Details

Time bar (total: 26.6s)

sample272.0ms

Algorithm
intervals
Results
61.0ms31×body1280valid
33.0ms288×body80nan
18.0ms155×body80valid
12.0ms20×body1280nan
11.0ms28×body640valid
10.0ms26×body640nan
9.0ms30×body320valid
3.0ms12×body160valid
2.0ms8×body320nan
0.0ms2×body160nan

simplify4.0s

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: 48.1b

localize22.0ms

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)
16.1b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
22.4b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite291.0ms

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:
97.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
25.0ms
(* (sqrt 2.0) t)
64.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
100.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.7s

Counts
4 → 12
Calls
4 calls:
583.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
56.0ms
(* (sqrt 2.0) t)
329.0ms
(- (* (/ (+ 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)))

simplify1.7s

Counts
92 → 92
Iterations

Useful iterations: 2 (438.0ms)

IterNodesCost
01682472
14572291
226272087
done50002087

prune529.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.6b

localize32.0ms

Local error

Found 4 expressions with local error:

3.8b
(+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x)))
8.3b
(/ (pow l 2) x)
9.8b
(/ (pow t 2) x)
29.7b
(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x))))

rewrite141.0ms

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:
56.0ms
(+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x)))
13.0ms
(/ (pow l 2) x)
9.0ms
(/ (pow t 2) x)
52.0ms
(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x))))

series549.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x)))
40.0ms
(/ (pow l 2) x)
26.0ms
(/ (pow t 2) x)
400.0ms
(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x))))

simplify1.6s

Counts
142 → 142
Iterations

Useful iterations: 2 (427.0ms)

IterNodesCost
02542312
15682086
229341875
done50001875

prune767.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.0b

localize47.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (* t t) (* (fabs l) (/ (fabs l) x)))
3.8b
(+ (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x)))) (* 4.0 (/ (pow t 2) x)))
9.8b
(/ (pow t 2) x)
29.7b
(sqrt (+ (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x)))) (* 4.0 (/ (pow t 2) x))))

rewrite113.0ms

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:
10.0ms
(+ (* t t) (* (fabs l) (/ (fabs l) x)))
32.0ms
(+ (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x)))) (* 4.0 (/ (pow t 2) x)))
19.0ms
(/ (pow t 2) x)
50.0ms
(sqrt (+ (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x)))) (* 4.0 (/ (pow t 2) x))))

series430.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(+ (* t t) (* (fabs l) (/ (fabs l) x)))
97.0ms
(+ (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x)))) (* 4.0 (/ (pow t 2) x)))
28.0ms
(/ (pow t 2) x)
260.0ms
(sqrt (+ (* 2.0 (+ (* t t) (* (fabs l) (/ (fabs l) x)))) (* 4.0 (/ (pow t 2) x))))

simplify2.1s

Counts
104 → 104
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02102171
15311901
229421732
done50021726

prune736.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.0b

localize50.0ms

Local error

Found 4 expressions with local error:

2.0b
(* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x))
3.8b
(+ (* 2.0 (+ (* t t) (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)))) (* 4.0 (/ (pow t 2) x)))
9.8b
(/ (pow t 2) x)
29.7b
(sqrt (+ (* 2.0 (+ (* t t) (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)))) (* 4.0 (/ (pow t 2) x))))

rewrite137.0ms

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:
59.0ms
(* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x))
37.0ms
(+ (* 2.0 (+ (* t t) (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)))) (* 4.0 (/ (pow t 2) x)))
14.0ms
(/ (pow t 2) x)
18.0ms
(sqrt (+ (* 2.0 (+ (* t t) (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)))) (* 4.0 (/ (pow t 2) x))))

series596.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x))
124.0ms
(+ (* 2.0 (+ (* t t) (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)))) (* 4.0 (/ (pow t 2) x)))
30.0ms
(/ (pow t 2) x)
389.0ms
(sqrt (+ (* 2.0 (+ (* t t) (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)))) (* 4.0 (/ (pow t 2) x))))

simplify537.0ms

Counts
187 → 187
Iterations

Useful iterations: done (531.0ms)

IterNodesCost
03443840
19203482
done50012939

prune1.4s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.0b

regimes772.0ms

Accuracy

77.8% (5.3b remaining)

Error of 9.2b against oracle of 3.9b and baseline of 27.8b

bsearch858.0ms

Steps
ItersRangePoint
6
5.7073382686318015e+118
6.873052400883988e+119
1.2779874262281365e+119
8
-1.2189785736955123e-260
-1.0581386398353699e-263
-1.323606909102099e-261
9
-2.2413056698092415e-178
-9.02348106815201e-184
-6.111047820265304e-179
9
-5.293841536497144e+53
-1.3313326719732008e+47
-2.6156735074350363e+50

simplify14.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
054190
168190
done68190

end0.0ms

sample6.3s

Algorithm
intervals
Results
2.0s9975×body80nan
721.0ms576×body640nan
604.0ms5071×body80valid
555.0ms886×body1280valid
476.0ms1002×body640valid
360.0ms564×body1280nan
202.0ms667×body320valid
140.0ms319×body320nan
116.0ms374×body160valid
33.0ms175×body160nan