Details

Time bar (total: 16.1s)

sample80.0ms

Algorithm
intervals
Results
24.0ms199×body80valid
16.0ms20×body1280valid
10.0ms18×body640valid
9.0ms12×body320valid
2.0ms7×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: 0.5b

Counts
2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin kx) 2.0)
0.5b
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
1.9b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
9.6b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
86×add-sqr-sqrt
72×*-un-lft-identity
64×times-frac
58×associate-*l*
51×unpow-prod-down
48×add-cube-cbrt
25×sqrt-prod
19×add-exp-log
15×unswap-sqr
14×associate-*r*
12×distribute-lft-out
8×pow1 associate-/r* add-cbrt-cube
6×prod-exp hypot-def
4×expm1-log1p-u sqrt-div pow-exp *-commutative log1p-expm1-u add-log-exp sqr-pow
3×pow-unpow flip3-+ div-exp flip-+ associate-/l*
2×+-commutative distribute-rgt-in pow-to-exp distribute-lft-in associate-*r/ associate-/r/ div-inv
1×cbrt-undiv rem-sqrt-square pow-pow frac-2neg sqrt-pow1 pow1/2 pow-prod-down clear-num cbrt-unprod
Counts
4 → 172
Calls
4 calls:
2.0ms
(pow (sin kx) 2.0)
33.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
24.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
37.0ms
(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 kx) 2.0)
397.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
391.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
325.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify93.0ms

Algorithm
egg-herbie
Counts
184 → 184
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
08582224
134762100
250012096

prune661.0ms

Filtered
184 candidates to 130 candidates (70.7%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1813184
Fresh000
Picked101
Done000
Total1823185

Merged error: 0.3b

Counts
185 → 3

localize32.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt Om)
0.7b
(cbrt Om)
1.2b
(* (pow (/ (cbrt l) (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
9.6b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 (* (cbrt l) (cbrt l))) (* (cbrt Om) (cbrt Om))) 2.0) (* (pow (/ (cbrt l) (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
5184×add-sqr-sqrt
2658×unswap-sqr
1330×cbrt-prod
1240×unpow-prod-down
1132×times-frac
745×hypot-def
304×swap-sqr
153×*-commutative
103×sqr-pow
45×associate-*l*
42×*-un-lft-identity
34×add-cube-cbrt
12×add-exp-log
7×pow1
6×add-cbrt-cube
5×associate-*r* sqrt-prod
4×expm1-log1p-u prod-exp log1p-expm1-u distribute-lft-out add-log-exp
2×+-commutative distribute-rgt-in distribute-lft-in flip3-+ pow1/3 sqrt-div associate-*r/ pow-exp flip-+
1×pow-to-exp rem-sqrt-square sqrt-pow1 pow1/2 div-exp pow-prod-down cbrt-unprod div-inv
Counts
4 → 868
Calls
4 calls:
1.0ms
(cbrt Om)
2.0ms
(cbrt Om)
26.0ms
(* (pow (/ (cbrt l) (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
1.4s
(sqrt (+ 1.0 (* (pow (/ (* 2.0 (* (cbrt l) (cbrt l))) (* (cbrt Om) (cbrt Om))) 2.0) (* (pow (/ (cbrt l) (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

series923.0ms

Counts
4 → 12
Calls
4 calls:
183.0ms
(cbrt Om)
184.0ms
(cbrt Om)
230.0ms
(* (pow (/ (cbrt l) (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
327.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 (* (cbrt l) (cbrt l))) (* (cbrt Om) (cbrt Om))) 2.0) (* (pow (/ (cbrt l) (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

simplify82.0ms

Algorithm
egg-herbie
Counts
880 → 880
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
05591684
122161615
250021611

prune3.9s

Filtered
880 candidates to 472 candidates (53.6%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New8791880
Fresh112
Picked101
Done000
Total8812883

Merged error: 0.3b

Counts
883 → 2

localize35.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt Om)
0.7b
(cbrt Om)
1.2b
(* (pow (/ (cbrt l) (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
6.9b
(sqrt (* (pow (/ (cbrt l) (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
113×add-sqr-sqrt
99×unpow-prod-down
90×cbrt-prod
88×associate-*l*
84×times-frac
69×*-un-lft-identity
61×add-cube-cbrt sqrt-prod
21×unswap-sqr
12×add-exp-log
10×associate-*r*
9×pow1
8×rem-sqrt-square
6×add-cbrt-cube
5×sqr-pow
4×expm1-log1p-u associate-*r/ prod-exp log1p-expm1-u distribute-lft-out add-log-exp
2×+-commutative distribute-rgt-in distribute-lft-in sqrt-pow1 flip3-+ pow1/3 sqrt-div pow-prod-down pow-exp *-commutative flip-+ div-inv
1×pow-to-exp pow1/2 div-exp cbrt-unprod
Counts
4 → 187
Calls
4 calls:
1.0ms
(cbrt Om)
1.0ms
(cbrt Om)
29.0ms
(* (pow (/ (cbrt l) (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
27.0ms
(sqrt (* (pow (/ (cbrt l) (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))

series905.0ms

Counts
4 → 12
Calls
4 calls:
183.0ms
(cbrt Om)
187.0ms
(cbrt Om)
223.0ms
(* (pow (/ (cbrt l) (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
312.0ms
(sqrt (* (pow (/ (cbrt l) (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))

simplify96.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
07562520
126172461
250012451

prune1.3s

Filtered
199 candidates to 170 candidates (85.4%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1981199
Fresh011
Picked011
Done000
Total1983201

Merged error: 0.1b

Counts
201 → 3

localize28.0ms

Local error

Found 4 expressions with local error:

5.7b
(cbrt (/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
9.6b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
9.6b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
9.6b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
85×add-sqr-sqrt
53×*-un-lft-identity
35×sqrt-prod
30×cbrt-prod times-frac
25×add-cube-cbrt
18×hypot-def unswap-sqr
14×cbrt-div distribute-lft-out
9×unpow-prod-down
8×sqrt-div associate-/r*
7×pow1 associate-*l*
4×add-exp-log expm1-log1p-u flip3-+ add-cbrt-cube flip-+ log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 associate-/l* sqr-pow
2×associate-/r/
1×frac-2neg pow1/3 clear-num div-inv
Counts
4 → 129
Calls
4 calls:
38.0ms
(cbrt (/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
34.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
36.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
34.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series1.4s

Counts
4 → 12
Calls
4 calls:
407.0ms
(cbrt (/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
326.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
330.0ms
(sqrt (+ 1.0 (* (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)))))

simplify105.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 3 (84.0ms)

IterNodesCost
02292177
16472117
228422082
350012075

prune633.0ms

Filtered
141 candidates to 97 candidates (68.8%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1410141
Fresh011
Picked011
Done011
Total1413144

Merged error: 0.1b

Counts
144 → 3

regimes570.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03525
13525

end0.0ms

sample2.1s

Algorithm
intervals
Results
796.0ms6195×body80valid
443.0ms551×body1280valid
360.0ms640×body640valid
158.0ms388×body320valid
63.0ms226×body160valid