Details

Time bar (total: 8.2s)

sample86.0ms

Algorithm
intervals
Results
20.0ms317×body80nan
8.0ms45×body640valid
8.0ms155×body80valid
5.0ms23×body1280valid
5.0ms22×body1280nan
4.0ms24×body640nan
3.0ms20×body320valid
2.0ms14×body320nan
1.0ms13×body160valid
1.0ms7×body160nan

simplify86.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03914
19314
219314
341414
471814
5119214
6281614
7500114
done500114

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.9b

localize18.0ms

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)
13.1b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
18.6b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite146.0ms

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:
55.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
10.0ms
(* (sqrt 2.0) t)
29.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
50.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.9s

Counts
4 → 12
Calls
4 calls:
435.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
41.0ms
(* (sqrt 2.0) t)
220.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.2s
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify59.0ms

Counts
92 → 92
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
04171207
120511099
250021094
done50021094

prune305.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 5.9b

localize17.0ms

Local error

Found 4 expressions with local error:

3.4b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
5.7b
(/ (pow l 2) x)
9.7b
(/ (pow t 2) x)
25.1b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite60.0ms

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:
18.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
8.0ms
(/ (pow l 2) x)
8.0ms
(/ (pow t 2) x)
21.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series276.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
19.0ms
(/ (pow l 2) x)
19.0ms
(/ (pow t 2) x)
167.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify60.0ms

Counts
142 → 142
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
05261067
12113984
25001978
done5001978

prune467.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.8b
(+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))
3.4b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))))
9.7b
(/ (pow t 2) x)
25.1b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity times-frac
23×add-sqr-sqrt
22×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×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 distribute-lft-out
Counts
4 → 93
Calls
4 calls:
56.0ms
(+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))
20.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))))
8.0ms
(/ (pow t 2) x)
17.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))

series291.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))
66.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))))
24.0ms
(/ (pow t 2) x)
161.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))

simplify55.0ms

Counts
105 → 105
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
04561099
119411003
25003982
done5003982

prune391.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.3b

localize22.0ms

Local error

Found 4 expressions with local error:

9.7b
(/ (pow t 2) x)
25.0b
(sqrt (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))
25.0b
(sqrt (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))
25.1b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (sqrt (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))) (sqrt (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))))

rewrite253.0ms

Algorithm
rewrite-expression-head
Rules
28×*-un-lft-identity
27×add-sqr-sqrt
26×sqrt-div
24×add-cube-cbrt times-frac
18×associate-*r/
12×unpow-prod-down
11×sqrt-prod
9×add-exp-log flip3-+ flip-+
8×frac-add associate-/l*
7×pow1
6×add-cbrt-cube
4×frac-times unpow2 add-log-exp sqr-pow
3×rem-sqrt-square sqrt-pow1 pow1/2 div-exp associate-/r*
2×associate-*l/ distribute-lft-out
1×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num div-inv
Counts
4 → 104
Calls
4 calls:
8.0ms
(/ (pow t 2) x)
105.0ms
(sqrt (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))
105.0ms
(sqrt (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))
31.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (sqrt (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))) (sqrt (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))))

series327.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(/ (pow t 2) x)
73.0ms
(sqrt (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))
67.0ms
(sqrt (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))
168.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (sqrt (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l)))) (sqrt (+ (pow t 2) (/ (pow l (/ 2 2)) (/ x l))))))))

simplify58.0ms

Counts
116 → 116
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
05111512
117881448
250011443
done50011443

prune491.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.3b

regimes407.0ms

Accuracy

77.2% (5.4b remaining)

Error of 9.4b against oracle of 4.0b and baseline of 27.9b

bsearch198.0ms

Steps
ItersRangePoint
9
2.0905671967622776e+119
1.7040592781240823e+127
1.4553050757724378e+123
8
-3.558670715240138e+83
-1.0288490828141835e+79
-1.9933181429979547e+82

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06358
16458
26458
done6458

end0.0ms

sample2.2s

Algorithm
intervals
Results
481.0ms10051×body80nan
256.0ms5103×body80valid
205.0ms1055×body640valid
188.0ms789×body1280valid
134.0ms600×body1280nan
109.0ms612×body640nan
94.0ms663×body320valid
46.0ms347×body320nan
40.0ms390×body160valid
16.0ms158×body160nan