Details

Time bar (total: 8.1s)

sample46.0ms

Algorithm
intervals
Results
25.0ms256×body80valid

simplify39.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05216
112316
229416
3108316
4500116

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin kx) 2.0)
0.6b
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
2.8b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
10.1b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite59.0ms

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:
1.0ms
(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))))))
46.0ms
(* (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:
103.0ms
(pow (sin kx) 2.0)
381.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
376.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
317.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify70.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
05051608
120471504
250011501

prune531.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.3b

localize28.0ms

Local error

Found 4 expressions with local error:

1.4b
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.7b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.7b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
10.1b
(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)))))))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
24×*-un-lft-identity
21×sqrt-prod
16×add-exp-log
15×unpow-prod-down
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×flip3-+ flip-+ add-log-exp
3×rem-sqrt-square sqrt-pow1 times-frac pow1/2 pow-exp sqr-pow
2×associate-*r/ div-exp
1×pow-to-exp *-commutative cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
44.0ms
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
18.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
16.0ms
(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)))))))

series965.0ms

Counts
4 → 12
Calls
4 calls:
488.0ms
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
76.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
76.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
325.0ms
(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)))))))

simplify48.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
03631506
111591433
250021433

prune514.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.3b

localize31.0ms

Local error

Found 4 expressions with local error:

3.7b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.7b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
10.1b
(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)))))))
12.8b
(cbrt (pow (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))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
19×sqrt-prod
18×cbrt-prod
15×add-sqr-sqrt
12×add-cube-cbrt
10×unpow-prod-down
8×sqrt-div
7×pow1
6×cube-prod
4×add-exp-log flip3-+ add-cbrt-cube flip-+ distribute-lft-out add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×cube-div cbrt-div
1×cube-mult pow1/3 unpow3 rem-cbrt-cube sqr-pow
Counts
4 → 78
Calls
4 calls:
16.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
19.0ms
(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)))))))
5.0ms
(cbrt (pow (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))

series802.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
78.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
325.0ms
(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)))))))
321.0ms
(cbrt (pow (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))

simplify161.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
02982004
19571985
246751985
350031985

prune449.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 1.3b

localize35.0ms

Local error

Found 4 expressions with local error:

1.5b
(log (exp (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)))))))))
3.7b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.7b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
10.1b
(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)))))))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
16×sqrt-prod
13×add-sqr-sqrt
10×add-cube-cbrt
8×pow1
7×log-pow
6×exp-prod sqrt-div
4×add-exp-log unpow-prod-down add-cbrt-cube distribute-lft-out add-log-exp
3×rem-sqrt-square log-prod sqrt-pow1 flip3-+ pow1/2 flip-+
1×rem-log-exp
Counts
4 → 67
Calls
4 calls:
9.0ms
(log (exp (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)))))))))
16.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
16.0ms
(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)))))))

series805.0ms

Counts
4 → 12
Calls
4 calls:
329.0ms
(log (exp (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)))))))))
74.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
79.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
323.0ms
(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)))))))

simplify127.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
02301450
16581356
234681356
350021356

prune474.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 1.3b

regimes331.0ms

Accuracy

0% (0.0b remaining)

Error of 1.5b against oracle of 1.5b and baseline of 1.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03532
13532

end0.0ms

sample1.2s

Algorithm
intervals
Results
930.0ms8000×body80valid