Details

Time bar (total: 12.6s)

sample103.0ms

Algorithm
intervals
Results
22.0ms308×body80nan
12.0ms162×body80valid
10.0ms29×body1280valid
9.0ms32×body640valid
6.0ms19×body1280nan
6.0ms18×body160valid
4.0ms15×body640nan
4.0ms15×body320valid
2.0ms11×body320nan
1.0ms4×body160nan

simplify3.6s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01827
13927
28627
317727
434427
555027
689927
7159327
8321727
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

localize21.0ms

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)))

rewrite53.0ms

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))))
5.0ms
(* (sqrt 2.0) t)
14.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
13.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series370.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(/ (* (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))
207.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify744.0ms

Counts
92 → 92
Iterations

Useful iterations: 2 (147.0ms)

IterNodesCost
01682472
14162283
215862085
done50012085

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

localize21.0ms

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)))))

rewrite37.0ms

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)))
5.0ms
(/ (pow l 2) x)
5.0ms
(/ (pow t 2) x)
14.0ms
(sqrt (+ (* 2.0 (/ (pow l 2) x)) (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (pow t 2)))))

series100.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (pow t 2)))
3.0ms
(/ (pow l 2) x)
4.0ms
(/ (pow t 2) x)
85.0ms
(sqrt (+ (* 2.0 (/ (pow l 2) x)) (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (pow t 2)))))

simplify631.0ms

Counts
138 → 138
Iterations

Useful iterations: 2 (221.0ms)

IterNodesCost
02472095
15231882
218551714
done50001714

prune413.0ms

Filtered
100 candidates to 138 candidates (-38.0%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1317138
Fresh044
Picked101
Done000
Total13211143

Merged error: 2.9b

Counts
143 → 11

localize20.0ms

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)))))

rewrite48.0ms

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))))
8.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (pow t 2)))
4.0ms
(/ (pow t 2) x)
87.0ms
(sqrt (+ (* 2.0 (/ l (/ x l))) (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (pow t 2)))))

simplify598.0ms

Counts
104 → 104
Iterations

Useful iterations: 2 (169.0ms)

IterNodesCost
01912241
14592043
216771882
done50011882

prune309.0ms

Filtered
78 candidates to 104 candidates (-33.3%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1022104
Fresh1910
Picked101
Done000
Total10411115

Merged error: 2.7b

Counts
115 → 11

localize25.0ms

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)))))

rewrite56.0ms

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)))
5.0ms
(/ (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)))))

series127.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(+ (* 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)
90.0ms
(sqrt (+ (* 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))) (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (pow t 2)))))

simplify755.0ms

Counts
112 → 112
Iterations

Useful iterations: 2 (263.0ms)

IterNodesCost
02223370
15643094
221752650
done50002650

prune311.0ms

Filtered
85 candidates to 112 candidates (-31.8%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1120112
Fresh01010
Picked011
Done000
Total11211123

Merged error: 2.7b

Counts
123 → 11

regimes791.0ms

Accuracy

78.8% (5.2b remaining)

Error of 8.6b against oracle of 3.5b and baseline of 27.9b

bsearch106.0ms

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
050122
166122
done66122

end0.0ms

sample3.1s

Algorithm
intervals
Results
701.0ms9703×body80nan
399.0ms5178×body80valid
303.0ms844×body1280valid
291.0ms1024×body640valid
208.0ms589×body1280nan
165.0ms593×body640nan
131.0ms627×body320valid
70.0ms319×body320nan
47.0ms327×body160valid
24.0ms172×body160nan

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