Details

Time bar (total: 26.5s)

sample439.0ms

Algorithm
intervals
Results
145.0ms323×body80nan
54.0ms32×body1280valid
22.0ms41×body640valid
21.0ms154×body80valid
17.0ms34×body640nan
9.0ms13×body1280nan
9.0ms20×body320valid
4.0ms11×body320nan
2.0ms9×body160valid
1.0ms4×body160nan

simplify3.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
01827
13927
29327
319927
442327
579727
6144927
7379927
done500027

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.6b

localize32.0ms

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)
13.9b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
18.3b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite152.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×sqrt-prod
12×*-un-lft-identity add-cube-cbrt
11×add-cbrt-cube add-exp-log
7×pow1
6×associate-/r* times-frac associate-*l* 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 rem-sqrt-square clear-num sub-neg frac-2neg distribute-lft-in sqrt-pow1 pow1/2 diff-log pow-prod-down *-commutative div-inv associate-/l*
Counts
4 → 80
Calls
4 calls:
56.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
8.0ms
(* (sqrt 2.0) t)
30.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
52.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.7s

Counts
4 → 12
Calls
4 calls:
590.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
59.0ms
(* (sqrt 2.0) t)
328.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.7s
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify1.3s

Counts
92 → 92
Iterations

Useful iterations: 2 (380.0ms)

IterNodesCost
01672472
14552291
226192087
done50002087

prune600.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.9b

localize50.0ms

Local error

Found 4 expressions with local error:

3.4b
(+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x)))
6.6b
(/ (pow l 2) x)
7.3b
(/ (pow t 2) x)
28.2b
(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x))))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
48×times-frac
40×add-sqr-sqrt
39×*-un-lft-identity add-cube-cbrt
24×unpow-prod-down
16×associate-/l*
14×add-exp-log
8×add-cbrt-cube associate-*r/ unpow2 sqr-pow
6×associate-/r* div-exp add-log-exp
5×pow1
4×flip3-+ sqrt-div frac-add flip-+
3×sqrt-prod
2×pow-to-exp cbrt-undiv associate-+l+ clear-num frac-2neg pow-exp div-inv
1×distribute-rgt-in +-commutative rem-sqrt-square sum-log distribute-lft-in sqrt-pow1 pow1/2
Counts
4 → 130
Calls
4 calls:
37.0ms
(+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x)))
14.0ms
(/ (pow l 2) x)
14.0ms
(/ (pow t 2) x)
62.0ms
(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x))))

series585.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x)))
28.0ms
(/ (pow l 2) x)
29.0ms
(/ (pow t 2) x)
426.0ms
(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x))))

simplify1.4s

Counts
142 → 142
Iterations

Useful iterations: 2 (437.0ms)

IterNodesCost
02532312
15642092
226571875
done50001875

prune993.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.5b

localize41.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (* t t) (/ l (/ x l)))
3.4b
(+ (* 2.0 (+ (* t t) (/ l (/ x l)))) (* 4.0 (/ (pow t 2) x)))
7.3b
(/ (pow t 2) x)
28.2b
(sqrt (+ (* 2.0 (+ (* t t) (/ l (/ x l)))) (* 4.0 (/ (pow t 2) x))))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
23×add-sqr-sqrt
22×*-un-lft-identity add-cube-cbrt
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×associate-/r* div-exp sqrt-prod
2×+-commutative associate-+l+ sum-log
1×distribute-rgt-in pow-to-exp cbrt-undiv rem-sqrt-square clear-num frac-2neg distribute-lft-in sqrt-pow1 pow1/2 pow-exp div-inv
Counts
4 → 92
Calls
4 calls:
31.0ms
(+ (* t t) (/ l (/ x l)))
25.0ms
(+ (* 2.0 (+ (* t t) (/ l (/ x l)))) (* 4.0 (/ (pow t 2) x)))
10.0ms
(/ (pow t 2) x)
61.0ms
(sqrt (+ (* 2.0 (+ (* t t) (/ l (/ x l)))) (* 4.0 (/ (pow t 2) x))))

series557.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(+ (* t t) (/ l (/ x l)))
106.0ms
(+ (* 2.0 (+ (* t t) (/ l (/ x l)))) (* 4.0 (/ (pow t 2) x)))
36.0ms
(/ (pow t 2) x)
366.0ms
(sqrt (+ (* 2.0 (+ (* t t) (/ l (/ x l)))) (* 4.0 (/ (pow t 2) x))))

simplify1.2s

Counts
104 → 104
Iterations

Useful iterations: 2 (409.0ms)

IterNodesCost
01991991
14911814
223321652
done50021652

prune812.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.5b

localize74.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (* t t) (* (/ (fabs l) (* (cbrt x) (cbrt x))) (/ (fabs l) (cbrt x))))
3.4b
(+ (* 2.0 (+ (* t t) (* (/ (fabs l) (* (cbrt x) (cbrt x))) (/ (fabs l) (cbrt x))))) (* 4.0 (/ (pow t 2) x)))
7.3b
(/ (pow t 2) x)
28.2b
(sqrt (+ (* 2.0 (+ (* t t) (* (/ (fabs l) (* (cbrt x) (cbrt x))) (/ (fabs l) (cbrt x))))) (* 4.0 (/ (pow t 2) x))))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
23×add-sqr-sqrt
22×*-un-lft-identity add-cube-cbrt
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×associate-/r* div-exp sqrt-prod
2×+-commutative associate-+l+ sum-log
1×distribute-rgt-in pow-to-exp cbrt-undiv rem-sqrt-square clear-num frac-2neg distribute-lft-in sqrt-pow1 pow1/2 pow-exp div-inv
Counts
4 → 92
Calls
4 calls:
7.0ms
(+ (* t t) (* (/ (fabs l) (* (cbrt x) (cbrt x))) (/ (fabs l) (cbrt x))))
13.0ms
(+ (* 2.0 (+ (* t t) (* (/ (fabs l) (* (cbrt x) (cbrt x))) (/ (fabs l) (cbrt x))))) (* 4.0 (/ (pow t 2) x)))
16.0ms
(/ (pow t 2) x)
26.0ms
(sqrt (+ (* 2.0 (+ (* t t) (* (/ (fabs l) (* (cbrt x) (cbrt x))) (/ (fabs l) (cbrt x))))) (* 4.0 (/ (pow t 2) x))))

series520.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(+ (* t t) (* (/ (fabs l) (* (cbrt x) (cbrt x))) (/ (fabs l) (cbrt x))))
122.0ms
(+ (* 2.0 (+ (* t t) (* (/ (fabs l) (* (cbrt x) (cbrt x))) (/ (fabs l) (cbrt x))))) (* 4.0 (/ (pow t 2) x)))
22.0ms
(/ (pow t 2) x)
306.0ms
(sqrt (+ (* 2.0 (+ (* t t) (* (/ (fabs l) (* (cbrt x) (cbrt x))) (/ (fabs l) (cbrt x))))) (* 4.0 (/ (pow t 2) x))))

simplify1.5s

Counts
104 → 104
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02122752
15402511
229092231
done50012222

prune1.0s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.5b

regimes1.0s

Accuracy

74.9% (5.9b remaining)

Error of 9.9b against oracle of 3.9b and baseline of 27.6b

bsearch1.6s

Steps
ItersRangePoint
6
8.623848016624398e+24
9.25260478315882e+25
9.046331744575269e+25
9
5.484638728691009e-165
1.2245728681896357e-155
5.50990658974305e-162
9
1.1519454628559112e-253
1.131608625978812e-245
1.1078784155040597e-245
4
-2.096749817466635e-267
-1.3269116759083333e-267
-1.6506396057830864e-267
3
-1.0354862889270409e-218
-7.765673620927192e-219
-9.222092584370252e-219
7
-3.1546277032128373e+125
-9.219607530101453e+123
-1.4587104671199554e+125

simplify10.0ms

Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
078295
1102254
done102254

end0.0ms

sample6.2s

Algorithm
intervals
Results
1.8s9978×body80nan
1.0s856×body1280valid
801.0ms5077×body80valid
587.0ms1084×body640valid
348.0ms601×body1280nan
254.0ms620×body320valid
227.0ms589×body640nan
125.0ms363×body160valid
94.0ms329×body320nan
29.0ms161×body160nan