Details

Time bar (total: 31.5s)

sample72.0ms

Algorithm
intervals
Results
36.0ms256×body80valid

simplify708.0ms

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

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

localize67.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin ky) 2.0)
0.7b
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
1.3b
(* (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)))))

rewrite179.0ms

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:
6.0ms
(pow (sin ky) 2.0)
17.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
136.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
12.0ms
(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:
150.0ms
(pow (sin ky) 2.0)
587.0ms
(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
582.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
542.0ms
(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

prune1.1s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize95.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 1.0 (sqrt (+ (* (pow (/ 2.0 (/ Om l)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0))) 1.0)))
1.3b
(* (pow (/ 2.0 (/ Om l)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)))
3.1b
(log (exp (/ 1.0 (sqrt (+ (* (pow (/ 2.0 (/ Om l)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0))) 1.0)))))
9.6b
(sqrt (+ (* (pow (/ 2.0 (/ Om l)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0))) 1.0))

rewrite434.0ms

Algorithm
rewrite-expression-head
Rules
105×times-frac
84×add-sqr-sqrt
75×*-un-lft-identity
71×add-cube-cbrt
49×unpow-prod-down
48×associate-*l*
25×log-pow
24×exp-prod sqrt-prod
18×add-exp-log
8×add-cbrt-cube
6×pow1 associate-/r* sqrt-div div-inv
5×associate-*r* prod-exp associate-/r/ unswap-sqr
4×flip3-+ div-exp flip-+ add-log-exp
3×log-prod pow-exp associate-/l*
2×associate-*r/ distribute-lft-out sqr-pow
1×distribute-rgt-in pow-to-exp cbrt-undiv rem-sqrt-square clear-num frac-2neg distribute-lft-in sqrt-pow1 pow1/2 rem-log-exp *-commutative cbrt-unprod
Counts
4 → 168
Calls
4 calls:
84.0ms
(/ 1.0 (sqrt (+ (* (pow (/ 2.0 (/ Om l)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0))) 1.0)))
116.0ms
(* (pow (/ 2.0 (/ Om l)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)))
155.0ms
(log (exp (/ 1.0 (sqrt (+ (* (pow (/ 2.0 (/ Om l)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0))) 1.0)))))
66.0ms
(sqrt (+ (* (pow (/ 2.0 (/ Om l)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0))) 1.0))

series2.2s

Counts
4 → 12
Calls
4 calls:
596.0ms
(/ 1.0 (sqrt (+ (* (pow (/ 2.0 (/ Om l)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0))) 1.0)))
525.0ms
(* (pow (/ 2.0 (/ Om l)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)))
622.0ms
(log (exp (/ 1.0 (sqrt (+ (* (pow (/ 2.0 (/ Om l)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0))) 1.0)))))
430.0ms
(sqrt (+ (* (pow (/ 2.0 (/ Om l)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0))) 1.0))

simplify2.1s

Counts
180 → 180
Iterations
IterNodes
done5000
24630
11076
0383

prune2.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize100.0ms

Local error

Found 4 expressions with local error:

3.2b
(log (sqrt (exp (/ 1.0 (sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) 2.0)) 1.0))))))
3.2b
(log (sqrt (exp (/ 1.0 (sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) 2.0)) 1.0))))))
9.6b
(sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) 2.0)) 1.0))
9.6b
(sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) 2.0)) 1.0))

rewrite475.0ms

Algorithm
rewrite-expression-head
Rules
54×log-pow
52×sqrt-pow1
48×exp-prod
38×add-sqr-sqrt
36×*-un-lft-identity times-frac add-cube-cbrt
30×sqrt-prod
12×log-prod
10×pow1
8×sqrt-div
6×add-exp-log
4×flip3-+ add-cbrt-cube pow1/2 associate-/r/ flip-+ add-log-exp
2×rem-sqrt-square rem-log-exp div-inv
Counts
4 → 112
Calls
4 calls:
155.0ms
(log (sqrt (exp (/ 1.0 (sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) 2.0)) 1.0))))))
162.0ms
(log (sqrt (exp (/ 1.0 (sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) 2.0)) 1.0))))))
90.0ms
(sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) 2.0)) 1.0))
63.0ms
(sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) 2.0)) 1.0))

series3.1s

Counts
4 → 12
Calls
4 calls:
941.0ms
(log (sqrt (exp (/ 1.0 (sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) 2.0)) 1.0))))))
995.0ms
(log (sqrt (exp (/ 1.0 (sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) 2.0)) 1.0))))))
529.0ms
(sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) 2.0)) 1.0))
594.0ms
(sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) 2.0)) 1.0))

simplify1.5s

Counts
124 → 124
Iterations
IterNodes
done5000
31965
2491
1226
0142

prune1.8s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize164.0ms

Local error

Found 4 expressions with local error:

1.3b
(* (pow (/ 2.0 (/ Om l)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)))
3.2b
(log (sqrt (exp (/ 1.0 (sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) 2.0)) 1.0))))))
9.6b
(sqrt (+ (* (pow (/ 2.0 (/ Om l)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0))) 1.0))
9.6b
(sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) 2.0)) 1.0))

rewrite506.0ms

Algorithm
rewrite-expression-head
Rules
87×times-frac
72×add-sqr-sqrt
62×*-un-lft-identity
58×add-cube-cbrt
49×unpow-prod-down
48×associate-*l*
27×sqrt-pow1 log-pow
24×exp-prod
18×sqrt-prod
17×add-exp-log
8×pow1
6×log-prod add-cbrt-cube sqrt-div
5×associate-*r* prod-exp div-inv unswap-sqr
4×flip3-+ flip-+ add-log-exp
3×pow1/2 div-exp pow-exp associate-/r/
2×rem-sqrt-square associate-*r/ distribute-lft-out sqr-pow
1×distribute-rgt-in pow-to-exp distribute-lft-in rem-log-exp *-commutative cbrt-unprod
Counts
4 → 147
Calls
4 calls:
154.0ms
(* (pow (/ 2.0 (/ Om l)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)))
176.0ms
(log (sqrt (exp (/ 1.0 (sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) 2.0)) 1.0))))))
93.0ms
(sqrt (+ (* (pow (/ 2.0 (/ Om l)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0))) 1.0))
74.0ms
(sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) 2.0)) 1.0))

series2.7s

Counts
4 → 12
Calls
4 calls:
594.0ms
(* (pow (/ 2.0 (/ Om l)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)))
994.0ms
(log (sqrt (exp (/ 1.0 (sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) 2.0)) 1.0))))))
474.0ms
(sqrt (+ (* (pow (/ 2.0 (/ Om l)) 2.0) (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0))) 1.0))
615.0ms
(sqrt (+ (* (+ (pow (sin ky) 2.0) (pow (sin kx) 2.0)) (pow (/ 2.0 (/ Om l)) 2.0)) 1.0))

simplify2.0s

Counts
159 → 159
Iterations
IterNodes
done5000
24660
11086
0392

prune2.9s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

regimes801.0ms

Accuracy

0% (0.4b remaining)

Error of 1.8b against oracle of 1.4b and baseline of 1.8b

bsearch0.0ms

simplify6.0ms

Iterations
IterNodes
done29
129
024

end0.0ms

sample3.1s

Algorithm
intervals
Results
2.6s8000×body80valid