Details

Time bar (total: 9.0s)

sample102.0ms

Algorithm
intervals
Results
21.0ms304×body80nan
18.0ms18×body320valid
12.0ms172×body80valid
9.0ms34×body640valid
7.0ms20×body1280valid
6.0ms17×body1280nan
3.0ms12×body640nan
2.0ms9×body320nan
2.0ms12×body160valid
0.0ms2×body160nan

simplify89.0ms

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 (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 43.5b

Counts
2 → 1

localize19.0ms

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)
13.0b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
22.5b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite57.0ms

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)
19.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
14.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.9s

Counts
4 → 12
Calls
4 calls:
424.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
39.0ms
(* (sqrt 2.0) t)
219.0ms
(- (* (/ (+ 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)))

simplify63.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
04171207
120511099
250021094

prune288.0ms

Filtered
92 candidates to 65 candidates (70.7%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New87592
Fresh000
Picked101
Done000
Total88593

Merged error: 6.4b

Counts
93 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

4.2b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
6.0b
(/ (pow l 2) x)
9.7b
(/ (pow t 2) x)
28.5b
(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:
8.0ms
(+ (* 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)))))

series266.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
23.0ms
(/ (pow l 2) x)
18.0ms
(/ (pow t 2) x)
163.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify68.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05261093
12235984
25001978

prune405.0ms

Filtered
142 candidates to 97 candidates (68.3%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1366142
Fresh134
Picked011
Done000
Total13710147

Merged error: 4.0b

Counts
147 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

0.8b
(+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
4.2b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
9.7b
(/ (pow t 2) x)
28.5b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

rewrite27.0ms

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 (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
8.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
5.0ms
(/ (pow t 2) x)
7.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

series337.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
83.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
18.0ms
(/ (pow t 2) x)
184.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

simplify67.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
04631308
119651213
250011210

prune330.0ms

Filtered
104 candidates to 73 candidates (70.2%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1040104
Fresh088
Picked011
Done011
Total10410114

Merged error: 4.0b

Counts
114 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

2.0b
(* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x))
4.2b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)))))
9.7b
(/ (pow t 2) x)
28.5b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x))))))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
101×add-sqr-sqrt
77×times-frac
56×unpow-prod-down
46×add-cube-cbrt *-un-lft-identity
37×associate-*r*
35×add-exp-log
24×unswap-sqr
22×cbrt-prod
18×sqr-pow
12×div-exp prod-exp
11×add-cbrt-cube unpow2
10×associate-*l*
9×associate-*r/
8×pow-to-exp pow-exp associate-/l*
6×add-log-exp
5×pow1
4×flip3-+ sqrt-div frac-add flip-+
3×associate-/r* sqrt-prod
2×cbrt-undiv associate-+r+ cbrt-unprod div-inv
1×+-commutative distribute-rgt-in rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 clear-num sum-log *-commutative
Counts
4 → 175
Calls
4 calls:
16.0ms
(* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x))
8.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)))))
5.0ms
(/ (pow t 2) x)
7.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x))))))

series349.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x))
91.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x)))))
18.0ms
(/ (pow t 2) x)
196.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (pow (cbrt l) 4) (/ (pow (cbrt l) 2) x))))))

simplify114.0ms

Algorithm
egg-herbie
Counts
187 → 187
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
08511971
138441773
250011684

prune590.0ms

Filtered
187 candidates to 122 candidates (65.2%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New1861187
Fresh167
Picked011
Done022
Total18710197

Merged error: 4.0b

Counts
197 → 10

regimes432.0ms

Accuracy

75.2% (6.0b remaining)

Error of 10.1b against oracle of 4.1b and baseline of 28.2b

bsearch773.0ms

Steps
ItersRangePoint
5
1.952280473510387e+112
5.406436796980895e+112
4.821310295058435e+112
8
3.1565074186698765e-188
1.1132744209343041e-184
7.352338276367582e-186
9
4.407973709519137e-253
4.3904410959619304e-246
2.567811084270563e-246
9
-1.0767111021961288e-270
-9.966878810300923e-279
-3.1169962438830795e-275
8
-1.0084933490494555e-137
-2.825285028898216e-142
-2.8738279771433875e-142
8
-1.1163809364810213e+60
-1.314515511745503e+56
-9.320808504410158e+59

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
086127
188127
288127

end0.0ms

sample2.7s

Algorithm
intervals
Results
673.0ms10035×body80nan
354.0ms5084×body80valid
280.0ms828×body1280valid
273.0ms1052×body640valid
204.0ms605×body1280nan
161.0ms624×body640nan
131.0ms667×body320valid
68.0ms354×body320nan
48.0ms369×body160valid
24.0ms186×body160nan

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