Details

Time bar (total: 15.5s)

sample107.0ms

Algorithm
intervals
Results
74.0ms256×body80valid

simplify1.1s

Counts
1 → 1
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
02229
15229
213228
334428
4124528
done500028

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin kx) 2.0)
0.3b
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
1.4b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
9.6b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite182.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
30×*-un-lft-identity
26×add-cube-cbrt
21×times-frac
19×add-exp-log
15×sqrt-prod
13×unpow-prod-down
11×associate-*l*
8×add-cbrt-cube
6×pow1 prod-exp associate-/r*
5×associate-*r*
4×expm1-log1p-u sqrt-div pow-exp log1p-expm1-u add-log-exp
3×pow-unpow flip3-+ div-exp flip-+ associate-/l* unswap-sqr sqr-pow
2×pow-to-exp associate-*r/ associate-/r/ div-inv distribute-lft-out
1×cbrt-undiv distribute-rgt-in rem-sqrt-square pow-pow frac-2neg distribute-lft-in sqrt-pow1 pow1/2 clear-num *-commutative cbrt-unprod
Counts
4 → 118
Calls
4 calls:
4.0ms
(pow (sin kx) 2.0)
13.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
143.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
16.0ms
(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:
154.0ms
(pow (sin kx) 2.0)
683.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
634.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
595.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify2.2s

Counts
130 → 130
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02303178
16062908
224842714
done50042712

prune1.0s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.5b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (sin ky) 2.0)
0.2b
(log1p (expm1 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
0.3b
(pow (sin kx) 2.0)
1.4b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log
17×add-sqr-sqrt
16×unpow-prod-down *-un-lft-identity
12×add-cube-cbrt
11×associate-*l*
6×pow1 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 unswap-sqr
2×pow-pow associate-*r/ div-exp distribute-lft-out
1×distribute-rgt-in log1p-udef distribute-lft-in flip3-+ log1p-expm1 *-commutative cbrt-unprod flip-+ div-inv
Counts
4 → 88
Calls
4 calls:
8.0ms
(pow (sin ky) 2.0)
1.0ms
(log1p (expm1 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
6.0ms
(pow (sin kx) 2.0)
120.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series1.7s

Counts
4 → 12
Calls
4 calls:
158.0ms
(pow (sin ky) 2.0)
751.0ms
(log1p (expm1 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
192.0ms
(pow (sin kx) 2.0)
641.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.6s

Counts
100 → 100
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01831508
15361427
221931332
done50001330

prune1.2s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.5b

regimes951.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02229
12829
done2829

end0.0ms

sample3.0s

Algorithm
intervals
Results
2.5s8000×body80valid