Details

Time bar (total: 11.9s)

sample49.0ms

Algorithm
intervals
Results
26.0ms256×body80valid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05216
113116
234216
3120216
4500216

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ (* 2.0 l) Om) 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))))))
2.5b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
9.4b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
31×*-un-lft-identity
27×add-cube-cbrt
24×add-exp-log times-frac
17×unpow-prod-down
15×sqrt-prod
11×associate-*l*
8×add-cbrt-cube
7×prod-exp
6×pow1 pow-exp associate-/r*
5×div-exp associate-*r*
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×pow-unpow flip3-+ flip-+ div-inv associate-/l* unswap-sqr sqr-pow
2×pow-to-exp associate-*r/ associate-/r/ 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 → 124
Calls
4 calls:
8.0ms
(pow (/ (* 2.0 l) Om) 2.0)
10.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
76.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
6.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
76.0ms
(pow (/ (* 2.0 l) Om) 2.0)
355.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
347.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
291.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify69.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05401756
122041637
250011633

prune910.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.9b

localize26.0ms

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)))))))
0.8b
(* (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))))
2.0b
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
9.4b
(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))))))

rewrite183.0ms

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:
10.0ms
(/ 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)))))))
83.0ms
(* (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))))
78.0ms
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
5.0ms
(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:
363.0ms
(/ 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)))))))
364.0ms
(* (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))))
368.0ms
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
300.0ms
(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))))))

simplify95.0ms

Algorithm
egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
06553207
126752873
250012838

prune1.4s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize35.0ms

Local error

Found 4 expressions with local error:

5.5b
(cbrt (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)))))))
9.4b
(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))))))
9.4b
(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))))))
9.4b
(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))))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
9×add-cube-cbrt *-un-lft-identity
8×sqrt-div
7×pow1
6×cbrt-prod
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
2×cbrt-div
1×pow1/3
Counts
4 → 69
Calls
4 calls:
4.0ms
(cbrt (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)))))))
5.0ms
(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))))))
5.0ms
(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))))))
5.0ms
(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))))))

series1.1s

Counts
4 → 12
Calls
4 calls:
264.0ms
(cbrt (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)))))))
286.0ms
(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))))))
287.0ms
(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))))))
289.0ms
(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))))))

simplify112.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
01391817
14481729
227961727
350011727

prune2.2s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.9b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin kx) 2.0)
0.3b
(pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2)))
1.1b
(log (pow (exp (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2)))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
1.9b
(pow (exp (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2)))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
25×unpow-prod-down
19×*-un-lft-identity
15×add-sqr-sqrt add-cube-cbrt
14×pow-pow
12×add-exp-log
11×exp-prod
9×pow-unpow
8×log-prod
7×pow1
6×times-frac pow-exp
5×sqr-pow
4×expm1-log1p-u pow-to-exp add-cbrt-cube log1p-expm1-u add-log-exp
3×rem-log-exp
2×unpow-prod-up div-exp div-inv distribute-lft-out
1×prod-exp log-pow
Counts
4 → 96
Calls
4 calls:
3.0ms
(pow (sin kx) 2.0)
8.0ms
(pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2)))
18.0ms
(log (pow (exp (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2)))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
38.0ms
(pow (exp (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2)))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series576.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(pow (sin kx) 2.0)
72.0ms
(pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2)))
209.0ms
(log (pow (exp (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2)))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
189.0ms
(pow (exp (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2)))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify59.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
04701182
121451084
250011056

prune779.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.9b

regimes471.0ms

Accuracy

0% (0.1b remaining)

Error of 1.4b against oracle of 1.3b and baseline of 1.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03661
13661

end0.0ms

sample1.1s

Algorithm
intervals
Results
861.0ms8000×body80valid