Details

Time bar (total: 19.0s)

sample169.0ms

Algorithm
intervals
Results
118.0ms256×body80valid

simplify968.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
02229
15229
212429
329829
4112529
done500129

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.8b

localize74.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (sin kx) 2.0)
0.3b
(pow (sin ky) 2.0)
3.4b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.5b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite164.0ms

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:
6.0ms
(pow (sin kx) 2.0)
4.0ms
(pow (sin ky) 2.0)
133.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
14.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series1.5s

Counts
4 → 12
Calls
4 calls:
160.0ms
(pow (sin kx) 2.0)
153.0ms
(pow (sin ky) 2.0)
614.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
574.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify1.7s

Counts
98 → 98
Iterations

Useful iterations: 2 (427.0ms)

IterNodesCost
01951635
15651485
223181429
done50001429

prune722.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.5b

localize78.0ms

Local error

Found 4 expressions with local error:

6.7b
(sqrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
6.7b
(sqrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
7.5b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.5b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
26×sqrt-prod
16×add-sqr-sqrt
12×sqrt-div
10×pow1 add-cube-cbrt *-un-lft-identity sqrt-pow1
6×rem-sqrt-square pow1/2
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
Counts
4 → 72
Calls
4 calls:
7.0ms
(sqrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
13.0ms
(sqrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
10.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
11.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series2.0s

Counts
4 → 12
Calls
4 calls:
478.0ms
(sqrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
504.0ms
(sqrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
534.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
518.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify2.2s

Counts
84 → 84
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
0692288
11401970
24541872
326581872
done50011872

prune680.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 1.5b

localize85.0ms

Local error

Found 4 expressions with local error:

3.4b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
6.7b
(sqrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
7.5b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.5b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite180.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
16×add-exp-log *-un-lft-identity sqrt-prod
12×add-cube-cbrt
11×associate-*l*
10×unpow-prod-down
8×pow1 sqrt-div
6×sqrt-pow1 prod-exp add-cbrt-cube
5×associate-*r*
4×rem-sqrt-square flip3-+ pow1/2 flip-+ add-log-exp
3×times-frac pow-exp unswap-sqr
2×associate-*r/ div-exp distribute-lft-out sqr-pow
1×distribute-rgt-in pow-to-exp distribute-lft-in *-commutative cbrt-unprod div-inv
Counts
4 → 88
Calls
4 calls:
139.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
13.0ms
(sqrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
10.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
12.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series2.1s

Counts
4 → 12
Calls
4 calls:
627.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
477.0ms
(sqrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
511.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
519.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify1.8s

Counts
100 → 100
Iterations

Useful iterations: 2 (334.0ms)

IterNodesCost
01582487
14022206
218072101
done50002101

prune890.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 1.5b

localize10.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune0.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 1.5b

regimes702.0ms

Accuracy

0% (0.3b remaining)

Error of 1.7b against oracle of 1.3b and baseline of 1.7b

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02452
13052
done3052

end0.0ms

sample2.9s

Algorithm
intervals
Results
2.4s8000×body80valid