Details

Time bar (total: 20.1s)

sample98.0ms

Algorithm
intervals
Results
61.0ms256×body80valid

simplify690.0ms

Counts
1 → 1

prune44.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.5b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin kx) 2.0)
0.3b
(pow (/ (* 2.0 l) Om) 2.0)
1.4b
(* (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)))))

rewrite154.0ms

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 kx) 2.0)
14.0ms
(pow (/ (* 2.0 l) Om) 2.0)
117.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
13.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series1.3s

Counts
4 → 12
Calls
4 calls:
115.0ms
(pow (sin kx) 2.0)
110.0ms
(pow (/ (* 2.0 l) Om) 2.0)
590.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
476.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify1.0s

Counts
104 → 104

prune712.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.1b

localize55.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin kx) 2.0)
0.4b
(* (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))))
2.8b
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
9.4b
(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))))))

rewrite308.0ms

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:
4.0ms
(pow (sin kx) 2.0)
154.0ms
(* (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))))
138.0ms
(* (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))))))

series1.8s

Counts
4 → 12
Calls
4 calls:
146.0ms
(pow (sin kx) 2.0)
582.0ms
(* (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))))
583.0ms
(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
445.0ms
(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))))))

simplify1.2s

Counts
139 → 139

prune874.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin kx) 2.0)
0.3b
(pow (/ (* 2.0 l) Om) 2.0)
1.4b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
1.6b
(log (exp (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite184.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
20×unpow-prod-down
19×add-sqr-sqrt
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×log-prod associate-*r* add-log-exp
4×div-exp sqr-pow
3×pow-to-exp log-pow unswap-sqr
2×distribute-rgt-in pow-pow distribute-lft-in associate-*r/ exp-sum div-inv distribute-lft-out
1×exp-prod exp-to-pow flip3-+ rem-log-exp *-commutative cbrt-unprod flip-+
Counts
4 → 93
Calls
4 calls:
8.0ms
(pow (sin kx) 2.0)
17.0ms
(pow (/ (* 2.0 l) Om) 2.0)
139.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
14.0ms
(log (exp (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series1.8s

Counts
4 → 12
Calls
4 calls:
173.0ms
(pow (sin kx) 2.0)
152.0ms
(pow (/ (* 2.0 l) Om) 2.0)
909.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
599.0ms
(log (exp (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify894.0ms

Counts
105 → 105

prune828.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 1.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin kx) 2.0)
0.3b
(pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2)))
1.2b
(log (pow (exp (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2)))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
1.2b
(pow (exp (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2)))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
25×unpow-prod-down
19×*-un-lft-identity
15×add-sqr-sqrt add-cube-cbrt
14×pow-pow
12×add-exp-log
11×exp-prod
9×pow-unpow
8×log-prod
7×pow1
6×times-frac pow-exp
5×sqr-pow
4×pow-to-exp add-cbrt-cube add-log-exp
3×rem-log-exp
2×unpow-prod-up div-exp div-inv distribute-lft-out
1×prod-exp log-pow
Counts
4 → 88
Calls
4 calls:
8.0ms
(pow (sin kx) 2.0)
18.0ms
(pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2)))
36.0ms
(log (pow (exp (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2)))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
68.0ms
(pow (exp (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2)))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series945.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(pow (sin kx) 2.0)
124.0ms
(pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2)))
350.0ms
(log (pow (exp (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2)))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
325.0ms
(pow (exp (pow (/ (* 2.0 l) Om) (* 2 (/ 2.0 2)))) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify944.0ms

Counts
100 → 100

prune763.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 1.1b

regimes829.0ms

Accuracy

0% (0.1b remaining)

Error of 1.3b against oracle of 1.2b and baseline of 1.3b

bsearch0.0ms

simplify1.3s

end0.0ms

sample3.1s

Algorithm
intervals
Results
2.6s7998×body80valid
1.0ms2×body160valid