Details

Time bar (total: 5.5s)

analyze2.2s

Algorithm
search
sampling

Space saved by range analysis: 0.146413%

Space saved by search: 43.832357%

Guaranteed chance to sample good point: 36.458333%

sample80.0ms

Algorithm
intervals
Results
12.0ms167×body80valid
11.0ms38×body640valid
10.0ms30×body1280valid
9.0ms17×body320nan
8.0ms29×body640nan
8.0ms22×body1280nan
3.0ms47×body80nan
2.0ms12×body320valid
1.0ms9×body160valid
1.0ms9×body160nan

simplify82.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03914
19314
219314
341414
471814
5119214
6281614
7500114

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 45.6b

Counts
2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (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)
10.2b
(- (* (/ (+ 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)))

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 → 80
Calls
4 calls:
15.0ms
(/ (* (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))
14.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series346.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(/ (* (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)
62.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
191.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify58.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
04171207
120511099
250021094

prune209.0ms

Filtered
65 candidates to 92 candidates (-41.5%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New86692
Fresh000
Picked101
Done000
Total87693

Merged error: 6.4b

Counts
93 → 6

localize17.0ms

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))))
4.8b
(/ (pow l 2) x)
7.3b
(/ (pow t 2) x)
30.1b
(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)
6.0ms
(/ (pow t 2) x)
7.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series46.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(+ (* 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 (49.0ms)

IterNodesCost
05261067
12113984
25001978

prune379.0ms

Filtered
97 candidates to 142 candidates (-46.4%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1366142
Fresh055
Picked101
Done000
Total13711148

Merged error: 4.1b

Counts
148 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b
(+ (pow t 2) (/ l (/ x l)))
4.2b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
7.3b
(/ (pow t 2) x)
30.1b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

rewrite43.0ms

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

series51.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(+ (pow t 2) (/ l (/ x l)))
15.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
3.0ms
(/ (pow t 2) x)
24.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

simplify55.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0453932
11835862
25001859

prune260.0ms

Filtered
76 candidates to 105 candidates (-38.2%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1032105
Fresh1910
Picked101
Done000
Total10511116

Merged error: 4.1b

Counts
116 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

7.3b
(/ (pow t 2) x)
7.3b
(/ (pow t 2) x)
30.1b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))
30.1b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
48×times-frac
42×add-sqr-sqrt
40×add-cube-cbrt *-un-lft-identity
24×unpow-prod-down
16×associate-/l*
14×add-exp-log
8×sqrt-div associate-*r/ add-cbrt-cube unpow2 sqr-pow
6×pow1 div-exp associate-/r* sqrt-prod
4×flip3-+ frac-add flip-+ add-log-exp
2×cbrt-undiv pow-to-exp rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-exp clear-num div-inv
Counts
4 → 132
Calls
4 calls:
5.0ms
(/ (pow t 2) x)
5.0ms
(/ (pow t 2) x)
7.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))
7.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

series58.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(/ (pow t 2) x)
3.0ms
(/ (pow t 2) x)
24.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))
27.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

simplify53.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
03811124
115361046
250021040

prune444.0ms

Filtered
100 candidates to 144 candidates (-44.0%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1431144
Fresh01010
Picked011
Done000
Total14312155

Merged error: 4.1b

Counts
155 → 12

regimes895.0ms

bsearch1.0ms

Profiling

Loading profile data...