Details

Time bar (total: 30.1s)

sample105.0ms

Algorithm
intervals
Results
61.0ms256×body80valid

simplify4.1s

Counts
1 → 1
Iterations
IterNodes
done5001
54017
4920
3263
2121
152
022

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.5b

localize98.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (sin ky) 2.0)
0.3b
(pow (/ (* 2.0 l) Om) 2.0)
3.1b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
6.8b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
20×add-sqr-sqrt unpow-prod-down
18×*-un-lft-identity
14×add-cube-cbrt
11×associate-*l*
7×pow1 pow-exp prod-exp
6×pow-unpow times-frac add-cbrt-cube
5×associate-*r*
4×div-exp add-log-exp sqr-pow
3×pow-to-exp sqrt-prod unswap-sqr
2×pow-pow flip3-+ sqrt-div associate-*r/ flip-+ div-inv distribute-lft-out
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 *-commutative cbrt-unprod
Counts
4 → 92
Calls
4 calls:
6.0ms
(pow (sin ky) 2.0)
13.0ms
(pow (/ (* 2.0 l) Om) 2.0)
92.0ms
(* (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)))))

series1.4s

Counts
4 → 12
Calls
4 calls:
142.0ms
(pow (sin ky) 2.0)
123.0ms
(pow (/ (* 2.0 l) Om) 2.0)
641.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
516.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify2.1s

Counts
104 → 104
Iterations
IterNodes
done5001
21871
1584
0205

prune1.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 2.0b

localize83.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (sin ky) 2.0)
0.9b
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
2.6b
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
6.8b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

rewrite212.0ms

Algorithm
rewrite-expression-head
Rules
124×add-exp-log
72×prod-exp
37×pow-exp
24×div-exp
22×associate-*l*
20×add-sqr-sqrt unpow-prod-down
18×*-un-lft-identity
14×add-cube-cbrt
13×pow-to-exp
11×add-cbrt-cube
6×pow1 times-frac associate-*r* associate-*r/
5×distribute-rgt-in distribute-lft-in
4×cbrt-unprod add-log-exp sqr-pow
3×pow-unpow flip3-+ sqrt-prod flip-+ unswap-sqr
2×sqrt-div *-commutative div-inv distribute-lft-out
1×rem-sqrt-square pow-pow sqrt-pow1 pow1/2
Counts
4 → 127
Calls
4 calls:
3.0ms
(pow (sin ky) 2.0)
104.0ms
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
95.0ms
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
5.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

series2.0s

Counts
4 → 12
Calls
4 calls:
201.0ms
(pow (sin ky) 2.0)
645.0ms
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
670.0ms
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
508.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

simplify2.3s

Counts
139 → 139
Iterations
IterNodes
done5006
22242
1654
0227

prune1.3s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 2.0b

localize116.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt Om)
3.4b
(* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
6.8b
(sqrt (+ 1.0 (* (pow (/ 2.0 (* (cbrt Om) (cbrt Om))) 2.0) (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
10.8b
(* (pow (/ 2.0 (* (cbrt Om) (cbrt Om))) 2.0) (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))

rewrite275.0ms

Algorithm
rewrite-expression-head
Rules
92×add-exp-log
54×prod-exp
37×associate-*l*
36×add-sqr-sqrt
34×unpow-prod-down
28×*-un-lft-identity
27×pow-exp
24×add-cube-cbrt
23×times-frac
16×div-exp
13×cbrt-prod
11×pow-to-exp add-cbrt-cube
6×associate-*r* associate-*r/
5×distribute-rgt-in pow1 distribute-lft-in unswap-sqr
4×cbrt-unprod add-log-exp
3×flip3-+ sqrt-prod flip-+ sqr-pow
2×sqrt-div *-commutative div-inv distribute-lft-out
1×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 132
Calls
4 calls:
1.0ms
(cbrt Om)
139.0ms
(* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.0ms
(sqrt (+ 1.0 (* (pow (/ 2.0 (* (cbrt Om) (cbrt Om))) 2.0) (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
119.0ms
(* (pow (/ 2.0 (* (cbrt Om) (cbrt Om))) 2.0) (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))

series2.6s

Counts
4 → 12
Calls
4 calls:
284.0ms
(cbrt Om)
583.0ms
(* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
854.0ms
(sqrt (+ 1.0 (* (pow (/ 2.0 (* (cbrt Om) (cbrt Om))) 2.0) (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
888.0ms
(* (pow (/ 2.0 (* (cbrt Om) (cbrt Om))) 2.0) (* (pow (/ l (cbrt Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))

simplify2.4s

Counts
144 → 144
Iterations
IterNodes
done5000
22992
1829
0299

prune1.6s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 1.0b

localize137.0ms

Local error

Found 4 expressions with local error:

3.5b
(/ (* (sin ky) l) Om)
3.5b
(/ (* (sin ky) l) Om)
4.2b
(/ (* (sin kx) l) Om)
4.2b
(/ (* (sin kx) l) Om)

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
24×add-cbrt-cube add-exp-log
12×add-sqr-sqrt associate-/r* *-un-lft-identity times-frac add-cube-cbrt
8×cbrt-undiv div-exp
4×pow1 clear-num frac-2neg prod-exp cbrt-unprod div-inv associate-/l* add-log-exp
Counts
4 → 84
Calls
4 calls:
19.0ms
(/ (* (sin ky) l) Om)
18.0ms
(/ (* (sin ky) l) Om)
18.0ms
(/ (* (sin kx) l) Om)
19.0ms
(/ (* (sin kx) l) Om)

series346.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(/ (* (sin ky) l) Om)
87.0ms
(/ (* (sin ky) l) Om)
66.0ms
(/ (* (sin kx) l) Om)
110.0ms
(/ (* (sin kx) l) Om)

simplify2.2s

Counts
96 → 96
Iterations
IterNodes
done5015
33680
2992
1262
098

prune1.1s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 1.0b

regimes1.3s

Accuracy

0% (0.2b remaining)

Error of 0.9b against oracle of 0.7b and baseline of 0.9b

bsearch0.0ms

simplify9.0ms

Iterations
IterNodes
done32
132
025

end0.0ms

sample3.0s

Algorithm
intervals
Results
2.6s8000×body80valid