Details

Time bar (total: 25.5s)

sample172.0ms

Algorithm
intervals
Results
138.0ms256×body80valid

simplify1.5s

Counts
1 → 1
Iterations
IterNodes
done2000
52000
41691
3564
2172
157
022

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize58.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin ky) (sin ky))
0.6b
(/ 1/2 (sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))
1.2b
(fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)
9.0b
(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
24×*-un-lft-identity add-cube-cbrt
18×times-frac
15×sqrt-prod
12×pow1
8×add-cbrt-cube add-exp-log
6×associate-/r*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×swap-sqr associate-*r* associate-*l* associate-/l*
1×pow2 cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow-plus pow1/2 div-exp pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod fma-udef sqr-sin div-inv sin-mult unswap-sqr
Counts
4 → 99
Calls
4 calls:
11.0ms
(* (sin ky) (sin ky))
4.0ms
(/ 1/2 (sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))
0.0ms
(fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)
3.0ms
(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

series985.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* (sin ky) (sin ky))
466.0ms
(/ 1/2 (sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))
178.0ms
(fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)
317.0ms
(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

simplify1.4s

Counts
111 → 111
Iterations
IterNodes
done2003
42003
31947
2766
1338
0159

prune1.9s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize68.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1/2 (sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))
1.2b
(fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)
2.2b
(log (exp (/ 1/2 (sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))))
9.0b
(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
35×add-sqr-sqrt
34×*-un-lft-identity add-cube-cbrt
24×sqrt-prod
23×log-pow
22×exp-prod
6×pow1 associate-/r* add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×log-prod associate-/l*
2×div-inv
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp rem-log-exp fma-udef
Counts
4 → 106
Calls
4 calls:
4.0ms
(/ 1/2 (sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))
0.0ms
(fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)
6.0ms
(log (exp (/ 1/2 (sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))))
1.0ms
(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

series1.4s

Counts
4 → 12
Calls
4 calls:
437.0ms
(/ 1/2 (sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))
179.0ms
(fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)
442.0ms
(log (exp (/ 1/2 (sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))))
319.0ms
(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

simplify1.1s

Counts
118 → 118
Iterations
IterNodes
done2001
32001
2644
1274
0170

prune2.4s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

localize65.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (* 2 l) Om) (/ (* 2 l) Om))
0.2b
(log (exp (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))
0.3b
(* (sin ky) (sin ky))
1.2b
(fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
42×add-cbrt-cube add-exp-log
22×add-sqr-sqrt
19×pow1
18×*-un-lft-identity add-cube-cbrt
16×prod-exp cbrt-unprod
12×cbrt-undiv times-frac div-exp
10×swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u log-prod log-pow insert-posit16 log1p-expm1-u div-inv add-log-exp
3×exp-prod
2×pow2 pow-plus pow-prod-down pow-sqr *-commutative pow-prod-up fma-udef unswap-sqr
1×frac-times rem-log-exp exp-sum associate-*l/ associate-*r/ sqr-sin sin-mult
Counts
4 → 119
Calls
4 calls:
35.0ms
(* (/ (* 2 l) Om) (/ (* 2 l) Om))
2.0ms
(log (exp (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))
11.0ms
(* (sin ky) (sin ky))
0.0ms
(fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)

series481.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (/ (* 2 l) Om) (/ (* 2 l) Om))
176.0ms
(log (exp (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))
33.0ms
(* (sin ky) (sin ky))
228.0ms
(fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)

simplify1.4s

Counts
131 → 131
Iterations
IterNodes
done2001
32001
21843
1535
0196

prune2.7s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize121.0ms

Local error

Found 4 expressions with local error:

3.4b
(log (cbrt (exp (/ 1/2 (sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))))))
9.0b
(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
9.0b
(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
9.0b
(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt sqrt-prod
8×pow1
6×log-prod
5×add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod rem-sqrt-square sqrt-pow1 pow1/2
2×log-pow
1×pow1/3 rem-log-exp
Counts
4 → 67
Calls
4 calls:
7.0ms
(log (cbrt (exp (/ 1/2 (sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))))))
2.0ms
(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
2.0ms
(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
2.0ms
(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

series1.6s

Counts
4 → 12
Calls
4 calls:
300.0ms
(log (cbrt (exp (/ 1/2 (sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))))))
341.0ms
(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
723.0ms
(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
241.0ms
(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

simplify1.5s

Counts
79 → 79
Iterations
IterNodes
done2000
52000
41787
3458
2185
1105
073

prune2.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

regimes814.0ms

Accuracy

0% (0.8b remaining)

Error of 1.6b against oracle of 0.8b and baseline of 1.6b

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done25
125
021

end0.0ms

sample3.7s

Algorithm
intervals
Results
3.4s8000×body80valid