Details

Time bar (total: 7.5s)

sample44.0ms

Algorithm
intervals
Results
26.0ms256×body80valid

simplify43.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05216
113116
234216
3120216
4500216

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin ky) 2.0)
0.3b
(pow (sin kx) 2.0)
1.5b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.5b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite52.0ms

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:
1.0ms
(pow (sin ky) 2.0)
2.0ms
(pow (sin kx) 2.0)
43.0ms
(* (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)))))

series875.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(pow (sin ky) 2.0)
98.0ms
(pow (sin kx) 2.0)
370.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
307.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify60.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0489887
11950857
25002857

prune447.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin kx) 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))))
1.9b
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.5b
(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))))))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
124×add-exp-log
72×prod-exp
37×pow-exp
24×div-exp
22×associate-*l*
20×add-sqr-sqrt unpow-prod-down
18×*-un-lft-identity
14×add-cube-cbrt
13×pow-to-exp
11×add-cbrt-cube
6×pow1 times-frac associate-*r/ associate-*r*
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp sqr-pow
3×pow-unpow flip3-+ sqrt-prod flip-+ unswap-sqr
2×sqrt-div *-commutative div-inv distribute-lft-out
1×rem-sqrt-square pow-pow sqrt-pow1 pow1/2
Counts
4 → 135
Calls
4 calls:
1.0ms
(pow (sin kx) 2.0)
48.0ms
(* (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))))
44.0ms
(* (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))))))

series1.2s

Counts
4 → 12
Calls
4 calls:
101.0ms
(pow (sin kx) 2.0)
377.0ms
(* (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))))
389.0ms
(* (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))))))

simplify84.0ms

Algorithm
egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
06362018
126471796
250011765

prune543.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 1.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin ky) 2.0)
0.3b
(pow (sin kx) 2.0)
1.7b
(log (pow (exp (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2)))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
2.2b
(pow (exp (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2)))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
21×unpow-prod-down
19×*-un-lft-identity
15×add-sqr-sqrt add-cube-cbrt
14×pow-pow
11×pow-unpow exp-prod
8×log-prod
7×pow1 add-exp-log
5×sqr-pow
4×expm1-log1p-u pow-to-exp pow-exp add-cbrt-cube log1p-expm1-u add-log-exp
3×times-frac rem-log-exp
2×unpow-prod-up distribute-lft-out
1×log-pow div-inv
Counts
4 → 92
Calls
4 calls:
1.0ms
(pow (sin ky) 2.0)
1.0ms
(pow (sin kx) 2.0)
9.0ms
(log (pow (exp (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2)))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
23.0ms
(pow (exp (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2)))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series637.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(pow (sin ky) 2.0)
101.0ms
(pow (sin kx) 2.0)
218.0ms
(log (pow (exp (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2)))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
209.0ms
(pow (exp (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2)))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify52.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
04571061
11888991
25001980

prune550.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 1.0b

localize30.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt 2.0)
1.0b
(cbrt 2.0)
1.2b
(pow (sin ky) (* (cbrt 2.0) (cbrt 2.0)))
4.2b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (pow (sin ky) (* (cbrt 2.0) (cbrt 2.0))) (cbrt 2.0))))))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-prod
5×add-exp-log
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×unpow-prod-down sqrt-prod
2×pow1/3 sqrt-div
1×pow-to-exp rem-sqrt-square pow-unpow pow-pow sqrt-pow1 flip3-+ pow1/2 pow-exp flip-+ sqr-pow
Counts
4 → 60
Calls
4 calls:
0.0ms
(cbrt 2.0)
0.0ms
(cbrt 2.0)
2.0ms
(pow (sin ky) (* (cbrt 2.0) (cbrt 2.0)))
3.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (pow (sin ky) (* (cbrt 2.0) (cbrt 2.0))) (cbrt 2.0))))))

series868.0ms

Counts
4 → 8
Calls
4 calls:
0.0ms
(cbrt 2.0)
0.0ms
(cbrt 2.0)
185.0ms
(pow (sin ky) (* (cbrt 2.0) (cbrt 2.0)))
683.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (pow (sin ky) (* (cbrt 2.0) (cbrt 2.0))) (cbrt 2.0))))))

simplify40.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0273645
11141613
25001603

prune382.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 1.0b

regimes368.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03222
13222

end0.0ms

sample1.0s

Algorithm
intervals
Results
812.0ms8000×body80valid