Details

Time bar (total: 13.2s)

sample109.0ms

Algorithm
intervals
Results
65.0ms256×body80valid

simplify1.0s

Counts
1 → 1
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
02229
15229
213228
334428
4124528
done500028

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.8b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin ky) 2.0)
0.3b
(pow (sin kx) 2.0)
2.0b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
9.4b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite141.0ms

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:
7.0ms
(pow (sin ky) 2.0)
7.0ms
(pow (sin kx) 2.0)
110.0ms
(* (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)))))

series1.4s

Counts
4 → 12
Calls
4 calls:
153.0ms
(pow (sin ky) 2.0)
196.0ms
(pow (sin kx) 2.0)
620.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
478.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify1.8s

Counts
106 → 106
Iterations

Useful iterations: 2 (493.0ms)

IterNodesCost
02031733
15821577
224021508
done50041508

prune717.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.1b

localize72.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin kx) 2.0)
1.9b
(fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0)
9.4b
(sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))
11.6b
(cbrt (pow (sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0)) 3))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-prod
13×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity
9×unpow-prod-down sqrt-prod
6×pow1 cube-prod
5×add-exp-log
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow-unpow
2×sqr-pow
1×cube-mult pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 pow1/3 unpow3 pow-exp rem-cbrt-cube fma-udef
Counts
4 → 73
Calls
4 calls:
4.0ms
(pow (sin kx) 2.0)
0.0ms
(fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0)
2.0ms
(sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))
4.0ms
(cbrt (pow (sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0)) 3))

series1.4s

Counts
4 → 12
Calls
4 calls:
177.0ms
(pow (sin kx) 2.0)
273.0ms
(fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0)
467.0ms
(sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0))
467.0ms
(cbrt (pow (sqrt (fma (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) (pow (/ (* 2.0 l) Om) 2.0) 1.0)) 3))

simplify2.2s

Counts
85 → 85
Iterations

Useful iterations: 2 (238.0ms)

IterNodesCost
01131919
12651493
214521451
done50001451

prune635.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 1.1b

localize8.0ms

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

2 alts after pruning (0 fresh and 2 done)

Merged error: 1.1b

regimes462.0ms

Accuracy

0% (0.3b remaining)

Error of 1.5b against oracle of 1.2b and baseline of 1.5b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02431
12831
done2831

end0.0ms

sample3.2s

Algorithm
intervals
Results
2.7s8000×body80valid