Details

Time bar (total: 9.9s)

sample110.0ms

Algorithm
intervals
Results
24.0ms308×body80nan
13.0ms162×body80valid
11.0ms19×body1280nan
10.0ms29×body1280valid
9.0ms32×body640valid
4.0ms15×body640nan
3.0ms15×body320valid
3.0ms18×body160valid
2.0ms11×body320nan
1.0ms4×body160nan

simplify1.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01827
13927
28627
317927
435327
558327
693327
7179927
8354727
done500027

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 45.4b

Counts
2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.4b
(* (sqrt 2.0) t)
15.4b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
22.3b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×sqrt-prod
12×add-cube-cbrt *-un-lft-identity
11×add-exp-log add-cbrt-cube
7×pow1
6×times-frac associate-*l* associate-/r* add-log-exp
4×sqrt-div
3×flip3-- associate-*r* flip--
2×cbrt-undiv div-exp prod-exp associate--l+ associate-/r/ cbrt-unprod unswap-sqr
1×distribute-rgt-in sub-neg rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 diff-log pow-prod-down clear-num *-commutative div-inv associate-/l*
Counts
4 → 80
Calls
4 calls:
19.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
6.0ms
(* (sqrt 2.0) t)
14.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
14.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series377.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
5.0ms
(* (sqrt 2.0) t)
63.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
211.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify461.0ms

Counts
92 → 92
Iterations

Useful iterations: 2 (130.0ms)

IterNodesCost
01682472
14252287
216682081
done50002081

prune238.0ms

Filtered
65 candidates to 92 candidates (-41.5%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New87592
Fresh000
Picked101
Done000
Total88593

Merged error: 5.5b

Counts
93 → 5

localize18.0ms

Local error

Found 4 expressions with local error:

4.6b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (pow t 2)))
8.4b
(/ (pow l 2) x)
9.7b
(/ (pow t 2) x)
27.1b
(sqrt (+ (* 2.0 (/ (pow l 2) x)) (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (pow t 2)))))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
48×times-frac
40×add-sqr-sqrt
39×add-cube-cbrt *-un-lft-identity
24×unpow-prod-down
16×associate-/l*
14×add-exp-log
8×add-cbrt-cube unpow2 sqr-pow
6×div-exp associate-/r* add-log-exp
5×pow1
4×sqrt-div
3×flip3-+ sqrt-prod flip-+
2×cbrt-undiv pow-to-exp frac-2neg associate-*r/ frac-add pow-exp clear-num div-inv
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log
Counts
4 → 126
Calls
4 calls:
8.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (pow t 2)))
6.0ms
(/ (pow l 2) x)
6.0ms
(/ (pow t 2) x)
17.0ms
(sqrt (+ (* 2.0 (/ (pow l 2) x)) (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (pow t 2)))))

series104.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (pow t 2)))
4.0ms
(/ (pow l 2) x)
4.0ms
(/ (pow t 2) x)
89.0ms
(sqrt (+ (* 2.0 (/ (pow l 2) x)) (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (pow t 2)))))

simplify494.0ms

Counts
138 → 138
Iterations

Useful iterations: 2 (161.0ms)

IterNodesCost
02472095
15271882
219471686
done50001686

prune379.0ms

Filtered
93 candidates to 138 candidates (-48.4%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1317138
Fresh044
Picked101
Done000
Total13211143

Merged error: 2.9b

Counts
143 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (* 2.0 (/ l (/ x l))) (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (pow t 2))))
4.6b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (pow t 2)))
9.7b
(/ (pow t 2) x)
27.1b
(sqrt (+ (* 2.0 (/ l (/ x l))) (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (pow t 2)))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
23×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
12×unpow-prod-down
11×add-log-exp
9×add-exp-log
8×associate-/l*
6×add-cbrt-cube
5×pow1 flip3-+ flip-+
4×sqrt-div associate-*r/ frac-add sum-log unpow2 sqr-pow
3×div-exp associate-/r* sqrt-prod
2×+-commutative
1×cbrt-undiv pow-to-exp rem-sqrt-square associate-+r+ frac-2neg sqrt-pow1 pow1/2 pow-exp clear-num div-inv
Counts
4 → 92
Calls
4 calls:
16.0ms
(+ (* 2.0 (/ l (/ x l))) (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (pow t 2))))
8.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (pow t 2)))
6.0ms
(/ (pow t 2) x)
16.0ms
(sqrt (+ (* 2.0 (/ l (/ x l))) (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (pow t 2)))))

series117.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(+ (* 2.0 (/ l (/ x l))) (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (pow t 2))))
10.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (pow t 2)))
4.0ms
(/ (pow t 2) x)
84.0ms
(sqrt (+ (* 2.0 (/ l (/ x l))) (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (pow t 2)))))

simplify479.0ms

Counts
104 → 104
Iterations

Useful iterations: 2 (134.0ms)

IterNodesCost
01912241
14612043
217381868
done50011868

prune297.0ms

Filtered
75 candidates to 104 candidates (-38.7%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1022104
Fresh1910
Picked101
Done000
Total10411115

Merged error: 2.7b

Counts
115 → 11

localize24.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (* 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))) (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (pow t 2))))
4.6b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (pow t 2)))
9.7b
(/ (pow t 2) x)
27.1b
(sqrt (+ (* 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))) (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (pow t 2)))))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
23×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
16×associate-*r/
12×unpow-prod-down frac-add
11×add-log-exp
9×add-exp-log flip3-+ flip-+
8×sqrt-div associate-/l*
6×add-cbrt-cube
5×pow1
4×frac-times associate-*l/ sum-log unpow2 sqr-pow
3×div-exp associate-/r* sqrt-prod
2×+-commutative
1×cbrt-undiv pow-to-exp rem-sqrt-square associate-+r+ frac-2neg sqrt-pow1 pow1/2 pow-exp clear-num div-inv
Counts
4 → 100
Calls
4 calls:
21.0ms
(+ (* 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))) (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (pow t 2))))
8.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (pow t 2)))
6.0ms
(/ (pow t 2) x)
19.0ms
(sqrt (+ (* 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))) (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (pow t 2)))))

series131.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(+ (* 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))) (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (pow t 2))))
8.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (pow t 2)))
4.0ms
(/ (pow t 2) x)
95.0ms
(sqrt (+ (* 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))) (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (pow t 2)))))

simplify614.0ms

Counts
112 → 112
Iterations

Useful iterations: 2 (182.0ms)

IterNodesCost
02223370
15663094
222302650
done50012650

prune308.0ms

Filtered
84 candidates to 112 candidates (-33.3%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1111112
Fresh01010
Picked011
Done000
Total11112123

Merged error: 2.7b

Counts
123 → 12

regimes846.0ms

Accuracy

78.2% (5.4b remaining)

Error of 8.6b against oracle of 3.3b and baseline of 27.9b

bsearch112.0ms

Steps
ItersRangePoint
8
6.5065225296113186e+109
1.3009312689647836e+113
3.3289760264210936e+110
8
-1.0538219094505121e+147
-2.2661782969104254e+143
-3.794989872061021e+143

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
049122
165122
done65122

end0.0ms

sample3.2s

Algorithm
intervals
Results
738.0ms9703×body80nan
423.0ms5178×body80valid
311.0ms844×body1280valid
310.0ms1024×body640valid
215.0ms589×body1280nan
170.0ms593×body640nan
140.0ms627×body320valid
68.0ms319×body320nan
49.0ms327×body160valid
25.0ms172×body160nan

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