Details

Time bar (total: 19.5s)

sample139.0ms

Algorithm
intervals
Results
51.0ms482×body80nan
28.0ms287×body80valid

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
0585928

prune17.0ms

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: 26.2b

Counts
2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

6.0b
(* n (* (pow (/ l Om) 2.0) (- U* U)))
6.4b
(* (pow (/ l Om) 2.0) (- U* U))
6.5b
(* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))
16.2b
(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
31×add-exp-log
25×add-sqr-sqrt
23×associate-*l*
21×pow1
17×*-un-lft-identity
16×associate-*r/ prod-exp add-cbrt-cube
15×add-cube-cbrt unpow-prod-down
14×distribute-rgt-in distribute-lft-in
10×times-frac pow-prod-down
7×associate-*r* cbrt-unprod
6×sub-neg
4×sqrt-pow1 pow-exp add-log-exp unswap-sqr
3×*-commutative
2×pow-to-exp flip3-- flip3-+ sqrt-div div-exp flip-- flip-+ sqr-pow
1×pow1/2 sqrt-prod div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 114
Calls
4 calls:
13.0ms
(* n (* (pow (/ l Om) 2.0) (- U* U)))
12.0ms
(* (pow (/ l Om) 2.0) (- U* U))
16.0ms
(* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))
18.0ms
(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))))

series2.9s

Counts
4 → 12
Calls
4 calls:
147.0ms
(* n (* (pow (/ l Om) 2.0) (- U* U)))
144.0ms
(* (pow (/ l Om) 2.0) (- U* U))
391.0ms
(* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))
2.2s
(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) 2.0) (- U* U))) (* 2.0 (* l (/ l Om)))))))))

simplify38.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
064302400

prune328.0ms

Filtered
85 candidates to 126 candidates (-48.2%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New11511126
Fresh011
Picked101
Done000
Total11612128

Merged error: 22.6b

Counts
128 → 12

localize22.0ms

Local error

Found 4 expressions with local error:

5.6b
(* (- U* U) (pow (/ l Om) (/ 2.0 2)))
6.0b
(* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))))
6.5b
(* n (* U (+ t (- (* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2))))) (* 2.0 (* l (/ l Om)))))))
16.2b
(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2))))) (* 2.0 (* l (/ l Om)))))))))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
95×add-exp-log
64×prod-exp
25×add-sqr-sqrt
21×pow1
20×pow-exp add-cbrt-cube
19×associate-*r*
17×*-un-lft-identity
15×add-cube-cbrt unpow-prod-down
14×associate-*r/
11×associate-*l*
10×pow-to-exp times-frac div-exp pow-prod-down cbrt-unprod
4×distribute-rgt-in distribute-lft-in sqrt-pow1 associate-*l/ add-log-exp unswap-sqr
3×*-commutative
2×flip3-- flip3-+ sqrt-div flip-- flip-+ sqr-pow
1×pow1/2 sqrt-prod div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 119
Calls
4 calls:
14.0ms
(* (- U* U) (pow (/ l Om) (/ 2.0 2)))
23.0ms
(* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))))
19.0ms
(* n (* U (+ t (- (* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2))))) (* 2.0 (* l (/ l Om)))))))
20.0ms
(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2))))) (* 2.0 (* l (/ l Om)))))))))

series2.9s

Counts
4 → 12
Calls
4 calls:
105.0ms
(* (- U* U) (pow (/ l Om) (/ 2.0 2)))
149.0ms
(* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))))
392.0ms
(* n (* U (+ t (- (* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2))))) (* 2.0 (* l (/ l Om)))))))
2.2s
(sqrt (* 2.0 (* n (* U (+ t (- (* n (* (pow (/ l Om) (/ 2.0 2)) (* (- U* U) (pow (/ l Om) (/ 2.0 2))))) (* 2.0 (* l (/ l Om)))))))))

simplify58.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
050472711

prune322.0ms

Filtered
84 candidates to 131 candidates (-56.0%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1283131
Fresh2911
Picked101
Done000
Total13112143

Merged error: 21.8b

Counts
143 → 12

localize22.0ms

Local error

Found 4 expressions with local error:

5.0b
(* U (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))) (* 2.0 (* l (/ l Om))))))
5.6b
(* (- U* U) (pow (/ l Om) (/ 2.0 2)))
6.5b
(* n (* U (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))) (* 2.0 (* l (/ l Om)))))))
16.2b
(sqrt (* 2.0 (* n (* U (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))) (* 2.0 (* l (/ l Om)))))))))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
22×associate-*r*
21×pow1
20×*-un-lft-identity
19×add-exp-log
16×add-cube-cbrt
15×unpow-prod-down
13×add-cbrt-cube
12×associate-*r/
11×associate-*l*
10×times-frac pow-prod-down
8×prod-exp
5×distribute-rgt-in distribute-lft-in cbrt-unprod unswap-sqr
4×sqrt-pow1 add-log-exp
3×flip3-+ *-commutative flip-+
2×sqrt-div associate-*l/ pow-exp sqr-pow
1×pow-to-exp flip3-- pow1/2 div-exp sqrt-prod flip-- div-inv distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 103
Calls
4 calls:
19.0ms
(* U (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))) (* 2.0 (* l (/ l Om))))))
14.0ms
(* (- U* U) (pow (/ l Om) (/ 2.0 2)))
21.0ms
(* n (* U (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))) (* 2.0 (* l (/ l Om)))))))
19.0ms
(sqrt (* 2.0 (* n (* U (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))) (* 2.0 (* l (/ l Om)))))))))

series3.3s

Counts
4 → 12
Calls
4 calls:
363.0ms
(* U (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))) (* 2.0 (* l (/ l Om))))))
105.0ms
(* (- U* U) (pow (/ l Om) (/ 2.0 2)))
396.0ms
(* n (* U (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))) (* 2.0 (* l (/ l Om)))))))
2.4s
(sqrt (* 2.0 (* n (* U (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))) (* 2.0 (* l (/ l Om)))))))))

simplify56.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
050152786

prune351.0ms

Filtered
87 candidates to 115 candidates (-32.2%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1132115
Fresh01111
Picked101
Done000
Total11413127

Merged error: 21.3b

Counts
127 → 13

localize23.0ms

Local error

Found 4 expressions with local error:

4.9b
(* n (pow (/ l Om) (/ 2.0 2)))
5.6b
(* (- U* U) (pow (/ l Om) (/ 2.0 2)))
8.5b
(* (* n U) (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))) (* 2.0 (* l (/ l Om))))))
16.2b
(sqrt (* 2.0 (* (* n U) (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))) (* 2.0 (* l (/ l Om))))))))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
38×associate-*r*
30×unpow-prod-down
27×*-un-lft-identity
25×add-exp-log
23×add-cube-cbrt
20×times-frac
19×pow1
13×add-cbrt-cube
11×prod-exp
9×associate-*l* pow-prod-down
8×unswap-sqr
6×associate-*r/
5×cbrt-unprod
4×sqrt-pow1 pow-exp add-log-exp sqr-pow
3×*-commutative
2×pow-to-exp flip3-+ sqrt-div div-exp associate-*l/ flip-+ div-inv
1×distribute-rgt-in flip3-- distribute-lft-in pow1/2 sqrt-prod flip-- distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 116
Calls
4 calls:
10.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
14.0ms
(* (- U* U) (pow (/ l Om) (/ 2.0 2)))
19.0ms
(* (* n U) (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))) (* 2.0 (* l (/ l Om))))))
18.0ms
(sqrt (* 2.0 (* (* n U) (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))) (* 2.0 (* l (/ l Om))))))))

series2.8s

Counts
4 → 12
Calls
4 calls:
56.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
107.0ms
(* (- U* U) (pow (/ l Om) (/ 2.0 2)))
386.0ms
(* (* n U) (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))) (* 2.0 (* l (/ l Om))))))
2.2s
(sqrt (* 2.0 (* (* n U) (+ t (- (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U* U) (pow (/ l Om) (/ 2.0 2)))) (* 2.0 (* l (/ l Om))))))))

simplify37.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
061282523

prune310.0ms

Filtered
97 candidates to 128 candidates (-32.0%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New1262128
Fresh01212
Picked011
Done000
Total12615141

Merged error: 21.1b

Counts
141 → 15

regimes1.5s

Accuracy

28.1% (5.5b remaining)

Error of 28.7b against oracle of 23.2b and baseline of 30.8b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094146
194146

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.5s15062×body80nan
911.0ms9219×body80valid

Profiling

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