Details

Time bar (total: 5.9s)

sample48.0ms

Algorithm
intervals
Results
28.0ms256×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: 1.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (sin kx) 2.0)
0.3b
(pow (sin ky) 2.0)
2.3b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
10.3b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite96.0ms

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:
4.0ms
(pow (sin kx) 2.0)
4.0ms
(pow (sin ky) 2.0)
81.0ms
(* (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)))))

series936.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(pow (sin kx) 2.0)
102.0ms
(pow (sin ky) 2.0)
388.0ms
(* (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)))))

simplify53.0ms

Counts
98 → 98
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0473829
11858802
25002802
done5002802

prune390.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.8b

localize34.0ms

Local error

Found 4 expressions with local error:

10.3b
(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))))))
15.5b
(cbrt (/ (* 2.0 l) Om))
15.5b
(cbrt (/ (* 2.0 l) Om))
15.5b
(cbrt (/ (* 2.0 l) Om))

rewrite18.0ms

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))))))
4.0ms
(cbrt (/ (* 2.0 l) Om))
4.0ms
(cbrt (/ (* 2.0 l) Om))
4.0ms
(cbrt (/ (* 2.0 l) Om))

series771.0ms

Counts
4 → 12
Calls
4 calls:
488.0ms
(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))))))
93.0ms
(cbrt (/ (* 2.0 l) Om))
94.0ms
(cbrt (/ (* 2.0 l) Om))
96.0ms
(cbrt (/ (* 2.0 l) Om))

simplify146.0ms

Counts
75 → 75
Iterations

Useful iterations: 3 (138.0ms)

IterNodesCost
0193798
1579751
23641744
35002741
done5002741

prune440.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.8b

localize39.0ms

Local error

Found 4 expressions with local error:

10.3b
(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))))))
15.5b
(cbrt (/ (* 2.0 l) Om))
15.5b
(cbrt (/ (* 2.0 l) Om))
15.5b
(cbrt (/ (* 2.0 l) Om))

rewrite18.0ms

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))
4.0ms
(cbrt (/ (* 2.0 l) Om))
4.0ms
(cbrt (/ (* 2.0 l) Om))

series773.0ms

Counts
4 → 12
Calls
4 calls:
487.0ms
(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))))))
95.0ms
(cbrt (/ (* 2.0 l) Om))
96.0ms
(cbrt (/ (* 2.0 l) Om))
95.0ms
(cbrt (/ (* 2.0 l) Om))

simplify151.0ms

Counts
75 → 75
Iterations

Useful iterations: 3 (138.0ms)

IterNodesCost
0193798
1579751
23641744
35002741
done5002741

prune483.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.8b

localize11.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify2.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000
done00

prune0.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.8b

regimes325.0ms

Accuracy

0% (0.2b remaining)

Error of 1.5b against oracle of 1.3b and baseline of 1.5b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03326
13326
done3326

end0.0ms

sample1.1s

Algorithm
intervals
Results
814.0ms8000×body80valid