Details

Time bar (total: 6.0s)

sample288.0ms

Algorithm
intervals
Results
193.0ms20×body640nan
23.0ms331×body80nan
12.0ms173×body80valid
8.0ms28×body640valid
7.0ms21×body1280valid
7.0ms19×body1280nan
4.0ms19×body320valid
3.0ms14×body320nan
2.0ms15×body160valid
1.0ms4×body160nan

simplify86.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03914
19314
219314
341414
471814
5119214
6281614
7500114

prune5.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 43.1b

Counts
2 → 1

localize26.0ms

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)
13.8b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
23.6b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite51.0ms

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:
16.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
4.0ms
(* (sqrt 2.0) t)
12.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
15.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series353.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
4.0ms
(* (sqrt 2.0) t)
58.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
201.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify61.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
04171207
120511099
250021094

prune208.0ms

Filtered
92 candidates to 65 candidates (29.3%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New88492
Fresh000
Picked101
Done000
Total89493

Merged error: 8.2b

Counts
93 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

5.0b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
6.7b
(/ (pow l 2) x)
10.6b
(/ (pow t 2) x)
30.2b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite30.0ms

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:
9.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
5.0ms
(/ (pow l 2) x)
5.0ms
(/ (pow t 2) x)
7.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series49.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
3.0ms
(/ (pow l 2) x)
3.0ms
(/ (pow t 2) x)
24.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify63.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05261067
12113984
25001978

prune340.0ms

Filtered
142 candidates to 97 candidates (31.7%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1375142
Fresh033
Picked101
Done000
Total1388146

Merged error: 5.3b

Counts
146 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b
(+ (pow t 2) (* l (/ l x)))
5.0b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
10.6b
(/ (pow t 2) x)
30.2b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

rewrite28.0ms

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:
4.0ms
(+ (pow t 2) (* l (/ l x)))
9.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
5.0ms
(/ (pow t 2) x)
7.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

series53.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(+ (pow t 2) (* l (/ l x)))
14.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
3.0ms
(/ (pow t 2) x)
27.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

simplify60.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0456925
11936858
25003855

prune233.0ms

Filtered
104 candidates to 75 candidates (27.9%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1031104
Fresh077
Picked011
Done000
Total1039112

Merged error: 5.3b

Counts
112 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b
(+ (pow t 2) (/ l (/ x l)))
5.0b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
10.6b
(/ (pow t 2) x)
30.2b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

rewrite45.0ms

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:
20.0ms
(+ (pow t 2) (/ l (/ x l)))
9.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
5.0ms
(/ (pow t 2) x)
9.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

series53.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(+ (pow t 2) (/ l (/ x l)))
17.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
3.0ms
(/ (pow t 2) x)
25.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

simplify57.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0453932
11835862
25001859

prune199.0ms

Filtered
105 candidates to 76 candidates (27.6%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1032105
Fresh167
Picked011
Done011
Total10410114

Merged error: 5.3b

Counts
114 → 10

regimes572.0ms

Accuracy

76.1% (5.7b remaining)

Error of 9.2b against oracle of 3.5b and baseline of 27.6b

bsearch150.0ms

Steps
ItersRangePoint
10
4.9301397366023513e-08
127140.91663662092
125819.77308325299
10
-5.0359879015660543e+89
-5.936058177369249e+79
-4.9949879458135887e+89

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06057
16057

end0.0ms

sample2.9s

Algorithm
intervals
Results
696.0ms9990×body80nan
365.0ms5165×body80valid
278.0ms821×body1280valid
266.0ms993×body640valid
214.0ms626×body1280nan
155.0ms583×body640nan
126.0ms622×body320valid
69.0ms345×body320nan
55.0ms399×body160valid
24.0ms181×body160nan

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