Details

Time bar (total: 37.4s)

sample321.0ms

Algorithm
intervals
Results
103.0ms296×body80nan
22.0ms166×body80valid
19.0ms26×body1280valid
18.0ms33×body640valid
10.0ms22×body640nan
9.0ms15×body1280nan
7.0ms20×body320valid
3.0ms8×body320nan
3.0ms11×body160valid
2.0ms7×body160nan

simplify5.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
01827
13927
29327
319827
443227
577727
6136727
7354627
done500027

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.9b

localize63.0ms

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)
13.8b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
20.7b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite322.0ms

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:
123.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
20.0ms
(* (sqrt 2.0) t)
65.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
106.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series3.6s

Counts
4 → 12
Calls
4 calls:
838.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
80.0ms
(* (sqrt 2.0) t)
434.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
2.2s
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify2.3s

Counts
92 → 92
Iterations

Useful iterations: 2 (620.0ms)

IterNodesCost
01682472
14572291
226272087
done50002087

prune875.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.1b

localize74.0ms

Local error

Found 4 expressions with local error:

3.8b
(+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x)))
5.9b
(/ (pow l 2) x)
10.0b
(/ (pow t 2) x)
27.5b
(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x))))

rewrite190.0ms

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×associate-*r/ add-cbrt-cube unpow2 sqr-pow
6×div-exp associate-/r* add-log-exp
5×pow1
4×flip3-+ sqrt-div frac-add flip-+
3×sqrt-prod
2×cbrt-undiv pow-to-exp associate-+l+ frac-2neg pow-exp clear-num div-inv
1×+-commutative distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 sum-log
Counts
4 → 130
Calls
4 calls:
64.0ms
(+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x)))
20.0ms
(/ (pow l 2) x)
19.0ms
(/ (pow t 2) x)
78.0ms
(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x))))

series720.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x)))
37.0ms
(/ (pow l 2) x)
36.0ms
(/ (pow t 2) x)
492.0ms
(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x))))

simplify2.2s

Counts
142 → 142
Iterations

Useful iterations: 2 (709.0ms)

IterNodesCost
02542312
15682086
229341875
done50001875

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.8b

localize68.0ms

Local error

Found 4 expressions with local error:

1.2b
(+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))
3.8b
(+ (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))) (* 4.0 (/ (pow t 2) x)))
10.0b
(/ (pow t 2) x)
27.5b
(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))) (* 4.0 (/ (pow t 2) x))))

rewrite317.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
23×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
12×unpow-prod-down
9×add-exp-log
8×associate-*r/ associate-/l* add-log-exp
6×add-cbrt-cube
5×pow1 flip3-+ flip-+
4×sqrt-div frac-add unpow2 sqr-pow
3×div-exp associate-/r* sqrt-prod
2×+-commutative associate-+l+ sum-log
1×cbrt-undiv distribute-rgt-in pow-to-exp rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 pow-exp clear-num div-inv
Counts
4 → 92
Calls
4 calls:
67.0ms
(+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))
80.0ms
(+ (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))) (* 4.0 (/ (pow t 2) x)))
19.0ms
(/ (pow t 2) x)
146.0ms
(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))) (* 4.0 (/ (pow t 2) x))))

series703.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))
134.0ms
(+ (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))) (* 4.0 (/ (pow t 2) x)))
33.0ms
(/ (pow t 2) x)
461.0ms
(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))) (* 4.0 (/ (pow t 2) x))))

simplify2.1s

Counts
104 → 104
Iterations

Useful iterations: 2 (631.0ms)

IterNodesCost
02022323
14971966
224421646
done50011646

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.8b

localize110.0ms

Local error

Found 4 expressions with local error:

3.8b
(+ (* 2.0 (+ (* t t) (* (/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x))) (/ (pow (cbrt l) 2) (cbrt x))))) (* 4.0 (/ (pow t 2) x)))
5.8b
(/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x)))
10.0b
(/ (pow t 2) x)
27.5b
(sqrt (+ (* 2.0 (+ (* t t) (* (/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x))) (/ (pow (cbrt l) 2) (cbrt x))))) (* 4.0 (/ (pow t 2) x))))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
34×times-frac
29×add-sqr-sqrt
28×add-cube-cbrt *-un-lft-identity
24×unpow-prod-down
22×add-exp-log
18×associate-/l*
9×div-exp add-cbrt-cube
8×associate-*r/
6×cbrt-prod add-log-exp sqr-pow
5×pow1
4×flip3-+ sqrt-div frac-add associate-/r* flip-+ unpow2
3×cbrt-undiv pow-to-exp pow-exp prod-exp sqrt-prod
2×associate-+l+ frac-2neg clear-num div-inv
1×+-commutative distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 sum-log cbrt-unprod
Counts
4 → 120
Calls
4 calls:
35.0ms
(+ (* 2.0 (+ (* t t) (* (/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x))) (/ (pow (cbrt l) 2) (cbrt x))))) (* 4.0 (/ (pow t 2) x)))
34.0ms
(/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x)))
18.0ms
(/ (pow t 2) x)
49.0ms
(sqrt (+ (* 2.0 (+ (* t t) (* (/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x))) (/ (pow (cbrt l) 2) (cbrt x))))) (* 4.0 (/ (pow t 2) x))))

series1.0s

Counts
4 → 12
Calls
4 calls:
188.0ms
(+ (* 2.0 (+ (* t t) (* (/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x))) (/ (pow (cbrt l) 2) (cbrt x))))) (* 4.0 (/ (pow t 2) x)))
224.0ms
(/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x)))
36.0ms
(/ (pow t 2) x)
563.0ms
(sqrt (+ (* 2.0 (+ (* t t) (* (/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x))) (/ (pow (cbrt l) 2) (cbrt x))))) (* 4.0 (/ (pow t 2) x))))

simplify2.6s

Counts
132 → 132
Iterations

Useful iterations: done (2.6s)

IterNodesCost
02883220
16702947
229762215
done50022129

prune1.4s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.8b

regimes1.4s

Accuracy

75.9% (5.9b remaining)

Error of 9.7b against oracle of 3.8b and baseline of 28.2b

bsearch903.0ms

Steps
ItersRangePoint
8
6.753203435084242e+100
2.2870795443321386e+105
1.5497059210109297e+104
7
-1.1980052479942145e+71
-3.057474683283312e+69
-5.89661864480626e+70

simplify46.0ms

Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
049117
163115
265113
done65113

end0.0ms

sample8.1s

Algorithm
intervals
Results
1.8s826×body1280valid
1.7s9955×body80nan
1.0s5080×body80valid
672.0ms1046×body640valid
482.0ms592×body1280nan
392.0ms693×body320valid
311.0ms370×body320nan
298.0ms591×body640nan
93.0ms178×body160nan
92.0ms355×body160valid