Details

Time bar (total: 19.9s)

analyze2.3s

Algorithm
search
Search
TrueOtherFalseIter
0%99.7%0.3%0
0%99.7%0.3%1
0%99.7%0.3%2
0%99.7%0.3%3
0%99.7%0.3%4
0%99.7%0.3%5
0%99.7%0.3%6
0%98.1%1.9%7
0%98.1%1.9%8
0%97.8%2.2%9
0%96.8%3.2%10
0%96.3%3.7%11
0%94.3%5.7%12
0.4%92.1%7.5%13
0.6%90.8%8.6%14

sample102.0ms

Algorithm
intervals
Results
38.0ms411×body80nan
24.0ms256×body80valid
4.0ms37×body80invalid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
0518628

prune19.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 27.6b

Counts
2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

4.1b
(* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))))
5.1b
(* n (* (pow (/ l Om) 2.0) (- U* U)))
5.7b
(* (pow (/ l Om) 2.0) (- U* U))
20.2b
(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log add-sqr-sqrt
23×associate-*l*
20×*-un-lft-identity
18×pow1
16×add-cube-cbrt
15×unpow-prod-down
14×associate-*r/ prod-exp
13×add-cbrt-cube
10×times-frac associate-*r*
pow-prod-down
distribute-rgt-in sub-neg distribute-lft-in
cbrt-unprod unswap-sqr
sqrt-pow1 pow-exp add-log-exp
*-commutative
pow-to-exp flip3-- flip3-+ sqrt-div div-exp flip-- flip-+ sqr-pow
pow1/2 sqrt-prod div-inv distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 107
Calls
4 calls:
14.0ms
(* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))))
11.0ms
(* n (* (pow (/ l Om) 2.0) (- U* U)))
11.0ms
(* (pow (/ l Om) 2.0) (- U* U))
17.0ms
(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))))

series2.5s

Counts
4 → 12
Calls
4 calls:
310.0ms
(* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om))))))
127.0ms
(* n (* (pow (/ l Om) 2.0) (- U* U)))
126.0ms
(* (pow (/ l Om) 2.0) (- U* U))
1.9s
(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))))

simplify42.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
062232211

prune301.0ms

Filtered
87 candidates to 119 candidates (-36.8%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New10712119
Fresh011
Picked101
Done000
Total10813121

Merged error: 24.6b

Counts
121 → 13

localize32.0ms

Local error

Found 4 expressions with local error:

3.7b
(* n (* U (+ t (- (* n (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om)))))))
4.1b
(* U (+ t (- (* n (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om))))))
5.1b
(* n (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0))))
20.2b
(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om)))))))))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
181×add-exp-log
123×prod-exp
39×pow-exp
27×div-exp
23×pow1
20×add-cbrt-cube
16×associate-*r/
12×pow-to-exp
11×pow-prod-down
10×add-sqr-sqrt *-un-lft-identity cbrt-unprod
associate-*l*
add-cube-cbrt
associate-*r*
distribute-rgt-in distribute-lft-in
sqrt-pow1 add-log-exp
flip3-+ *-commutative flip-+
sqrt-div associate-*l/
flip3-- pow1/2 sqrt-prod flip-- distribute-lft-out unswap-sqr
Counts
4 → 116
Calls
4 calls:
27.0ms
(* n (* U (+ t (- (* n (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om)))))))
24.0ms
(* U (+ t (- (* n (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om))))))
22.0ms
(* n (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0))))
26.0ms
(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om)))))))))

series2.7s

Counts
4 → 12
Calls
4 calls:
331.0ms
(* n (* U (+ t (- (* n (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om)))))))
301.0ms
(* U (+ t (- (* n (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om))))))
125.0ms
(* n (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0))))
1.9s
(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om)))))))))

simplify72.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
049754400
149754400

prune269.0ms

Filtered
70 candidates to 128 candidates (-82.9%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New1226128
Fresh4812
Picked101
Done000
Total12714141

Merged error: 23.1b

Counts
141 → 14

localize43.0ms

Local error

Found 4 expressions with local error:

16.4b
(cbrt (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om)))))))
16.4b
(cbrt (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om)))))))
16.4b
(cbrt (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om)))))))
20.2b
(sqrt (* 2.0 (* n (* (* (cbrt (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om))))))) (cbrt (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om)))))))) (cbrt (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om)))))))))))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
120×associate-*r/
60×cbrt-div
30×flip3-+ flip-+
28×frac-times
26×sqrt-div
19×pow1
14×associate-*l/
10×pow-prod-down
sqrt-pow1
add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
cbrt-prod pow1/3
pow1/2 sqrt-prod
Counts
4 → 73
Calls
4 calls:
21.0ms
(cbrt (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om)))))))
21.0ms
(cbrt (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om)))))))
24.0ms
(cbrt (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om)))))))
18.0ms
(sqrt (* 2.0 (* n (* (* (cbrt (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om))))))) (cbrt (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om)))))))) (cbrt (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om)))))))))))

series3.1s

Counts
4 → 12
Calls
4 calls:
370.0ms
(cbrt (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om)))))))
375.0ms
(cbrt (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om)))))))
381.0ms
(cbrt (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om)))))))
1.9s
(sqrt (* 2.0 (* n (* (* (cbrt (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om))))))) (cbrt (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om)))))))) (cbrt (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om)))))))))))

simplify83.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
049919396
149919396

prune411.0ms

Filtered
59 candidates to 85 candidates (-44.1%)
Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New85085
Fresh01313
Picked011
Done000
Total851499

Merged error: 23.1b

Counts
99 → 14

localize44.0ms

Local error

Found 4 expressions with local error:

20.2b
(sqrt (* 2.0 (* (* (cbrt (* n (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om)))))))) (cbrt (* n (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om))))))))) (cbrt (* n (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om)))))))))))
21.2b
(cbrt (* n (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om))))))))
21.2b
(cbrt (* n (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om))))))))
21.2b
(cbrt (* n (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om))))))))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
154×associate-*r/
60×cbrt-div
30×flip3-+ flip-+
28×frac-times
26×sqrt-div
14×pow1 associate-*l/
pow-prod-down
add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity sqrt-pow1 add-cbrt-cube add-log-exp
cbrt-prod pow1/3
pow1/2 sqrt-prod
Counts
4 → 72
Calls
4 calls:
18.0ms
(sqrt (* 2.0 (* (* (cbrt (* n (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om)))))))) (cbrt (* n (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om))))))))) (cbrt (* n (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om)))))))))))
24.0ms
(cbrt (* n (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om))))))))
24.0ms
(cbrt (* n (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om))))))))
23.0ms
(cbrt (* n (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om))))))))

series3.0s

Counts
4 → 12
Calls
4 calls:
1.9s
(sqrt (* 2.0 (* (* (cbrt (* n (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om)))))))) (cbrt (* n (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om))))))))) (cbrt (* n (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om)))))))))))
358.0ms
(cbrt (* n (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om))))))))
351.0ms
(cbrt (* n (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om))))))))
350.0ms
(cbrt (* n (* U (+ t (- (* n (* (pow (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) 2.0) (* (- U* U) (pow (/ (cbrt l) (cbrt Om)) 2.0)))) (* 2.0 (* l (/ l Om))))))))

simplify71.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
052219554

prune361.0ms

Filtered
62 candidates to 84 candidates (-35.5%)
Pruning

14 alts after pruning (12 fresh and 2 done)

PrunedKeptTotal
New84084
Fresh01212
Picked011
Done011
Total841498

Merged error: 23.1b

Counts
98 → 14

regimes1.3s

Accuracy

29% (6.1b remaining)

Error of 29.6b against oracle of 23.6b and baseline of 32.1b

bsearch2.0ms

simplify11.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (10.0ms)

IterNodesCost
0562105
1562105

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.3s13117×body80nan
752.0ms8000×body80valid
114.0ms1190×body80invalid

Profiling

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