Details

Time bar (total: 24.5s)

sample112.0ms

Algorithm
intervals
Results
66.0ms256×body80valid

simplify5.2s

Counts
1 → 1
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
02229
15229
213128
333028
4115228
5477228
done500028

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.0b

localize79.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (sin ky) 2.0)
0.3b
(pow (sin kx) 2.0)
2.3b
(fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0)
9.0b
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
7×pow1
6×add-exp-log unpow-prod-down pow-unpow
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×sqrt-prod
2×pow-to-exp pow-pow pow-exp sqr-pow
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
4 → 63
Calls
4 calls:
9.0ms
(pow (sin ky) 2.0)
8.0ms
(pow (sin kx) 2.0)
1.0ms
(fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0)
7.0ms
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))

series1.2s

Counts
4 → 12
Calls
4 calls:
171.0ms
(pow (sin ky) 2.0)
156.0ms
(pow (sin kx) 2.0)
303.0ms
(fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0)
546.0ms
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))

simplify1.4s

Counts
75 → 75
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01371098
12801019
2684899
32173895
done5001883

prune444.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 2.1b

localize64.0ms

Local error

Found 4 expressions with local error:

8.3b
(cbrt (sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0)))
9.0b
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
9.0b
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
9.0b
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
9×add-cube-cbrt *-un-lft-identity
7×pow1
6×cbrt-prod
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
1×pow1/3
Counts
4 → 61
Calls
4 calls:
11.0ms
(cbrt (sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0)))
2.0ms
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
2.0ms
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
2.0ms
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))

series2.2s

Counts
4 → 12
Calls
4 calls:
556.0ms
(cbrt (sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0)))
553.0ms
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
527.0ms
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
539.0ms
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))

simplify3.0s

Counts
73 → 73
Iterations

Useful iterations: done (3.0s)

IterNodesCost
0821961
11571774
23281571
39101560
433461536
done50001512

prune591.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 2.1b

localize14.0ms

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

prune7.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 2.1b

localize70.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin kx) 2.0)
7.5b
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (- (fma 0.04444444444444444 (pow ky 6) (pow ky 2)) (* 0.3333333333333333 (pow ky 4)))) 1.0))
9.2b
(fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (- (fma 0.04444444444444444 (pow ky 6) (pow ky 2)) (* 0.3333333333333333 (pow ky 4)))) 1.0)
18.2b
(- (fma 0.04444444444444444 (pow ky 6) (pow ky 2)) (* 0.3333333333333333 (pow ky 4)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
6×pow1 add-log-exp
5×add-exp-log
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×unpow-prod-down pow-unpow fma-neg prod-diff sqrt-prod
2×fma-udef
1×pow-to-exp sub-neg rem-sqrt-square flip3-- pow-pow sqrt-pow1 pow1/2 diff-log pow-exp associate--l+ flip-- sqr-pow
Counts
4 → 65
Calls
4 calls:
7.0ms
(pow (sin kx) 2.0)
3.0ms
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (- (fma 0.04444444444444444 (pow ky 6) (pow ky 2)) (* 0.3333333333333333 (pow ky 4)))) 1.0))
1.0ms
(fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (- (fma 0.04444444444444444 (pow ky 6) (pow ky 2)) (* 0.3333333333333333 (pow ky 4)))) 1.0)
13.0ms
(- (fma 0.04444444444444444 (pow ky 6) (pow ky 2)) (* 0.3333333333333333 (pow ky 4)))

series4.7s

Counts
4 → 12
Calls
4 calls:
140.0ms
(pow (sin kx) 2.0)
2.5s
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (- (fma 0.04444444444444444 (pow ky 6) (pow ky 2)) (* 0.3333333333333333 (pow ky 4)))) 1.0))
1.9s
(fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (- (fma 0.04444444444444444 (pow ky 6) (pow ky 2)) (* 0.3333333333333333 (pow ky 4)))) 1.0)
100.0ms
(- (fma 0.04444444444444444 (pow ky 6) (pow ky 2)) (* 0.3333333333333333 (pow ky 4)))

simplify1.0s

Counts
77 → 77
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01871900
14451796
213671607
done50001503

prune815.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 1.6b

regimes454.0ms

Accuracy

0% (0.6b remaining)

Error of 1.7b against oracle of 1.1b and baseline of 1.7b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02471
12871
done2871

end0.0ms

sample3.1s

Algorithm
intervals
Results
2.6s8000×body80valid