Details

Time bar (total: 28.4s)

sample315.0ms

Algorithm
intervals
Results
73.0ms34×body640nan
44.0ms318×body80nan
23.0ms166×body80valid
20.0ms32×body1280valid
13.0ms21×body1280nan
12.0ms24×body640valid
11.0ms27×body320valid
3.0ms9×body320nan
2.0ms7×body160valid
1.0ms4×body160nan

simplify3.7s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
01827
13927
29327
319827
443227
577727
6136727
7354627
done500027

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.5b

localize27.0ms

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))))
0.5b
(* (sqrt 2.0) t)
12.5b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
23.8b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite225.0ms

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:
71.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
22.0ms
(* (sqrt 2.0) t)
52.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
73.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series3.0s

Counts
4 → 12
Calls
4 calls:
736.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
58.0ms
(* (sqrt 2.0) t)
415.0ms
(- (* (/ (+ 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)))

simplify1.6s

Counts
92 → 92
Iterations

Useful iterations: 2 (443.0ms)

IterNodesCost
01682472
14572291
226272087
done50002087

prune504.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.8b

localize54.0ms

Local error

Found 4 expressions with local error:

4.7b
(+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x)))
5.3b
(/ (pow l 2) x)
10.2b
(/ (pow t 2) x)
30.5b
(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x))))

rewrite147.0ms

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:
54.0ms
(+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x)))
15.0ms
(/ (pow l 2) x)
9.0ms
(/ (pow t 2) x)
64.0ms
(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x))))

series566.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x)))
29.0ms
(/ (pow l 2) x)
24.0ms
(/ (pow t 2) x)
403.0ms
(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x))))

simplify1.8s

Counts
142 → 142
Iterations

Useful iterations: 2 (552.0ms)

IterNodesCost
02542312
15682086
229341875
done50001875

prune835.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.9b

localize29.0ms

Local error

Found 4 expressions with local error:

0.8b
(+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))
4.7b
(+ (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))) (* 4.0 (/ (pow t 2) x)))
10.2b
(/ (pow t 2) x)
30.5b
(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))) (* 4.0 (/ (pow t 2) x))))

rewrite269.0ms

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:
41.0ms
(+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))
68.0ms
(+ (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))) (* 4.0 (/ (pow t 2) x)))
18.0ms
(/ (pow t 2) x)
136.0ms
(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))) (* 4.0 (/ (pow t 2) x))))

series590.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))
118.0ms
(+ (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))) (* 4.0 (/ (pow t 2) x)))
21.0ms
(/ (pow t 2) x)
400.0ms
(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 (506.0ms)

IterNodesCost
02022323
14971966
224421646
done50011646

prune576.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.9b

localize51.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x))
4.7b
(+ (* 2.0 (+ (* t t) (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)))) (* 4.0 (/ (pow t 2) x)))
10.2b
(/ (pow t 2) x)
30.5b
(sqrt (+ (* 2.0 (+ (* t t) (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)))) (* 4.0 (/ (pow t 2) x))))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
101×add-sqr-sqrt
77×times-frac
56×unpow-prod-down
46×add-cube-cbrt *-un-lft-identity
37×associate-*r*
35×add-exp-log
24×unswap-sqr
22×cbrt-prod
18×sqr-pow
12×div-exp prod-exp
11×add-cbrt-cube unpow2
10×associate-*l*
9×associate-*r/
8×pow-to-exp pow-exp associate-/l*
6×add-log-exp
5×pow1
4×flip3-+ sqrt-div frac-add flip-+
3×associate-/r* sqrt-prod
2×cbrt-undiv associate-+l+ cbrt-unprod div-inv
1×+-commutative distribute-rgt-in rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 clear-num sum-log *-commutative
Counts
4 → 175
Calls
4 calls:
62.0ms
(* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x))
27.0ms
(+ (* 2.0 (+ (* t t) (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)))) (* 4.0 (/ (pow t 2) x)))
9.0ms
(/ (pow t 2) x)
21.0ms
(sqrt (+ (* 2.0 (+ (* t t) (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)))) (* 4.0 (/ (pow t 2) x))))

series665.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x))
138.0ms
(+ (* 2.0 (+ (* t t) (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)))) (* 4.0 (/ (pow t 2) x)))
40.0ms
(/ (pow t 2) x)
414.0ms
(sqrt (+ (* 2.0 (+ (* t t) (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)))) (* 4.0 (/ (pow t 2) x))))

simplify943.0ms

Counts
187 → 187
Iterations

Useful iterations: done (934.0ms)

IterNodesCost
03443840
19203482
done50012939

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.9b

regimes901.0ms

Accuracy

69.1% (7.3b remaining)

Error of 11.1b against oracle of 3.8b and baseline of 27.5b

bsearch2.2s

Steps
ItersRangePoint
8
1.6408579458501768e-121
4.556522159544336e-119
4.517101072782233e-119
9
2.0972313946662681e-184
1.2402052730190393e-177
5.156014301754716e-183
9
7.118961009208154e-257
8.264861022207576e-250
1.2838506268746495e-253
9
-3.148120069625892e-299
-2.2879652291577596e-306
-3.973880744580358e-300
8
-4.004652054920314e-256
-4.149126620126526e-259
-4.702934921132744e-259
10
-1.5855763995020358e-183
-8.487635768128844e-198
-3.093321223031471e-189
9
-2.9914453904952074e-147
-2.9474571731553717e-155
-2.995919227120962e-155
10
-1.0062559782947483e+141
-3.931503708037643e+123
-2.893044424140444e+127

simplify31.0ms

Iterations

Useful iterations: done (31.0ms)

IterNodesCost
067348
184301
289269
392269
done92268

end0.0ms

sample6.6s

Algorithm
intervals
Results
1.9s10100×body80nan
1.5s5124×body80valid
629.0ms838×body1280valid
569.0ms1025×body640valid
376.0ms630×body1280nan
227.0ms583×body640nan
186.0ms640×body320valid
82.0ms305×body320nan
74.0ms373×body160valid
31.0ms169×body160nan