Details

Time bar (total: 5.5s)

sample86.0ms

Algorithm
intervals
Results
29.0ms191×body80valid
16.0ms20×body1280valid
13.0ms22×body640valid
7.0ms16×body320valid
2.0ms7×body160valid

simplify40.0ms

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: 0.8b

Counts
2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (sin kx) 2.0)
0.3b
(pow (sin ky) 2.0)
2.7b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.0b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
18×add-exp-log
17×*-un-lft-identity
16×unpow-prod-down
13×add-cube-cbrt
11×associate-*l*
7×pow1
6×pow-unpow prod-exp add-cbrt-cube
5×associate-*r* pow-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp sqr-pow
3×pow-to-exp times-frac sqrt-prod unswap-sqr
2×pow-pow flip3-+ sqrt-div associate-*r/ div-exp flip-+ distribute-lft-out
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 *-commutative cbrt-unprod div-inv
Counts
4 → 94
Calls
4 calls:
3.0ms
(pow (sin kx) 2.0)
3.0ms
(pow (sin ky) 2.0)
19.0ms
(* (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)))))

series904.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(pow (sin kx) 2.0)
103.0ms
(pow (sin ky) 2.0)
381.0ms
(* (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)))))

simplify68.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0489887
11950857
25002857

prune391.0ms

Filtered
106 candidates to 75 candidates (70.8%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1042106
Fresh000
Picked101
Done000
Total1052107

Merged error: 0.5b

Counts
107 → 2

localize26.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
2.9b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.9b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.0b
(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)))))))

rewrite38.0ms

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:
15.0ms
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
8.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.0ms
(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)))))))

series944.0ms

Counts
4 → 12
Calls
4 calls:
481.0ms
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
73.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
75.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
315.0ms
(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)))))))

simplify58.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
03781610
112321509
250011507

prune582.0ms

Filtered
129 candidates to 95 candidates (73.6%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1290129
Fresh011
Picked011
Done000
Total1292131

Merged error: 0.5b

Counts
131 → 2

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

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New000
Fresh000
Picked011
Done011
Total022

Merged error: 0.5b

Counts
2 → 2

regimes229.0ms

Accuracy

0% (0.1b remaining)

Error of 0.8b against oracle of 0.7b and baseline of 0.8b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03230
13230

end0.0ms

sample2.0s

Algorithm
intervals
Results
791.0ms6280×body80valid
462.0ms546×body1280valid
337.0ms600×body640valid
149.0ms364×body320valid
55.0ms210×body160valid