Details

Time bar (total: 5.9s)

analyze927.0ms (15.8%)

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

sample67.0ms (1.1%)

Algorithm
intervals
Results
12.0ms166×body80valid
10.0ms37×body640valid
8.0ms23×body1280valid
7.0ms22×body1280nan
6.0ms22×body640nan
4.0ms19×body320valid
4.0ms56×body80nan
2.0ms12×body320nan
1.0ms11×body160valid
1.0msbody160nan

simplify39.0ms (0.7%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
0522527

prune10.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 44.0b

Counts
2 → 1

localize17.0ms (0.3%)

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))
21.5b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite50.0ms (0.8%)

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
pow1
times-frac associate-*l* associate-/r* add-log-exp
sqrt-div
flip3-- associate-*r* flip--
cbrt-undiv div-exp prod-exp associate--l+ associate-/r/ cbrt-unprod unswap-sqr
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:

17.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
13.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
13.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))
4.0ms
(* (sqrt 2.0) t)

series342.0ms (5.8%)

Counts
4 → 12
Calls

4 calls:

191.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))
91.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
56.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
4.0ms
(* (sqrt 2.0) t)

simplify42.0ms (0.7%)

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
050442021

prune267.0ms (4.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New85691
Fresh000
Picked101
Done000
Total86692

Merged error: 6.4b

Counts
92 → 6

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

3.8b
(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* t t) (/ (* l l) x))))
5.9b
(/ (* l l) x)
8.6b
(/ (* t t) x)
29.0b
(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* t t) (/ (* l l) x)))))

rewrite26.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-cbrt-cube
10×add-sqr-sqrt
add-cube-cbrt *-un-lft-identity
associate-*r/
times-frac associate-/r* add-log-exp
pow1
cbrt-undiv flip3-+ sqrt-div div-exp frac-add flip-+
sqrt-prod
associate-+r+ frac-2neg prod-exp clear-num cbrt-unprod div-inv associate-/l*
+-commutative distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 sum-log
Counts
4 → 74
Calls

4 calls:

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

series47.0ms (0.8%)

Counts
4 → 12
Calls

4 calls:

25.0ms
(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* t t) (/ (* l l) x)))))
15.0ms
(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* t t) (/ (* l l) x))))
3.0ms
(/ (* t t) x)
3.0ms
(/ (* l l) x)

simplify56.0ms (0.9%)

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
049751345
149751345

prune217.0ms (3.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New80686
Fresh055
Picked101
Done000
Total811192

Merged error: 4.0b

Counts
92 → 11

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt 2.0) t)
3.8b
(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* t t) (* l (/ l x)))))
8.6b
(/ (* t t) x)
29.0b
(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* t t) (* l (/ l x))))))

rewrite26.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
11×add-exp-log add-cbrt-cube
10×add-cube-cbrt *-un-lft-identity
associate-*r/
pow1 sqrt-prod
associate-*l* add-log-exp
flip3-+ sqrt-div frac-add flip-+
times-frac associate-*r* associate-/r*
cbrt-undiv associate-+r+ div-exp prod-exp cbrt-unprod unswap-sqr
+-commutative distribute-rgt-in rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down clear-num sum-log *-commutative div-inv associate-/l*
Counts
4 → 75
Calls

4 calls:

8.0ms
(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* t t) (* l (/ l x)))))
8.0ms
(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* t t) (* l (/ l x))))))
5.0ms
(/ (* t t) x)
4.0ms
(* (sqrt 2.0) t)

series47.0ms (0.8%)

Counts
4 → 12
Calls

4 calls:

25.0ms
(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* t t) (* l (/ l x))))))
15.0ms
(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* t t) (* l (/ l x)))))
4.0ms
(* (sqrt 2.0) t)
3.0ms
(/ (* t t) x)

simplify26.0ms (0.4%)

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 0 (17.0ms)

IterNodesCost
050581337

prune221.0ms (3.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New86187
Fresh1910
Picked011
Done000
Total871198

Merged error: 4.0b

Counts
98 → 11

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt x) (cbrt x))
3.8b
(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
8.6b
(/ (* t t) x)
29.0b
(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

rewrite30.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
16×cbrt-prod
15×add-cube-cbrt *-un-lft-identity
12×pow1
11×add-exp-log
add-cbrt-cube
associate-*r/
pow1/3 swap-sqr associate-*r* associate-*l* add-log-exp
flip3-+ sqrt-div frac-add flip-+ unswap-sqr
times-frac associate-/r* sqrt-prod
cbrt-undiv associate-+r+ div-exp pow-prod-down prod-exp pow-sqr pow-prod-up cbrt-unprod
+-commutative pow2 distribute-rgt-in rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow-plus pow1/2 clear-num sum-log *-commutative div-inv associate-/l*
Counts
4 → 93
Calls

4 calls:

8.0ms
(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
8.0ms
(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))
6.0ms
(/ (* t t) x)
6.0ms
(* (cbrt x) (cbrt x))

series77.0ms (1.3%)

Counts
4 → 12
Calls

4 calls:

29.0ms
(* (cbrt x) (cbrt x))
28.0ms
(sqrt (+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))
18.0ms
(+ (* 4.0 (/ (* t t) x)) (* 2.0 (+ (* t t) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
3.0ms
(/ (* t t) x)

simplify45.0ms (0.8%)

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
050011771

prune203.0ms (3.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New1041105
Fresh189
Picked011
Done011
Total10511116

Merged error: 4.0b

Counts
116 → 11

regimes654.0ms (11.1%)

Accuracy

Total 5.6b remaining (59.9%)

Threshold costs 0b (0%)

bsearch475.0ms (8.1%)

Steps
ItersRangePoint
5
5.755926755557875e+106
1.6559792646790436e+107
1.400943711969558e+107
8
1.4474758852172723e-170
1.3099153101412675e-167
1.4633199475026642e-170
8
4.031360803645653e-277
1.7202346864725826e-273
1.6984376092331043e-273
5
-1.6375116051793367e-280
-7.230139701499095e-281
-1.6173039977917613e-280
5
-4.3996886225171295e-246
-1.603266749035457e-246
-1.6304660526178e-246
7
-2.2376876751237564e+75
-5.873251286343534e+73
-2.0540059517808046e+75

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0154183
1154183

end0.0ms (0%)

sample1.9s (32.4%)

Algorithm
intervals
Results
370.0ms5140×body80valid
299.0ms871×body1280valid
261.0ms994×body640valid
185.0ms561×body1280nan
157.0ms595×body640nan
129.0ms651×body320valid
99.0ms1421×body80nan
65.0ms325×body320nan
46.0ms344×body160valid
23.0ms179×body160nan

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