Details

Time bar (total: 23.6s)

sample109.0ms

Algorithm
intervals
Results
70.0ms256×body80valid

simplify757.0ms

Counts
1 → 1
Iterations
IterNodes
done5001
41131
3299
2124
152
022

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

localize66.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin ky) 2.0)
0.4b
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
2.2b
(* (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)))))

rewrite119.0ms

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 associate-/r* prod-exp
5×associate-*r*
4×sqrt-div pow-exp 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×distribute-rgt-in cbrt-undiv rem-sqrt-square clear-num pow-pow frac-2neg distribute-lft-in sqrt-pow1 pow1/2 *-commutative cbrt-unprod
Counts
4 → 110
Calls
4 calls:
5.0ms
(pow (sin ky) 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))))))
86.0ms
(* (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)))))

series1.9s

Counts
4 → 12
Calls
4 calls:
169.0ms
(pow (sin ky) 2.0)
676.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
506.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
533.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify1.4s

Counts
122 → 122
Iterations
IterNodes
done5001
22401
1590
0222

prune1.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.8b

localize64.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1.0 (sqrt (+ 1.0 (* (* (pow (/ 2.0 (/ Om l)) (/ 2.0 2)) (sqrt (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)))) (* (pow (/ 2.0 (/ Om l)) (/ 2.0 2)) (sqrt (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0))))))))
2.6b
(sqrt (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)))
2.6b
(sqrt (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)))
9.6b
(sqrt (+ 1.0 (* (* (pow (/ 2.0 (/ Om l)) (/ 2.0 2)) (sqrt (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)))) (* (pow (/ 2.0 (/ Om l)) (/ 2.0 2)) (sqrt (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)))))))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
30×*-un-lft-identity
25×add-sqr-sqrt sqrt-prod
22×add-cube-cbrt
18×times-frac
8×sqrt-div
7×pow1
6×associate-/r* add-cbrt-cube add-exp-log
4×unpow-prod-down flip3-+ flip-+ distribute-lft-out add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 associate-/l*
2×associate-/r/
1×cbrt-undiv clear-num frac-2neg div-exp div-inv
Counts
4 → 90
Calls
4 calls:
16.0ms
(/ 1.0 (sqrt (+ 1.0 (* (* (pow (/ 2.0 (/ Om l)) (/ 2.0 2)) (sqrt (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)))) (* (pow (/ 2.0 (/ Om l)) (/ 2.0 2)) (sqrt (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0))))))))
51.0ms
(sqrt (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)))
25.0ms
(sqrt (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)))
5.0ms
(sqrt (+ 1.0 (* (* (pow (/ 2.0 (/ Om l)) (/ 2.0 2)) (sqrt (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)))) (* (pow (/ 2.0 (/ Om l)) (/ 2.0 2)) (sqrt (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)))))))

series1.5s

Counts
4 → 12
Calls
4 calls:
635.0ms
(/ 1.0 (sqrt (+ 1.0 (* (* (pow (/ 2.0 (/ Om l)) (/ 2.0 2)) (sqrt (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)))) (* (pow (/ 2.0 (/ Om l)) (/ 2.0 2)) (sqrt (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0))))))))
120.0ms
(sqrt (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)))
135.0ms
(sqrt (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)))
583.0ms
(sqrt (+ 1.0 (* (* (pow (/ 2.0 (/ Om l)) (/ 2.0 2)) (sqrt (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)))) (* (pow (/ 2.0 (/ Om l)) (/ 2.0 2)) (sqrt (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)))))))

simplify740.0ms

Counts
102 → 102
Iterations
IterNodes
done5002
21501
1384
0166

prune930.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.8b

localize95.0ms

Local error

Found 4 expressions with local error:

6.7b
(sqrt (/ 1.0 (sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) (* 2 (/ 2.0 2)))) 1.0))))
6.7b
(sqrt (/ 1.0 (sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) (* 2 (/ 2.0 2)))) 1.0))))
9.6b
(sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) (* 2 (/ 2.0 2)))) 1.0))
9.6b
(sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) (* 2 (/ 2.0 2)))) 1.0))

rewrite348.0ms

Algorithm
rewrite-expression-head
Rules
74×sqrt-prod
44×add-sqr-sqrt
40×times-frac
32×*-un-lft-identity add-cube-cbrt
10×sqrt-div
8×pow1 rem-sqrt-square
4×sqrt-pow1 flip3-+ add-cbrt-cube pow1/2 add-exp-log associate-/r/ flip-+ add-log-exp
2×div-inv
Counts
4 → 104
Calls
4 calls:
79.0ms
(sqrt (/ 1.0 (sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) (* 2 (/ 2.0 2)))) 1.0))))
85.0ms
(sqrt (/ 1.0 (sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) (* 2 (/ 2.0 2)))) 1.0))))
87.0ms
(sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) (* 2 (/ 2.0 2)))) 1.0))
93.0ms
(sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) (* 2 (/ 2.0 2)))) 1.0))

series2.7s

Counts
4 → 12
Calls
4 calls:
768.0ms
(sqrt (/ 1.0 (sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) (* 2 (/ 2.0 2)))) 1.0))))
738.0ms
(sqrt (/ 1.0 (sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) (* 2 (/ 2.0 2)))) 1.0))))
581.0ms
(sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) (* 2 (/ 2.0 2)))) 1.0))
644.0ms
(sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) (* 2 (/ 2.0 2)))) 1.0))

simplify1.0s

Counts
116 → 116
Iterations
IterNodes
done5000
31895
2471
1206
0126

prune1.3s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.8b

localize463.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) (* 2 (/ 2.0 2))))
6.7b
(sqrt (/ 1.0 (sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) (* 2 (/ 2.0 2)))) 1.0))))
9.6b
(sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) (* 2 (/ 2.0 2)))) 1.0))
9.6b
(sqrt (+ 1.0 (* (pow (/ 2.0 (/ Om l)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)))))

rewrite373.0ms

Algorithm
rewrite-expression-head
Rules
89×times-frac
75×add-sqr-sqrt
60×*-un-lft-identity
56×add-cube-cbrt
49×unpow-prod-down
48×associate-*r*
40×sqrt-prod
16×add-exp-log
7×pow1 sqrt-div
6×add-cbrt-cube
5×rem-sqrt-square associate-*l* prod-exp div-inv unswap-sqr
4×flip3-+ flip-+ add-log-exp
3×sqrt-pow1 pow1/2 div-exp pow-exp associate-/r/
2×associate-*l/ distribute-lft-out sqr-pow
1×pow-to-exp *-commutative cbrt-unprod
Counts
4 → 141
Calls
4 calls:
169.0ms
(* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) (* 2 (/ 2.0 2))))
99.0ms
(sqrt (/ 1.0 (sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) (* 2 (/ 2.0 2)))) 1.0))))
88.0ms
(sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) (* 2 (/ 2.0 2)))) 1.0))
9.0ms
(sqrt (+ 1.0 (* (pow (/ 2.0 (/ Om l)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)))))

series2.3s

Counts
4 → 12
Calls
4 calls:
548.0ms
(* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) (* 2 (/ 2.0 2))))
724.0ms
(sqrt (/ 1.0 (sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) (* 2 (/ 2.0 2)))) 1.0))))
565.0ms
(sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) (* 2 (/ 2.0 2)))) 1.0))
502.0ms
(sqrt (+ 1.0 (* (pow (/ 2.0 (/ Om l)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)))))

simplify571.0ms

Counts
153 → 153
Iterations
IterNodes
done5000
1903
0390

prune2.2s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.8b

regimes524.0ms

Accuracy

0% (0.0b remaining)

Error of 1.4b against oracle of 1.4b and baseline of 1.4b

bsearch0.0ms

simplify8.0ms

Iterations
IterNodes
done31
131
026

end0.0ms

sample2.9s

Algorithm
intervals
Results
2.4s8000×body80valid