Details

Time bar (total: 27.3s)

sample258.0ms

Algorithm
intervals
Results
84.0ms322×body80nan
18.0ms167×body80valid
15.0ms35×body640valid
10.0ms20×body1280valid
7.0ms13×body1280nan
6.0ms19×body320valid
5.0ms14×body640nan
4.0ms14×body320nan
3.0ms15×body160valid
2.0ms8×body160nan

simplify6.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
01827
13927
29327
318927
439727
566127
6112227
7262427
8413127
done500027

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.5b

localize26.0ms

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)
12.7b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
24.0b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite237.0ms

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:
89.0ms
(/ (* (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)
39.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
82.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.8s

Counts
4 → 12
Calls
4 calls:
614.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
53.0ms
(* (sqrt 2.0) t)
383.0ms
(- (* (/ (+ 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)))

simplify1.4s

Counts
92 → 92
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01682472
14142283
215522077
done50002025

prune461.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.8b

localize23.0ms

Local error

Found 4 expressions with local error:

5.5b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))
5.5b
(/ (pow l 2) x)
10.0b
(/ (pow t 2) x)
29.5b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))

rewrite95.0ms

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-+r+ 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:
27.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))
17.0ms
(/ (pow l 2) x)
17.0ms
(/ (pow t 2) x)
29.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))

series352.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))
34.0ms
(/ (pow l 2) x)
22.0ms
(/ (pow t 2) x)
212.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))

simplify1.2s

Counts
142 → 142
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02542317
15352084
217251868
done50011862

prune736.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.8b

localize55.0ms

Local error

Found 4 expressions with local error:

0.6b
(+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))
5.5b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))))
10.0b
(/ (pow t 2) x)
29.5b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l))))))

rewrite120.0ms

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-+r+ 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:
45.0ms
(+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))
32.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))))
9.0ms
(/ (pow t 2) x)
28.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l))))))

series490.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))
117.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))))
24.0ms
(/ (pow t 2) x)
284.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l))))))

simplify1.6s

Counts
104 → 104
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02002320
14671956
216161639
done50001625

prune610.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.8b

localize90.0ms

Local error

Found 4 expressions with local error:

4.4b
(/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x)))
5.5b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x))) (/ (pow (cbrt l) 2) (cbrt x))))))
10.0b
(/ (pow t 2) x)
29.5b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x))) (/ (pow (cbrt l) 2) (cbrt x)))))))

rewrite81.0ms

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-+r+ 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:
19.0ms
(/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x)))
17.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x))) (/ (pow (cbrt l) 2) (cbrt x))))))
9.0ms
(/ (pow t 2) x)
33.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x))) (/ (pow (cbrt l) 2) (cbrt x)))))))

series601.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x)))
137.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x))) (/ (pow (cbrt l) 2) (cbrt x))))))
21.0ms
(/ (pow t 2) x)
295.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ (pow (cbrt l) 4) (* (cbrt x) (cbrt x))) (/ (pow (cbrt l) 2) (cbrt x)))))))

simplify1.5s

Counts
132 → 132
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02863199
16432893
220942178
done50002098

prune848.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.8b

regimes730.0ms

Accuracy

78.1% (5.2b remaining)

Error of 9.0b against oracle of 3.9b and baseline of 27.5b

bsearch321.0ms

Steps
ItersRangePoint
4
2.8615303770675884e+117
4.371962998755528e+117
3.380741590772817e+117
8
-2.123549231421323e+124
-2.3823582692630786e+120
-3.696744411039917e+122

simplify13.0ms

Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
044109
154107
256105
done56105

end0.0ms

sample6.2s

Algorithm
intervals
Results
2.1s10131×body80nan
783.0ms5121×body80valid
506.0ms1035×body640valid
430.0ms881×body1280valid
415.0ms608×body1280nan
368.0ms611×body320valid
268.0ms613×body640nan
159.0ms352×body160valid
135.0ms362×body320nan
38.0ms156×body160nan