Details

Time bar (total: 21.6s)

sample86.0ms

Algorithm
intervals
Results
60.0ms256×body80valid

simplify1.5s

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.1b

localize91.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (* 2 l) Om) (/ (* 2 l) Om))
0.3b
(* (sin ky) (sin ky))
1.8b
(fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)
11.1b
(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
42×add-cbrt-cube add-exp-log
22×add-sqr-sqrt
19×pow1
17×*-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 insert-posit16 log1p-expm1-u div-inv add-log-exp
3×sqrt-prod
2×pow2 pow-plus pow-prod-down pow-sqr *-commutative pow-prod-up unswap-sqr
1×frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ associate-*r/ fma-udef sqr-sin sin-mult
Counts
4 → 116
Calls
4 calls:
53.0ms
(* (/ (* 2 l) Om) (/ (* 2 l) Om))
23.0ms
(* (sin ky) (sin ky))
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))

series670.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(* (/ (* 2 l) Om) (/ (* 2 l) Om))
26.0ms
(* (sin ky) (sin ky))
208.0ms
(fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)
373.0ms
(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

simplify1.3s

Counts
128 → 128
Iterations
IterNodes
done2004
32004
21981
1554
0189

prune873.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize68.0ms

Local error

Found 4 expressions with local error:

11.1b
(sqrt (* (* (cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)) (cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))) (cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))))
15.3b
(cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
15.3b
(cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
15.3b
(cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
24×pow1
15×sqrt-pow1
12×pow1/3
9×cbrt-prod pow-prod-up
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow-plus
5×pow-prod-down
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow-sqr
2×pow2
1×pow1/2 pow3 sqrt-prod
Counts
4 → 69
Calls
4 calls:
25.0ms
(sqrt (* (* (cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)) (cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))) (cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))))
1.0ms
(cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
1.0ms
(cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
1.0ms
(cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

series1.7s

Counts
4 → 12
Calls
4 calls:
300.0ms
(sqrt (* (* (cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)) (cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))) (cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))))
512.0ms
(cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
451.0ms
(cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
435.0ms
(cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

simplify949.0ms

Counts
81 → 81
Iterations
IterNodes
done2003
42003
3927
2336
1171
091

prune753.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize136.0ms

Local error

Found 4 expressions with local error:

15.3b
(cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
15.3b
(cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
15.3b
(cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
15.3b
(cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube pow1/3 add-exp-log insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 56
Calls
4 calls:
1.0ms
(cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
1.0ms
(cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
2.0ms
(cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
2.0ms
(cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

series1.8s

Counts
4 → 12
Calls
4 calls:
495.0ms
(cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
412.0ms
(cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
485.0ms
(cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
397.0ms
(cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

simplify1.2s

Counts
68 → 68
Iterations
IterNodes
done2013
42013
3802
2261
1113
058

prune1.5s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

localize110.0ms

Local error

Found 4 expressions with local error:

15.3b
(cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
15.3b
(cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
15.3b
(cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
27.1b
(posit16->real (real->posit16 (cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
1×remove-posit16
Counts
4 → 53
Calls
4 calls:
1.0ms
(cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
1.0ms
(cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
1.0ms
(cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
0.0ms
(posit16->real (real->posit16 (cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))))

series1.7s

Counts
4 → 12
Calls
4 calls:
440.0ms
(cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
445.0ms
(cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
446.0ms
(cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
391.0ms
(posit16->real (real->posit16 (cbrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))))

simplify1.1s

Counts
65 → 65
Iterations
IterNodes
done2000
42000
3786
2274
1126
069

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

regimes856.0ms

Accuracy

49.1% (0.4b remaining)

Error of 1.3b against oracle of 0.9b and baseline of 1.7b

bsearch210.0ms

Steps
ItersRangePoint
10
4.1836124357929313e+145
5.86343653387453e+160
1.328905807719447e+154

simplify31.0ms

Iterations
IterNodes
done41
141
034

end0.0ms

sample3.8s

Algorithm
intervals
Results
3.5s7999×body80valid
1.0ms1×body160valid