Details

Time bar (total: 21.9s)

sample93.0ms

Algorithm
intervals
Results
58.0ms256×body80valid

simplify2.0s

Counts
1 → 1
Iterations
IterNodes
done5000
41691
3564
2172
157
022

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.4b

localize82.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin ky) (sin ky))
0.4b
(/ 1/2 (sqrt (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))
2.9b
(fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)
10.4b
(sqrt (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (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:
26.0ms
(* (sin ky) (sin ky))
13.0ms
(/ 1/2 (sqrt (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))
1.0ms
(fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)
7.0ms
(sqrt (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

series903.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(* (sin ky) (sin ky))
407.0ms
(/ 1/2 (sqrt (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))
163.0ms
(fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)
310.0ms
(sqrt (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

simplify2.0s

Counts
111 → 111
Iterations
IterNodes
done5001
32034
2753
1325
0153

prune775.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma (sin kx) (sin kx) (* (sin ky) (sin ky)))
0.2b
(* (* (/ 2 Om) l) (* (/ 2 Om) l))
0.3b
(* (sin ky) (sin ky))
2.9b
(fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
50×pow1
42×add-cbrt-cube add-exp-log
22×prod-exp cbrt-unprod
18×pow-prod-down
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-undiv div-exp
5×associate-*l/ pow-sqr pow-prod-up
4×expm1-log1p-u swap-sqr associate-*r* associate-*l* insert-posit16 log1p-expm1-u add-log-exp
3×pow-plus
2×pow2 *-commutative fma-udef
1×frac-times associate-*r/ sqr-sin sin-mult unswap-sqr
Counts
4 → 102
Calls
4 calls:
1.0ms
(fma (sin kx) (sin kx) (* (sin ky) (sin ky)))
110.0ms
(* (* (/ 2 Om) l) (* (/ 2 Om) l))
15.0ms
(* (sin ky) (sin ky))
0.0ms
(fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)

series392.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(fma (sin kx) (sin kx) (* (sin ky) (sin ky)))
68.0ms
(* (* (/ 2 Om) l) (* (/ 2 Om) l))
39.0ms
(* (sin ky) (sin ky))
184.0ms
(fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)

simplify1.7s

Counts
114 → 114
Iterations
IterNodes
done5002
21516
1424
0157

prune815.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize74.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1/2 (posit16->real (real->posit16 (sqrt (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))))
2.9b
(fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)
10.4b
(sqrt (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
22.9b
(posit16->real (real->posit16 (sqrt (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
9×times-frac
6×add-cbrt-cube add-exp-log
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* sqrt-prod associate-/l*
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp fma-udef div-inv remove-posit16
Counts
4 → 68
Calls
4 calls:
5.0ms
(/ 1/2 (posit16->real (real->posit16 (sqrt (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))))
0.0ms
(fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)
2.0ms
(sqrt (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
0.0ms
(posit16->real (real->posit16 (sqrt (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))))

series1.6s

Counts
4 → 12
Calls
4 calls:
856.0ms
(/ 1/2 (posit16->real (real->posit16 (sqrt (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))))
138.0ms
(fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)
284.0ms
(sqrt (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
308.0ms
(posit16->real (real->posit16 (sqrt (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))))

simplify1.8s

Counts
80 → 80
Iterations
IterNodes
done5001
31908
2507
1196
0108

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize105.0ms

Local error

Found 4 expressions with local error:

3.0b
(* (/ l Om) (sin ky))
3.0b
(* (/ l Om) (sin ky))
10.4b
(sqrt (fma (fma (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om) (* (* (/ l Om) (sin ky)) (* (/ l Om) (sin ky)))) 4 1))
22.9b
(posit16->real (real->posit16 (sqrt (fma (fma (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om) (* (* (/ l Om) (sin ky)) (* (/ l Om) (sin ky)))) 4 1))))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
26×associate-*l*
21×*-un-lft-identity add-cube-cbrt
20×times-frac
14×add-cbrt-cube add-exp-log
9×pow1
6×associate-*r*
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×sqrt-prod
2×cbrt-undiv div-exp pow-prod-down associate-*l/ *-commutative div-inv
1×rem-sqrt-square sqrt-pow1 pow1/2 remove-posit16
Counts
4 → 97
Calls
4 calls:
29.0ms
(* (/ l Om) (sin ky))
33.0ms
(* (/ l Om) (sin ky))
3.0ms
(sqrt (fma (fma (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om) (* (* (/ l Om) (sin ky)) (* (/ l Om) (sin ky)))) 4 1))
1.0ms
(posit16->real (real->posit16 (sqrt (fma (fma (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om) (* (* (/ l Om) (sin ky)) (* (/ l Om) (sin ky)))) 4 1))))

series1.1s

Counts
4 → 12
Calls
4 calls:
83.0ms
(* (/ l Om) (sin ky))
101.0ms
(* (/ l Om) (sin ky))
438.0ms
(sqrt (fma (fma (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om) (* (* (/ l Om) (sin ky)) (* (/ l Om) (sin ky)))) 4 1))
469.0ms
(posit16->real (real->posit16 (sqrt (fma (fma (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om) (* (* (/ l Om) (sin ky)) (* (/ l Om) (sin ky)))) 4 1))))

simplify2.2s

Counts
109 → 109
Iterations
IterNodes
done5000
32178
2709
1258
0123

prune1.4s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

regimes566.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations
IterNodes
done25
125
020

end0.0ms

sample2.8s

Algorithm
intervals
Results
2.5s8000×body80valid