Details

Time bar (total: 28.0s)

sample431.0ms

Algorithm
intervals
Results
120.0ms31×body1280valid
44.0ms20×body640nan
40.0ms301×body80nan
35.0ms10×body160nan
21.0ms160×body80valid
15.0ms28×body640valid
12.0ms18×body1280nan
10.0ms26×body320valid
7.0ms15×body320nan
3.0ms11×body160valid

simplify5.9s

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
01827
13927
29327
318927
439727
566127
6112227
7262427
8413127
done500027

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 46.2b

localize34.0ms

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)))

rewrite218.0ms

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:
85.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
11.0ms
(* (sqrt 2.0) t)
38.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
78.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series3.3s

Counts
4 → 12
Calls
4 calls:
676.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
72.0ms
(* (sqrt 2.0) t)
356.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
2.2s
(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

prune469.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 5.4b

localize45.0ms

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)))))

rewrite129.0ms

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:
46.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))
18.0ms
(/ (pow l 2) x)
17.0ms
(/ (pow t 2) x)
41.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x)))))

series341.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l 2) x))))
25.0ms
(/ (pow l 2) x)
28.0ms
(/ (pow t 2) x)
198.0ms
(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

prune802.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.8b

localize46.0ms

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))))))

rewrite123.0ms

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:
60.0ms
(+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))
22.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))))
17.0ms
(/ (pow t 2) x)
21.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l))))))

series465.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))
89.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l)))))
35.0ms
(/ (pow t 2) x)
284.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (/ (pow l (/ 2 2)) (/ x l))))))

simplify1.3s

Counts
104 → 104
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02002320
14671956
216161639
done50001625

prune552.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.8b

localize44.0ms

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)))))))

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:
9.0ms
(+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
31.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
18.0ms
(/ (pow t 2) x)
37.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

series568.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
114.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
30.0ms
(/ (pow t 2) x)
323.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

simplify1.3s

Counts
104 → 104
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02002563
14752316
217282084
done50012029

prune631.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 2.8b

regimes527.0ms

Accuracy

76.5% (5.7b remaining)

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

bsearch878.0ms

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

simplify11.0ms

Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
050182
160178
262174
done62174

end0.0ms

sample7.1s

Algorithm
intervals
Results
2.0s10206×body80nan
1.1s1024×body640valid
869.0ms581×body1280nan
788.0ms5116×body80valid
646.0ms867×body1280valid
266.0ms599×body640nan
195.0ms630×body320valid
144.0ms346×body320nan
73.0ms363×body160valid
38.0ms198×body160nan