Details

Time bar (total: 13.2s)

sample75.0ms

Algorithm
intervals
Results
44.0ms256×body80valid

simplify34.0ms

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (sin ky) 2.0)
0.3b
(pow (sin kx) 2.0)
2.9b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
9.0b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite99.0ms

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 ky) 2.0)
4.0ms
(pow (sin kx) 2.0)
82.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series1.0s

Counts
4 → 12
Calls
4 calls:
116.0ms
(pow (sin ky) 2.0)
118.0ms
(pow (sin kx) 2.0)
432.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
375.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify55.0ms

Counts
98 → 98

prune460.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 2.1b

localize52.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
9×add-cube-cbrt *-un-lft-identity
8×sqrt-div
7×pow1
6×cbrt-prod
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×cbrt-div
1×pow1/3
Counts
4 → 61
Calls
4 calls:
4.0ms
(cbrt (sqrt (+ 1.0 (* (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)))))
5.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
6.0ms
(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:
353.0ms
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
373.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
371.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
387.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify79.0ms

Counts
73 → 73

prune469.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 2.1b

localize8.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify2.0ms

Counts
0 → 0

prune7.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 2.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin kx) 2.0)
7.5b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (- (+ (* 0.04444444444444444 (pow ky 6)) (pow ky 2)) (* 0.3333333333333333 (pow ky 4)))))))
10.1b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (- (+ (* 0.04444444444444444 (pow ky 6)) (pow ky 2)) (* 0.3333333333333333 (pow ky 4)))))
18.2b
(- (+ (* 0.04444444444444444 (pow ky 6)) (pow ky 2)) (* 0.3333333333333333 (pow ky 4)))

rewrite543.0ms

Algorithm
rewrite-expression-head
Rules
17×add-exp-log add-sqr-sqrt
13×*-un-lft-identity
11×add-cube-cbrt unpow-prod-down associate-*l*
9×add-log-exp
6×pow1 prod-exp add-cbrt-cube
4×associate-*r* pow-exp
3×pow-unpow times-frac sqrt-prod unswap-sqr sqr-pow
2×pow-to-exp flip3-+ sqrt-div diff-log associate-*r/ div-exp flip-+
1×distribute-rgt-in sub-neg rem-sqrt-square flip3-- pow-pow distribute-lft-in sqrt-pow1 pow1/2 associate--l+ sum-log *-commutative flip-- cbrt-unprod div-inv distribute-lft-out
Counts
4 → 82
Calls
4 calls:
4.0ms
(pow (sin kx) 2.0)
6.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (- (+ (* 0.04444444444444444 (pow ky 6)) (pow ky 2)) (* 0.3333333333333333 (pow ky 4)))))))
429.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (- (+ (* 0.04444444444444444 (pow ky 6)) (pow ky 2)) (* 0.3333333333333333 (pow ky 4)))))
102.0ms
(- (+ (* 0.04444444444444444 (pow ky 6)) (pow ky 2)) (* 0.3333333333333333 (pow ky 4)))

series5.4s

Counts
4 → 12
Calls
4 calls:
115.0ms
(pow (sin kx) 2.0)
4.0s
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (- (+ (* 0.04444444444444444 (pow ky 6)) (pow ky 2)) (* 0.3333333333333333 (pow ky 4)))))))
1.3s
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (- (+ (* 0.04444444444444444 (pow ky 6)) (pow ky 2)) (* 0.3333333333333333 (pow ky 4)))))
72.0ms
(- (+ (* 0.04444444444444444 (pow ky 6)) (pow ky 2)) (* 0.3333333333333333 (pow ky 4)))

simplify79.0ms

Counts
94 → 94

prune551.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 2.1b

regimes515.0ms

Accuracy

0% (0.4b remaining)

Error of 1.7b against oracle of 1.2b and baseline of 1.7b

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.8s8000×body80valid