Details

Time bar (total: 27.2s)

sample99.0ms

Algorithm
intervals
Results
77.0ms256×body80valid

simplify1.4s

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

prune37.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.4b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin ky) (sin ky))
0.4b
(/ 1/2 (sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))
2.2b
(fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)
9.6b
(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

rewrite53.0ms

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:
35.0ms
(* (sin ky) (sin ky))
9.0ms
(/ 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)
5.0ms
(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

series965.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(* (sin ky) (sin ky))
407.0ms
(/ 1/2 (sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))
185.0ms
(fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)
347.0ms
(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

simplify1.3s

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

prune2.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.9b

localize99.0ms

Local error

Found 4 expressions with local error:

7.6b
(cbrt (sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))
9.6b
(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
9.6b
(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
9.6b
(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
9×*-un-lft-identity add-cube-cbrt
7×pow1
6×cbrt-prod
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
1×pow1/3
Counts
4 → 65
Calls
4 calls:
1.0ms
(cbrt (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))
1.0ms
(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:
380.0ms
(cbrt (sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))
325.0ms
(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
357.0ms
(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
326.0ms
(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

simplify1.2s

Counts
77 → 77
Iterations
IterNodes
done2000
42000
3855
2296
1140
078

prune1.8s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.9b

localize65.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1/2 (sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))
2.2b
(fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)
3.5b
(log (exp (/ 1/2 (sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))))
9.6b
(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

rewrite20.0ms

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:
5.0ms
(/ 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)
12.0ms
(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))

series1.5s

Counts
4 → 12
Calls
4 calls:
423.0ms
(/ 1/2 (sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))
229.0ms
(fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)
488.0ms
(log (exp (/ 1/2 (sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))))
346.0ms
(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

simplify1.0s

Counts
118 → 118
Iterations
IterNodes
done2001
32001
2644
1274
0170

prune2.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.9b

localize84.0ms

Local error

Found 4 expressions with local error:

3.5b
(log (exp (/ 1/2 (sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky)))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)))))
4.2b
(/ (sin kx) (/ Om l))
4.2b
(/ (sin kx) (/ Om l))
9.6b
(sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky)))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
168×times-frac
104×add-sqr-sqrt
103×*-un-lft-identity add-cube-cbrt
26×associate-/r*
23×log-pow
22×exp-prod
14×add-cbrt-cube add-exp-log
12×sqrt-prod
11×div-inv
6×pow1 cbrt-undiv div-exp associate-/l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×log-prod
2×clear-num frac-2neg associate-/r/
1×rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp
Counts
4 → 199
Calls
4 calls:
20.0ms
(log (exp (/ 1/2 (sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky)))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)))))
19.0ms
(/ (sin kx) (/ Om l))
19.0ms
(/ (sin kx) (/ Om l))
2.0ms
(sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky)))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))

series1.0s

Counts
4 → 12
Calls
4 calls:
432.0ms
(log (exp (/ 1/2 (sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky)))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)))))
125.0ms
(/ (sin kx) (/ Om l))
134.0ms
(/ (sin kx) (/ Om l))
324.0ms
(sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky)))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))

simplify1.2s

Counts
211 → 211
Iterations
IterNodes
done2000
32000
21344
1566
0277

prune4.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.9b

regimes1.3s

Accuracy

0% (0.0b remaining)

Error of 0.6b against oracle of 0.6b and baseline of 0.6b

bsearch0.0ms

simplify9.0ms

Iterations
IterNodes
done27
127
023

end0.0ms

sample3.7s

Algorithm
intervals
Results
3.4s8000×body80valid