Details

Time bar (total: 7.9s)

sample75.0ms

Algorithm
intervals
Results
24.0ms207×body80valid
10.0ms20×body640valid
10.0ms12×body1280valid
6.0ms13×body320valid
1.0ms4×body160valid

simplify42.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05216
113116
234216
3120216
4500216

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: 0.3b

Counts
2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin ky) 2.0)
0.3b
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
2.3b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.7b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
30×*-un-lft-identity
26×add-cube-cbrt
21×times-frac
19×add-exp-log
15×sqrt-prod
13×unpow-prod-down
11×associate-*l*
8×add-cbrt-cube
6×pow1 prod-exp associate-/r*
5×associate-*r*
4×expm1-log1p-u sqrt-div pow-exp log1p-expm1-u add-log-exp
3×pow-unpow flip3-+ div-exp flip-+ associate-/l* unswap-sqr sqr-pow
2×pow-to-exp associate-*r/ associate-/r/ div-inv distribute-lft-out
1×cbrt-undiv distribute-rgt-in rem-sqrt-square pow-pow frac-2neg distribute-lft-in sqrt-pow1 pow1/2 clear-num *-commutative cbrt-unprod
Counts
4 → 118
Calls
4 calls:
3.0ms
(pow (sin ky) 2.0)
6.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
21.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
108.0ms
(pow (sin ky) 2.0)
398.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
389.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
328.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify69.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05211686
121361580
250011576

prune553.0ms

Filtered
130 candidates to 91 candidates (70.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1282130
Fresh000
Picked101
Done000
Total1292131

Merged error: 0.2b

Counts
131 → 2

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.2b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.2b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.7b
(sqrt (+ 1.0 (* (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
50×add-sqr-sqrt
27×unpow-prod-down
24×*-un-lft-identity
21×sqrt-prod
19×hypot-def
16×add-exp-log
15×sqr-pow
12×add-cube-cbrt
11×associate-*l*
8×sqrt-div associate-*r*
7×pow1
6×prod-exp add-cbrt-cube distribute-lft-out unswap-sqr
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 times-frac pow1/2 pow-exp
2×associate-*r/ div-exp
1×pow-to-exp *-commutative cbrt-unprod div-inv
Counts
4 → 117
Calls
4 calls:
16.0ms
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
9.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
9.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0ms
(sqrt (+ 1.0 (* (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))

series989.0ms

Counts
4 → 12
Calls
4 calls:
497.0ms
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
81.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
80.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
330.0ms
(sqrt (+ 1.0 (* (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))

simplify51.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
03781610
112321509
250011507

prune704.0ms

Filtered
129 candidates to 96 candidates (74.4%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New1281129
Fresh101
Picked101
Done000
Total1301131

Merged error: 0.2b

Counts
131 → 1

localize33.0ms

Local error

Found 4 expressions with local error:

5.5b
(sqrt (sqrt (+ 1.0 (* (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))))
5.5b
(sqrt (sqrt (+ 1.0 (* (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))))
8.7b
(sqrt (+ 1.0 (* (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
8.7b
(sqrt (+ 1.0 (* (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
26×sqrt-prod
18×add-sqr-sqrt
12×sqrt-div
10×pow1 add-cube-cbrt *-un-lft-identity sqrt-pow1
6×rem-sqrt-square pow1/2
4×add-exp-log expm1-log1p-u flip3-+ add-cbrt-cube flip-+ log1p-expm1-u add-log-exp
2×hypot-def
Counts
4 → 82
Calls
4 calls:
4.0ms
(sqrt (sqrt (+ 1.0 (* (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))))
4.0ms
(sqrt (sqrt (+ 1.0 (* (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))))
3.0ms
(sqrt (+ 1.0 (* (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
6.0ms
(sqrt (+ 1.0 (* (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))

series1.3s

Counts
4 → 12
Calls
4 calls:
308.0ms
(sqrt (sqrt (+ 1.0 (* (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))))
300.0ms
(sqrt (sqrt (+ 1.0 (* (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))))
324.0ms
(sqrt (+ 1.0 (* (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
327.0ms
(sqrt (+ 1.0 (* (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))

simplify113.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 3 (90.0ms)

IterNodesCost
01412750
14222626
224252624
350012620

prune565.0ms

Filtered
94 candidates to 72 candidates (76.6%)
Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New94094
Fresh000
Picked011
Done000
Total94195

Merged error: 0.2b

Counts
95 → 1

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03458
13458

end0.0ms

sample2.0s

Algorithm
intervals
Results
778.0ms6238×body80valid
412.0ms496×body1280valid
373.0ms672×body640valid
156.0ms386×body320valid
58.0ms208×body160valid