Details

Time bar (total: 4.2s)

analyze1.0s (24.6%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
25%74.9%0.1%3
25%74.9%0.1%4
25%74.9%0.1%5
31.2%68.6%0.1%6
32.8%67.1%0.1%7
34.3%65.5%0.1%8
38.2%61.2%0.5%9
39.6%53%7.4%10
40.3%52.4%7.4%11
41.6%49.6%8.8%12
42%39.9%18.1%13
42.3%39.6%18.2%14

sample43.0ms (1%)

Algorithm
intervals
Results
16.0ms256×body80valid
9.0ms105×body80invalid
3.0ms64×body80nan

simplify83.0ms (2%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (81.0ms)

IterNodesCost
0496113
1496113

prune12.0ms (0.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 1.4b

Counts
2 → 2

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (* 10.0 k))
0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b
(* a (pow k m))
1.4b
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite23.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
19×add-exp-log
14×add-sqr-sqrt
11×add-cbrt-cube add-log-exp
add-cube-cbrt *-un-lft-identity
associate-*r*
prod-exp
pow1 unpow-prod-down div-exp sum-log
flip3-+ times-frac associate-*l* associate-/r* flip-+ unswap-sqr
cbrt-undiv +-commutative pow-to-exp pow-exp associate-/r/ cbrt-unprod sqr-pow
associate-+l+ frac-2neg clear-num *-commutative div-inv associate-/l*
Counts
4 → 74
Calls

4 calls:

9.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))
5.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
5.0ms
(* a (pow k m))
3.0ms
(+ 1.0 (* 10.0 k))

series55.0ms (1.3%)

Counts
4 → 12
Calls

4 calls:

35.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))
14.0ms
(* a (pow k m))
3.0ms
(+ 1.0 (* 10.0 k))
3.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))

simplify52.0ms (1.2%)

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
04953920
14953920

prune140.0ms (3.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New82486
Fresh101
Picked011
Done000
Total83588

Merged error: 0.0b

Counts
88 → 5

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (* 10.0 k))
0.0b
(/ (* (/ a (sqrt (+ 1.0 (* k (+ k 10.0))))) (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
13.8b
(sqrt (+ 1.0 (* k (+ k 10.0))))
13.8b
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite26.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
25×add-exp-log
13×add-cbrt-cube
12×add-sqr-sqrt sqrt-prod
10×add-cube-cbrt *-un-lft-identity div-exp
pow1 times-frac sqrt-div prod-exp associate-/r* add-log-exp
cbrt-undiv flip3-+ flip-+
pow-to-exp rem-sqrt-square sqrt-pow1 pow1/2 pow-exp associate-/r/ cbrt-unprod
+-commutative frac-2neg associate-*l/ clear-num sum-log div-inv associate-/l/ associate-/l*
Counts
4 → 77
Calls

4 calls:

14.0ms
(/ (* (/ a (sqrt (+ 1.0 (* k (+ k 10.0))))) (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
5.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
3.0ms
(+ 1.0 (* 10.0 k))
3.0ms
(sqrt (+ 1.0 (* k (+ k 10.0))))

series45.0ms (1.1%)

Counts
4 → 12
Calls

4 calls:

34.0ms
(/ (* (/ a (sqrt (+ 1.0 (* k (+ k 10.0))))) (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
4.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
4.0ms
(sqrt (+ 1.0 (* k (+ k 10.0))))
3.0ms
(+ 1.0 (* 10.0 k))

simplify44.0ms (1.1%)

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
051211306

prune190.0ms (4.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New88189
Fresh123
Picked011
Done011
Total89594

Merged error: 0.0b

Counts
94 → 5

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b
(* k (+ k 10.0))
0.0b
(* a (pow k m))
0.1b
(/ 1 (/ (+ 1.0 (* k (+ k 10.0))) (* a (pow k m))))
1.4b
(/ (+ 1.0 (* k (+ k 10.0))) (* a (pow k m)))

rewrite33.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
59×add-exp-log
36×times-frac
34×add-sqr-sqrt
29×*-un-lft-identity
27×add-cube-cbrt
26×div-exp
22×add-cbrt-cube
16×prod-exp
11×associate-*r*
associate-/r*
pow1 cbrt-undiv
associate-*l* div-inv associate-/l*
pow-to-exp rec-exp 1-exp pow-exp
unpow-prod-down cbrt-unprod add-log-exp unswap-sqr
frac-2neg flip3-+ associate-*r/ clear-num *-commutative flip-+ associate-/l/ sqr-pow
distribute-rgt-in pow-flip distribute-lft-in pow-prod-down associate-/r/ distribute-lft-out inv-pow
Counts
4 → 135
Calls

4 calls:

8.0ms
(/ 1 (/ (+ 1.0 (* k (+ k 10.0))) (* a (pow k m))))
8.0ms
(/ (+ 1.0 (* k (+ k 10.0))) (* a (pow k m)))
7.0ms
(* a (pow k m))
6.0ms
(* k (+ k 10.0))

series78.0ms (1.8%)

Counts
4 → 12
Calls

4 calls:

30.0ms
(/ (+ 1.0 (* k (+ k 10.0))) (* a (pow k m)))
29.0ms
(/ 1 (/ (+ 1.0 (* k (+ k 10.0))) (* a (pow k m))))
15.0ms
(* a (pow k m))
4.0ms
(* k (+ k 10.0))

simplify68.0ms (1.6%)

Algorithm
egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
049432014
149432014

prune225.0ms (5.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1461147
Fresh202
Picked101
Done022
Total1493152

Merged error: 0.0b

Counts
152 → 3

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (* a (pow k m)))
0.1b
(* 10.0 (/ k (* a (pow k m))))
0.1b
(/ 1 (+ (* 10.0 (/ k (* a (pow k m)))) (+ (/ 1.0 (* a (pow k m))) (* (/ k a) (/ k (pow k m))))))
3.1b
(* (/ k a) (/ k (pow k m)))

rewrite50.0ms (1.2%)

Algorithm
rewrite-expression-head
Rules
64×add-sqr-sqrt
58×add-exp-log
55×times-frac
38×add-cube-cbrt *-un-lft-identity
32×associate-*r* add-cbrt-cube
20×div-exp
19×prod-exp
16×associate-*l*
11×unpow-prod-down
pow1 cbrt-undiv cbrt-unprod unswap-sqr
associate-*r/ frac-add
associate-/r/
associate-/l*
div-inv sqr-pow
pow-to-exp pow-exp associate-/r* add-log-exp
frac-times frac-2neg flip3-+ pow-prod-down associate-*l/ clear-num *-commutative flip-+
rec-exp pow-flip 1-exp inv-pow
Counts
4 → 160
Calls

4 calls:

16.0ms
(/ 1 (+ (* 10.0 (/ k (* a (pow k m)))) (+ (/ 1.0 (* a (pow k m))) (* (/ k a) (/ k (pow k m))))))
15.0ms
(* (/ k a) (/ k (pow k m)))
8.0ms
(* 10.0 (/ k (* a (pow k m))))
5.0ms
(/ 1.0 (* a (pow k m)))

series125.0ms (3%)

Counts
4 → 12
Calls

4 calls:

51.0ms
(/ 1 (+ (* 10.0 (/ k (* a (pow k m)))) (+ (/ 1.0 (* a (pow k m))) (* (/ k a) (/ k (pow k m))))))
27.0ms
(* (/ k a) (/ k (pow k m)))
26.0ms
(* 10.0 (/ k (* a (pow k m))))
21.0ms
(/ 1.0 (* a (pow k m)))

simplify64.0ms (1.5%)

Algorithm
egg-herbie
Counts
172 → 172
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
049943169
149943169

prune280.0ms (6.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1711172
Fresh000
Picked011
Done022
Total1714175

Merged error: 0.0b

Counts
175 → 4

regimes242.0ms (5.7%)

Accuracy

Total 0.0b remaining (16.9%)

Threshold costs 0.0b (16.9%)

bsearch13.0ms (0.3%)

Steps
ItersRangePoint
4
7.436985620791089e+149
1.147695884361297e+150
1.1028227832196924e+150

simplify1.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03448
13448

end0.0ms (0%)

sample1.2s (29.2%)

Algorithm
intervals
Results
539.0ms8000×body80valid
271.0ms3309×body80invalid
92.0ms1999×body80nan

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