Details

Time bar (total: 9.3s)

sample88.0ms

Algorithm
intervals
Results
29.0ms196×body80valid
18.0ms19×body1280valid
14.0ms23×body640valid
5.0ms11×body320valid
2.0ms7×body160valid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05216
112316
229416
3108316
4500116

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

localize29.0ms

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)))))

rewrite30.0ms

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×sqrt-div pow-exp 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 → 110
Calls
4 calls:
3.0ms
(pow (sin kx) 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))))))
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:
99.0ms
(pow (sin kx) 2.0)
377.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
377.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
316.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify73.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05051609
120461504
250021501

prune447.0ms

Filtered
122 candidates to 83 candidates (68.0%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1193122
Fresh000
Picked101
Done000
Total1203123

Merged error: 1.0b

Counts
123 → 3

localize24.0ms

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))))))

rewrite52.0ms

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×flip3-+ sqrt-div cbrt-unprod flip-+ 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 → 151
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))))
15.0ms
(* (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:
375.0ms
(/ 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)))))))
369.0ms
(* (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))))
385.0ms
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
307.0ms
(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))))))

simplify94.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
06253076
125752742
250022739

prune536.0ms

Filtered
163 candidates to 94 candidates (57.7%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1630163
Fresh022
Picked011
Done000
Total1633166

Merged error: 1.0b

Counts
166 → 3

localize30.0ms

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)))))

rewrite38.0ms

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×flip3-+ associate-/r/ flip-+ 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 → 129
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))))))
16.0ms
(* (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:
383.0ms
(/ 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)))
377.0ms
(log (exp (/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))))
312.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify67.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
05022096
118331924
250011919

prune565.0ms

Filtered
141 candidates to 98 candidates (69.5%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1410141
Fresh011
Picked011
Done011
Total1413144

Merged error: 1.0b

Counts
144 → 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

regimes659.0ms

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
1.1s6296×body80valid
483.0ms519×body1280valid
397.0ms622×body640valid
172.0ms352×body320valid
68.0ms211×body160valid