

Local error

Found 4 expressions with local error:

5.9b
(* (* n (pow (/ l Om) 2.0)) (* (cbrt (- U U*)) (cbrt (- U U*))))
8.4b
(* n (pow (/ l Om) 2.0))
11.9b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) 2.0)) (* (cbrt (- U U*)) (cbrt (- U U*)))) (cbrt (- U U*)))))
17.4b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) 2.0)) (* (cbrt (- U U*)) (cbrt (- U U*)))) (cbrt (- U U*))))))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
246×associate-*r/
228×cbrt-div
168×flip3-- flip--
116×frac-times
104×frac-sub
58×associate-*l/
54×add-exp-log sqrt-div
33×prod-exp
28×pow1
23×add-cbrt-cube
22×add-sqr-sqrt
21×associate-*r*
15×unpow-prod-down pow-prod-down cbrt-unprod
14×add-cube-cbrt *-un-lft-identity
10×times-frac
6×pow-exp
5×associate-*l*
4×distribute-rgt-in sub-neg distribute-lft-in sqrt-pow1 associate--l+ add-log-exp unswap-sqr
3×pow-to-exp div-exp *-commutative
2×sqr-pow
1×pow1/2 sqrt-prod div-inv
Counts
4 → 221
Calls
4 calls:
19.0ms
(* (* n (pow (/ l Om) 2.0)) (* (cbrt (- U U*)) (cbrt (- U U*))))
8.0ms
(* n (pow (/ l Om) 2.0))
21.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) 2.0)) (* (cbrt (- U U*)) (cbrt (- U U*)))) (cbrt (- U U*)))))
20.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) 2.0)) (* (cbrt (- U U*)) (cbrt (- U U*)))) (cbrt (- U U*))))))

series2.4s

Counts
4 → 12
Calls
4 calls:
98.0ms
(* (* n (pow (/ l Om) 2.0)) (* (cbrt (- U U*)) (cbrt (- U U*))))
41.0ms
(* n (pow (/ l Om) 2.0))
355.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) 2.0)) (* (cbrt (- U U*)) (cbrt (- U U*)))) (cbrt (- U U*)))))
1.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) 2.0)) (* (cbrt (- U U*)) (cbrt (- U U*)))) (cbrt (- U U*))))))

simplify101.0ms

Algorithm
egg-herbie
Counts
233 → 233
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
019218151
150017844

prune653.0ms

Filtered
159 candidates to 233 candidates (-46.5%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New2312233
Fresh11213
Picked011
Done000
Total23215247

Merged error: 20.8b

Counts
247 → 15

localize24.0ms

Local error

Found 4 expressions with local error:

11.9b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
11.9b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
17.4b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
17.4b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
42×pow1
40×associate-*r/
24×pow-prod-down
22×add-exp-log add-cbrt-cube
20×flip3-- flip--
16×frac-sub
12×sqrt-div prod-exp cbrt-unprod
8×distribute-rgt-in sub-neg distribute-lft-in sqrt-pow1 associate--l+
6×add-sqr-sqrt add-cube-cbrt *-un-lft-identity associate-*r*
4×add-log-exp
2×pow1/2 associate-*l* sqrt-prod *-commutative
Counts
4 → 108
Calls
4 calls:
12.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
11.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
9.0ms
(sqrt (* (* (* 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*)))))

series4.7s

Counts
4 → 12
Calls
4 calls:
351.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
552.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
1.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
1.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify106.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
07322568
135812320
250012320

prune367.0ms

Filtered
80 candidates to 120 candidates (-50.0%)
Pruning

15 alts after pruning (13 fresh and 2 done)

PrunedKeptTotal
New1200120
Fresh01313
Picked011
Done011
Total12015135

Merged error: 20.8b

Counts
135 → 15

regimes993.0ms

Accuracy

9.1% (9.1b remaining)

Error of 30.8b against oracle of 21.7b and baseline of 31.7b

bsearch165.0ms

Steps
ItersRangePoint
9
1.2421588888583933e-179
4.0065550987920697e-174
9.766108094203416e-176
7
-4.681232428732589e-175
-1.9410387578284007e-176
-3.8610079068797945e-176

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06455
16455

end0.0ms

sample3.7s

Algorithm
intervals
Results
1.4s14687×body80nan
877.0ms9212×body80valid

Profiling

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