Details

Time bar (total: 5.9s)

sample108.0ms

Algorithm
intervals
Results
30.0ms351×body80nan
11.0ms155×body80valid
10.0ms37×body640valid
9.0ms27×body1280valid
9.0ms26×body1280nan
6.0ms30×body320valid
6.0ms22×body640nan
3.0ms14×body320nan
1.0ms7×body160valid
1.0ms5×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: 43.9b

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)
12.8b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
19.1b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite58.0ms

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:
17.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
5.0ms
(* (sqrt 2.0) t)
13.0ms
(- (* (/ (+ 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)))

series1.9s

Counts
4 → 12
Calls
4 calls:
440.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
46.0ms
(* (sqrt 2.0) t)
221.0ms
(- (* (/ (+ 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)))

simplify62.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
04171207
120511099
250021094

prune290.0ms

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: 5.4b

Counts
93 → 5

localize21.0ms

Local error

Found 4 expressions with local error:

2.8b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
5.0b
(/ (pow l 2) x)
10.2b
(/ (pow t 2) x)
27.0b
(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)))))

series274.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(+ (* 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)
169.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify64.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05261093
12235984
25001978

prune435.0ms

Filtered
142 candidates to 97 candidates (68.3%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1357142
Fresh134
Picked101
Done000
Total13710147

Merged error: 3.7b

Counts
147 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

1.4b
(+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
2.8b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
10.2b
(/ (pow t 2) x)
27.0b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

rewrite70.0ms

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:
5.0ms
(+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
9.0ms
(+ (* 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)))))))

series350.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
86.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
19.0ms
(/ (pow t 2) x)
186.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

simplify64.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
04631308
119651213
250011210

prune353.0ms

Filtered
104 candidates to 74 candidates (71.2%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1040104
Fresh099
Picked011
Done000
Total10410114

Merged error: 3.7b

Counts
114 → 10

localize32.0ms

Local error

Found 4 expressions with local error:

2.8b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (pow (cbrt l) 4) (* (* (cbrt x) (cbrt x)) 1)) (/ (pow (cbrt l) 2) (cbrt x))))))
5.1b
(/ (pow (cbrt l) 4) (* (* (cbrt x) (cbrt x)) 1))
10.2b
(/ (pow t 2) x)
27.0b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (pow (cbrt l) 4) (* (* (cbrt x) (cbrt x)) 1)) (/ (pow (cbrt l) 2) (cbrt x)))))))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
46×add-exp-log
34×times-frac
29×add-sqr-sqrt
28×add-cube-cbrt *-un-lft-identity
24×unpow-prod-down
18×div-exp prod-exp associate-/l*
13×add-cbrt-cube
8×associate-*r/
6×cbrt-prod pow-to-exp 1-exp pow-exp add-log-exp sqr-pow
5×pow1
4×cbrt-undiv flip3-+ sqrt-div frac-add associate-/r* flip-+ unpow2
3×sqrt-prod cbrt-unprod
2×associate-+r+ frac-2neg 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 (cbrt l) 4) (* (* (cbrt x) (cbrt x)) 1)) (/ (pow (cbrt l) 2) (cbrt x))))))
11.0ms
(/ (pow (cbrt l) 4) (* (* (cbrt x) (cbrt x)) 1))
5.0ms
(/ (pow t 2) x)
7.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (pow (cbrt l) 4) (* (* (cbrt x) (cbrt x)) 1)) (/ (pow (cbrt l) 2) (cbrt x)))))))

series423.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (pow (cbrt l) 4) (* (* (cbrt x) (cbrt x)) 1)) (/ (pow (cbrt l) 2) (cbrt x))))))
121.0ms
(/ (pow (cbrt l) 4) (* (* (cbrt x) (cbrt x)) 1))
19.0ms
(/ (pow t 2) x)
193.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (pow (cbrt l) 4) (* (* (cbrt x) (cbrt x)) 1)) (/ (pow (cbrt l) 2) (cbrt x)))))))

simplify97.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
07391861
133741719
250011688

prune529.0ms

Filtered
142 candidates to 94 candidates (66.2%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1420142
Fresh088
Picked011
Done011
Total14210152

Merged error: 3.7b

Counts
152 → 10

regimes530.0ms

bsearch6.0ms

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