Details

Time bar (total: 7.1s)

analyze971.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
0%99.9%0.1%7
0%74.9%25.1%8
0%74.9%25.1%9
9.4%65.5%25.1%10
9.4%53%37.6%11
14%48.4%37.6%12
16.4%46%37.6%13
16.4%39.8%43.8%14

sample64.0ms

Algorithm
intervals
Results
13.0ms175×body80valid
10.0ms35×body640valid
7.0ms20×body1280nan
6.0ms17×body1280valid
5.0ms21×body320valid
4.0ms16×body640nan
2.0ms31×body80nan
2.0ms9×body320nan
1.0ms8×body160valid
0.0ms3×body160nan

simplify25.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
0112727
1112727

prune15.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 41.4b

Counts
2 → 2

localize17.0ms

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))))
0.5b
(* (sqrt 2.0) t)
12.6b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.3b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite47.0ms

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 → 79
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))
12.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series346.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(/ (* (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)
56.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
194.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify56.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
049842021
149842021

prune215.0ms

Filtered
67 candidates to 91 candidates (-35.8%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New87491
Fresh101
Picked011
Done000
Total88593

Merged error: 4.1b

Counts
93 → 5

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt 2.0) t)
1.0b
(+ (* t t) (/ l (/ x l)))
3.4b
(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
27.9b
(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity associate-*r/ add-log-exp
7×pow1 sqrt-prod
6×add-exp-log associate-*l* add-cbrt-cube
5×flip3-+ flip-+
4×sqrt-div frac-add
3×associate-*r*
2×+-commutative associate-+r+ sum-log unswap-sqr
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod
Counts
4 → 65
Calls
4 calls:
4.0ms
(* (sqrt 2.0) t)
10.0ms
(+ (* t t) (/ l (/ x l)))
9.0ms
(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
9.0ms
(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

series54.0ms

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

simplify44.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
057311357

prune172.0ms

Filtered
61 candidates to 77 candidates (-26.2%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New70777
Fresh213
Picked101
Done011
Total73982

Merged error: 4.1b

Counts
82 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

3.4b
(+ (* 4.0 (/ t (/ x t))) (* 2.0 (* (sqrt (+ (* t t) (* l (/ l x)))) (sqrt (+ (* t t) (* l (/ l x)))))))
27.8b
(sqrt (+ (* t t) (* l (/ l x))))
27.8b
(sqrt (+ (* t t) (* l (/ l x))))
27.9b
(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (* (sqrt (+ (* t t) (* l (/ l x)))) (sqrt (+ (* t t) (* l (/ l x))))))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
38×sqrt-div
36×associate-*r/
16×flip3-+ frac-add flip-+
10×add-sqr-sqrt
9×sqrt-prod
8×frac-times
7×pow1 add-cube-cbrt *-un-lft-identity
6×add-log-exp
4×add-exp-log associate-*l/ add-cbrt-cube
3×rem-sqrt-square sqrt-pow1 pow1/2
1×+-commutative sum-log
Counts
4 → 72
Calls
4 calls:
11.0ms
(+ (* 4.0 (/ t (/ x t))) (* 2.0 (* (sqrt (+ (* t t) (* l (/ l x)))) (sqrt (+ (* t t) (* l (/ l x)))))))
4.0ms
(sqrt (+ (* t t) (* l (/ l x))))
4.0ms
(sqrt (+ (* t t) (* l (/ l x))))
12.0ms
(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (* (sqrt (+ (* t t) (* l (/ l x)))) (sqrt (+ (* t t) (* l (/ l x))))))))

series70.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(+ (* 4.0 (/ t (/ x t))) (* 2.0 (* (sqrt (+ (* t t) (* l (/ l x)))) (sqrt (+ (* t t) (* l (/ l x)))))))
14.0ms
(sqrt (+ (* t t) (* l (/ l x))))
14.0ms
(sqrt (+ (* t t) (* l (/ l x))))
27.0ms
(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (* (sqrt (+ (* t t) (* l (/ l x)))) (sqrt (+ (* t t) (* l (/ l x))))))))

simplify42.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
052122398

prune173.0ms

Filtered
65 candidates to 84 candidates (-29.2%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New84084
Fresh077
Picked011
Done011
Total84993

Merged error: 4.1b

Counts
93 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (sqrt 2.0)) (* t (sqrt (sqrt 2.0))))
1.0b
(+ (* t t) (/ l (/ x l)))
3.4b
(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
27.9b
(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
12×sqrt-prod
10×pow1
9×add-exp-log add-sqr-sqrt associate-*l* add-cbrt-cube
8×add-cube-cbrt *-un-lft-identity associate-*r/ add-log-exp
5×flip3-+ flip-+
4×sqrt-div frac-add
3×pow-prod-down prod-exp cbrt-unprod
2×+-commutative associate-+r+ sum-log
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 associate-*r* *-commutative
Counts
4 → 67
Calls
4 calls:
9.0ms
(* (sqrt (sqrt 2.0)) (* t (sqrt (sqrt 2.0))))
10.0ms
(+ (* t t) (/ l (/ x l)))
9.0ms
(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
8.0ms
(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

series56.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(* (sqrt (sqrt 2.0)) (* t (sqrt (sqrt 2.0))))
12.0ms
(+ (* t t) (/ l (/ x l)))
15.0ms
(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
25.0ms
(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

simplify40.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
055271378

prune165.0ms

Filtered
60 candidates to 79 candidates (-31.7%)
Pruning

12 alts after pruning (9 fresh and 3 done)

PrunedKeptTotal
New75479
Fresh156
Picked011
Done022
Total761288

Merged error: 4.1b

Counts
88 → 12

regimes784.0ms

Accuracy

77.9% (5.3b remaining)

Error of 9.2b against oracle of 3.9b and baseline of 27.7b

bsearch731.0ms

Steps
ItersRangePoint
10
1.3351783773904564e+100
2.3430025405351912e+111
9.838482525780048e+101
4
-3.5400301657293667e+106
-2.2829771165908745e+106
-3.0293523645168547e+106

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05195
15195

end0.0ms

analyze832.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
0%99.9%0.1%7
0%74.9%25.1%8
0%74.9%25.1%9
9.4%65.5%25.1%10
9.4%53%37.6%11
14%48.4%37.6%12
16.4%46%37.6%13
16.4%39.8%43.8%14

sample2.0s

Algorithm
intervals
Results
388.0ms5076×body80valid
307.0ms1058×body640valid
297.0ms832×body1280valid
207.0ms583×body1280nan
157.0ms558×body640nan
145.0ms669×body320valid
101.0ms1416×body80nan
69.0ms338×body320nan
54.0ms365×body160valid
24.0ms177×body160nan

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