Details

Time bar (total: 27.9s)

sample294.0ms

Algorithm
intervals
Results
66.0ms22×body320valid
34.0ms294×body80nan
24.0ms160×body80valid
20.0ms32×body1280valid
17.0ms34×body640valid
10.0ms17×body1280nan
8.0ms17×body640nan
2.0ms8×body320nan
2.0ms8×body160valid
2.0ms7×body160nan

simplify3.9s

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
01827
13927
29327
319827
443227
577727
6136727
7354627
done500027

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (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)
12.9b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.0b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite202.0ms

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:
90.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
16.0ms
(* (sqrt 2.0) t)
34.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
58.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.8s

Counts
4 → 12
Calls
4 calls:
644.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
60.0ms
(* (sqrt 2.0) t)
344.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.8s
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify1.5s

Counts
92 → 92
Iterations

Useful iterations: 2 (418.0ms)

IterNodesCost
01682472
14572291
226272087
done50002087

prune494.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.1b

localize34.0ms

Local error

Found 4 expressions with local error:

4.4b
(+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x)))
5.0b
(/ (pow l 2) x)
10.9b
(/ (pow t 2) x)
28.5b
(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x))))

rewrite136.0ms

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:
32.0ms
(+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x)))
15.0ms
(/ (pow l 2) x)
18.0ms
(/ (pow t 2) x)
64.0ms
(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x))))

series580.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x)))
42.0ms
(/ (pow l 2) x)
34.0ms
(/ (pow t 2) x)
388.0ms
(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x))))

simplify1.7s

Counts
142 → 142
Iterations

Useful iterations: 2 (523.0ms)

IterNodesCost
02542312
15682086
229341875
done50001875

prune865.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.9b

localize52.0ms

Local error

Found 4 expressions with local error:

1.2b
(+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))
4.4b
(+ (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))) (* 4.0 (/ (pow t 2) x)))
10.9b
(/ (pow t 2) x)
28.5b
(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))) (* 4.0 (/ (pow t 2) x))))

rewrite252.0ms

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:
72.0ms
(+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))
73.0ms
(+ (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))) (* 4.0 (/ (pow t 2) x)))
11.0ms
(/ (pow t 2) x)
90.0ms
(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))) (* 4.0 (/ (pow t 2) x))))

series599.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))
119.0ms
(+ (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))) (* 4.0 (/ (pow t 2) x)))
26.0ms
(/ (pow t 2) x)
390.0ms
(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))) (* 4.0 (/ (pow t 2) x))))

simplify1.5s

Counts
104 → 104
Iterations

Useful iterations: 2 (547.0ms)

IterNodesCost
02022323
14971966
224421646
done50011646

prune694.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.9b

localize56.0ms

Local error

Found 4 expressions with local error:

1.4b
(/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2)))
4.4b
(+ (* 2.0 (+ (* t t) (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))) (* 4.0 (/ (pow t 2) x)))
10.9b
(/ (pow t 2) x)
28.5b
(sqrt (+ (* 2.0 (+ (* t t) (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))) (* 4.0 (/ (pow t 2) x))))

rewrite364.0ms

Algorithm
rewrite-expression-head
Rules
477×times-frac
208×add-sqr-sqrt
207×add-cube-cbrt *-un-lft-identity
176×unpow-prod-down
63×cbrt-prod unpow2 sqr-pow
49×add-exp-log
40×associate-/r*
31×div-exp
14×associate-/l*
13×pow-exp
11×add-cbrt-cube
9×pow-to-exp div-inv
8×associate-*r/
6×add-log-exp
5×pow1
4×cbrt-undiv flip3-+ sqrt-div frac-add prod-exp flip-+
3×sqrt-prod
2×associate-+l+ frac-2neg clear-num
1×+-commutative distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 sum-log associate-/r/
Counts
4 → 375
Calls
4 calls:
35.0ms
(/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2)))
92.0ms
(+ (* 2.0 (+ (* t t) (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))) (* 4.0 (/ (pow t 2) x)))
11.0ms
(/ (pow t 2) x)
190.0ms
(sqrt (+ (* 2.0 (+ (* t t) (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))) (* 4.0 (/ (pow t 2) x))))

series612.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2)))
129.0ms
(+ (* 2.0 (+ (* t t) (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))) (* 4.0 (/ (pow t 2) x)))
36.0ms
(/ (pow t 2) x)
382.0ms
(sqrt (+ (* 2.0 (+ (* t t) (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))) (* 4.0 (/ (pow t 2) x))))

simplify1.6s

Counts
387 → 387
Iterations

Useful iterations: done (1.6s)

IterNodesCost
070110745
120228678
done50017804

prune1.7s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.9b

regimes843.0ms

Accuracy

74.3% (6.1b remaining)

Error of 10.1b against oracle of 3.9b and baseline of 27.8b

bsearch402.0ms

Steps
ItersRangePoint
4
3.6682554499002217e+39
5.731397073736236e+39
4.568115772869942e+39
9
-1.9548292921352193e-18
-3.0117965680222497e-24
-1.9221230409501015e-18

simplify21.0ms

Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
049117
163115
265113
done65113

end0.0ms

sample6.6s

Algorithm
intervals
Results
1.8s10085×body80nan
1.1s868×body1280valid
900.0ms5076×body80valid
521.0ms1034×body640valid
356.0ms660×body320valid
317.0ms695×body640nan
297.0ms589×body1280nan
95.0ms322×body320nan
79.0ms362×body160valid
38.0ms196×body160nan