Details

Time bar (total: 9.3s)

sample85.0ms

Algorithm
intervals
Results
28.0ms196×body80valid
17.0ms19×body1280valid
14.0ms23×body640valid
5.0ms11×body320valid
2.0ms7×body160valid

simplify41.0ms

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: 1.8b

Counts
2 → 1

localize28.0ms

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))))))
2.7b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
9.9b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite29.0ms

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 kx) 2.0)
5.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
15.0ms
(* (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:
101.0ms
(pow (sin kx) 2.0)
376.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
369.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
309.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify76.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05201686
121361580
250011576

prune472.0ms

Filtered
130 candidates to 91 candidates (70.0%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1273130
Fresh000
Picked101
Done000
Total1283131

Merged error: 1.0b

Counts
131 → 3

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
0.6b
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.3b
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
9.9b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
125×add-exp-log
72×prod-exp
36×pow-exp
33×add-sqr-sqrt
31×*-un-lft-identity
27×add-cube-cbrt
25×div-exp
24×times-frac
22×associate-*l*
17×unpow-prod-down
15×sqrt-prod
13×add-cbrt-cube
12×pow-to-exp
6×associate-*r/ associate-*r* associate-/r*
5×pow1 distribute-rgt-in distribute-lft-in
4×expm1-log1p-u flip3-+ sqrt-div cbrt-unprod flip-+ log1p-expm1-u add-log-exp
3×div-inv associate-/l* unswap-sqr sqr-pow
2×associate-/r/ *-commutative distribute-lft-out
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
Counts
4 → 159
Calls
4 calls:
5.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
18.0ms
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
14.0ms
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

series1.4s

Counts
4 → 12
Calls
4 calls:
378.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
372.0ms
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
383.0ms
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
310.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

simplify102.0ms

Algorithm
egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
06553207
126752873
250012838

prune555.0ms

Filtered
171 candidates to 102 candidates (59.6%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1710171
Fresh022
Picked011
Done000
Total1713174

Merged error: 1.0b

Counts
174 → 3

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
2.7b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0b
(log (exp (/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))))
9.9b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
42×*-un-lft-identity
39×times-frac
38×add-cube-cbrt
25×log-pow
24×exp-prod sqrt-prod
18×add-exp-log
11×associate-*l*
10×unpow-prod-down
8×add-cbrt-cube
6×pow1 sqrt-div prod-exp associate-/r*
5×associate-*r*
4×expm1-log1p-u flip3-+ associate-/r/ flip-+ log1p-expm1-u add-log-exp
3×log-prod div-exp pow-exp div-inv associate-/l* unswap-sqr
2×associate-*r/ distribute-lft-out sqr-pow
1×cbrt-undiv distribute-rgt-in pow-to-exp rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 rem-log-exp clear-num *-commutative cbrt-unprod
Counts
4 → 137
Calls
4 calls:
6.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
14.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.0ms
(log (exp (/ 1.0 (sqrt (+ 1.0 (* (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)))))

series1.4s

Counts
4 → 12
Calls
4 calls:
375.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
372.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
368.0ms
(log (exp (/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))))
309.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify75.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05172194
119132021
250012014

prune599.0ms

Filtered
149 candidates to 106 candidates (71.1%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1490149
Fresh011
Picked011
Done011
Total1493152

Merged error: 1.0b

Counts
152 → 3

localize6.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify2.0ms

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000

prune0.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New000
Fresh000
Picked011
Done022
Total033

Merged error: 1.0b

Counts
3 → 3

regimes651.0ms

Accuracy

0% (0.1b remaining)

Error of 0.7b against oracle of 0.6b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03222
13222

end0.0ms

sample2.4s

Algorithm
intervals
Results
904.0ms6296×body80valid
630.0ms519×body1280valid
393.0ms622×body640valid
160.0ms352×body320valid
63.0ms211×body160valid