Details

Time bar (total: 26.6s)

sample187.0ms

Algorithm
intervals
Results
62.0ms301×body80nan
11.0ms160×body80valid
11.0ms31×body1280valid
11.0ms18×body1280nan
8.0ms28×body640valid
5.0ms20×body640nan
5.0ms26×body320valid
3.0ms15×body320nan
1.0ms11×body160valid
1.0ms10×body160nan

simplify6.1s

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: 46.2b

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))))
0.4b
(* (sqrt 2.0) t)
14.0b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
22.8b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite250.0ms

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:
91.0ms
(/ (* (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)
67.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
64.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.7s

Counts
4 → 12
Calls
4 calls:
605.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
80.0ms
(* (sqrt 2.0) t)
306.0ms
(- (* (/ (+ 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: done (1.3s)

IterNodesCost
01682472
14142283
215522077
done50002025

prune405.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 5.4b

localize25.0ms

Local error

Found 4 expressions with local error:

3.8b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))
6.6b
(/ (pow l 2) x)
11.1b
(/ (pow t 2) x)
29.2b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))

rewrite92.0ms

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:
34.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))
18.0ms
(/ (pow l 2) x)
15.0ms
(/ (pow t 2) x)
20.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))

series333.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))
20.0ms
(/ (pow l 2) x)
20.0ms
(/ (pow t 2) x)
202.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))

simplify1.3s

Counts
142 → 142
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02542317
15352084
217251868
done50011862

prune721.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.8b

localize36.0ms

Local error

Found 4 expressions with local error:

0.6b
(+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))
3.8b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))))
11.1b
(/ (pow t 2) x)
29.2b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l))))))

rewrite102.0ms

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:
41.0ms
(+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))
26.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))))
12.0ms
(/ (pow t 2) x)
20.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l))))))

series444.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))
112.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))))
20.0ms
(/ (pow t 2) x)
245.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l))))))

simplify1.3s

Counts
104 → 104
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02002320
14671956
216161639
done50001625

prune570.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.8b

localize61.0ms

Local error

Found 4 expressions with local error:

0.6b
(+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
3.8b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
11.1b
(/ (pow t 2) x)
29.2b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

rewrite104.0ms

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:
10.0ms
(+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
24.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
28.0ms
(/ (pow t 2) x)
38.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

series485.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
133.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
22.0ms
(/ (pow t 2) x)
244.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

simplify1.4s

Counts
104 → 104
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02002563
14752316
217282084
done50012029

prune1.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 2.8b

regimes623.0ms

Accuracy

76.5% (5.7b remaining)

Error of 9.6b against oracle of 4.0b and baseline of 28.1b

bsearch793.0ms

Steps
ItersRangePoint
7
3.5982350656865885e+59
1.9521708875942868e+61
6.84155195153334e+60
9
-1.6826171280496676e-273
-8.479631811913159e-279
-3.6001123721869805e-276
9
-3.6665974651226154e-165
-3.612130989595206e-170
-7.265062434046063e-166
3
-1.516374921943784e+82
-1.2093633317186018e+82
-1.49718669755471e+82

simplify12.0ms

Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
050182
160178
262174
done62174

end0.0ms

sample6.1s

Algorithm
intervals
Results
2.2s10206×body80nan
891.0ms5116×body80valid
542.0ms867×body1280valid
496.0ms1024×body640valid
441.0ms578×body1280nan
348.0ms601×body640nan
214.0ms630×body320valid
161.0ms347×body320nan
76.0ms363×body160valid
37.0ms198×body160nan