Details

Time bar (total: 7.9s)

sample43.0ms

Algorithm
intervals
Results
24.0ms256×body80valid

simplify39.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05216
112316
229416
3108316
4500116
done500116

prune5.0ms

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)))
9.1b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite95.0ms

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×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 → 86
Calls
4 calls:
3.0ms
(pow (sin ky) 2.0)
3.0ms
(pow (sin kx) 2.0)
80.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
5.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series945.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(pow (sin ky) 2.0)
103.0ms
(pow (sin kx) 2.0)
387.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
347.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify55.0ms

Counts
98 → 98
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0473830
11856802
25002802
done5002802

prune406.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize28.0ms

Local error

Found 4 expressions with local error:

9.1b
(sqrt (+ 1.0 (* (pow (* (cbrt (/ (* 2.0 l) Om)) (cbrt (/ (* 2.0 l) Om))) 2.0) (* (pow (cbrt (/ (* 2.0 l) Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
14.1b
(cbrt (/ (* 2.0 l) Om))
14.1b
(cbrt (/ (* 2.0 l) Om))
14.1b
(cbrt (/ (* 2.0 l) Om))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
12×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
9×times-frac
5×pow1
4×add-exp-log add-cbrt-cube add-log-exp
3×cbrt-div pow1/3 sqrt-prod div-inv
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 63
Calls
4 calls:
5.0ms
(sqrt (+ 1.0 (* (pow (* (cbrt (/ (* 2.0 l) Om)) (cbrt (/ (* 2.0 l) Om))) 2.0) (* (pow (cbrt (/ (* 2.0 l) Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
3.0ms
(cbrt (/ (* 2.0 l) Om))
3.0ms
(cbrt (/ (* 2.0 l) Om))
3.0ms
(cbrt (/ (* 2.0 l) Om))

series768.0ms

Counts
4 → 12
Calls
4 calls:
492.0ms
(sqrt (+ 1.0 (* (pow (* (cbrt (/ (* 2.0 l) Om)) (cbrt (/ (* 2.0 l) Om))) 2.0) (* (pow (cbrt (/ (* 2.0 l) Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
91.0ms
(cbrt (/ (* 2.0 l) Om))
93.0ms
(cbrt (/ (* 2.0 l) Om))
92.0ms
(cbrt (/ (* 2.0 l) Om))

simplify145.0ms

Counts
75 → 75
Iterations

Useful iterations: 3 (138.0ms)

IterNodesCost
0193798
1579751
23641744
35002741
done5002741

prune452.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize42.0ms

Local error

Found 4 expressions with local error:

5.6b
(cbrt (/ l (cbrt Om)))
9.1b
(sqrt (+ 1.0 (* (pow (* (cbrt (/ (* 2.0 l) Om)) (* (cbrt (/ 2.0 (* (cbrt Om) (cbrt Om)))) (cbrt (/ l (cbrt Om))))) 2.0) (* (pow (cbrt (/ (* 2.0 l) Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
14.1b
(cbrt (/ (* 2.0 l) Om))
14.1b
(cbrt (/ (* 2.0 l) Om))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
45×cbrt-prod
24×times-frac
23×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
5×pow1
4×add-exp-log add-cbrt-cube add-log-exp
3×cbrt-div pow1/3 sqrt-prod div-inv
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 78
Calls
4 calls:
3.0ms
(cbrt (/ l (cbrt Om)))
5.0ms
(sqrt (+ 1.0 (* (pow (* (cbrt (/ (* 2.0 l) Om)) (* (cbrt (/ 2.0 (* (cbrt Om) (cbrt Om)))) (cbrt (/ l (cbrt Om))))) 2.0) (* (pow (cbrt (/ (* 2.0 l) Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
3.0ms
(cbrt (/ (* 2.0 l) Om))
4.0ms
(cbrt (/ (* 2.0 l) Om))

series861.0ms

Counts
4 → 12
Calls
4 calls:
168.0ms
(cbrt (/ l (cbrt Om)))
501.0ms
(sqrt (+ 1.0 (* (pow (* (cbrt (/ (* 2.0 l) Om)) (* (cbrt (/ 2.0 (* (cbrt Om) (cbrt Om)))) (cbrt (/ l (cbrt Om))))) 2.0) (* (pow (cbrt (/ (* 2.0 l) Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
96.0ms
(cbrt (/ (* 2.0 l) Om))
96.0ms
(cbrt (/ (* 2.0 l) Om))

simplify39.0ms

Counts
90 → 90
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
03231080
19341029
250011022
done50011022

prune842.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.6b

localize28.0ms

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)))
1.6b
(log (exp (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-sqr-sqrt
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×log-prod associate-*r* pow-exp add-log-exp
4×sqr-pow
3×pow-to-exp times-frac log-pow unswap-sqr
2×distribute-rgt-in pow-pow distribute-lft-in associate-*r/ div-exp exp-sum distribute-lft-out
1×exp-prod exp-to-pow flip3-+ rem-log-exp *-commutative cbrt-unprod flip-+ div-inv
Counts
4 → 87
Calls
4 calls:
3.0ms
(pow (sin ky) 2.0)
3.0ms
(pow (sin kx) 2.0)
76.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
10.0ms
(log (exp (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series989.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(pow (sin ky) 2.0)
103.0ms
(pow (sin kx) 2.0)
391.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
389.0ms
(log (exp (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify53.0ms

Counts
99 → 99
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0447832
11728766
25001766
done5001766

prune445.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.6b

regimes364.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04232
14232
done4232

end0.0ms

sample1.1s

Algorithm
intervals
Results
772.0ms8000×body80valid