Details

Time bar (total: 29.1s)

sample150.0ms

Algorithm
intervals
Results
112.0ms256×body80valid

simplify913.0ms

Counts
1 → 1

prune38.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.3b

localize65.0ms

Local error

Found 4 expressions with local error:

9.4b
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
2.2b
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
0.4b
(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
0.2b
(* (sin kx) (sin kx))

rewrite28.0ms

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:
Slowest
11.0ms
(* (sin kx) (sin kx))
9.0ms
(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
5.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
0.0ms
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
443.0ms
(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
343.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
198.0ms
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
23.0ms
(* (sin kx) (sin kx))

simplify1.0s

Counts
111 → 111

prune2.0s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize89.0ms

Local error

Found 4 expressions with local error:

9.4b
(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
2.1b
(/ (sin ky) (/ Om l))
2.1b
(/ (sin ky) (/ Om l))
2.1b
(/ (sin kx) (/ Om l))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
225×times-frac
132×add-sqr-sqrt
131×*-un-lft-identity add-cube-cbrt
39×associate-/r*
19×add-cbrt-cube add-exp-log
15×div-inv
9×cbrt-undiv div-exp associate-/l*
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg associate-/r/ sqrt-prod
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 235
Calls
4 calls:
Slowest
17.0ms
(/ (sin kx) (/ Om l))
10.0ms
(/ (sin ky) (/ Om l))
9.0ms
(/ (sin ky) (/ Om l))
1.0ms
(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))

series589.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
322.0ms
(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
106.0ms
(/ (sin kx) (/ Om l))
84.0ms
(/ (sin ky) (/ Om l))
76.0ms
(/ (sin ky) (/ Om l))

simplify836.0ms

Counts
247 → 247

prune5.0s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize102.0ms

Local error

Found 4 expressions with local error:

46.5b
(posit16->real (real->posit16 (/ (sin kx) (/ Om l))))
9.4b
(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (posit16->real (real->posit16 (/ (sin kx) (/ Om l)))))) 1))
2.1b
(/ (sin ky) (/ Om l))
2.1b
(/ (sin ky) (/ Om l))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
150×times-frac
90×add-sqr-sqrt
89×*-un-lft-identity add-cube-cbrt
26×associate-/r*
14×add-cbrt-cube add-exp-log
10×div-inv
6×cbrt-undiv div-exp associate-/l*
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-prod
2×clear-num frac-2neg associate-/r/
1×rem-sqrt-square sqrt-pow1 pow1/2 remove-posit16
Counts
4 → 173
Calls
4 calls:
Slowest
19.0ms
(/ (sin ky) (/ Om l))
18.0ms
(/ (sin ky) (/ Om l))
2.0ms
(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (posit16->real (real->posit16 (/ (sin kx) (/ Om l)))))) 1))
1.0ms
(posit16->real (real->posit16 (/ (sin kx) (/ Om l))))

series608.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
335.0ms
(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (posit16->real (real->posit16 (/ (sin kx) (/ Om l)))))) 1))
95.0ms
(/ (sin ky) (/ Om l))
94.0ms
(posit16->real (real->posit16 (/ (sin kx) (/ Om l))))
84.0ms
(/ (sin ky) (/ Om l))

simplify1.7s

Counts
185 → 185

prune5.9s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize131.0ms

Local error

Found 4 expressions with local error:

46.5b
(posit16->real (real->posit16 (/ (sin kx) (/ Om l))))
46.5b
(posit16->real (real->posit16 (/ (sin kx) (/ Om l))))
46.5b
(posit16->real (real->posit16 (/ (sin kx) (/ Om l))))
9.4b
(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (posit16->real (real->posit16 (/ (sin kx) (/ Om l)))))) 1))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×pow1 *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-prod remove-posit16
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 49
Calls
4 calls:
Slowest
2.0ms
(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (posit16->real (real->posit16 (/ (sin kx) (/ Om l)))))) 1))
0.0ms
(posit16->real (real->posit16 (/ (sin kx) (/ Om l))))
0.0ms
(posit16->real (real->posit16 (/ (sin kx) (/ Om l))))
0.0ms
(posit16->real (real->posit16 (/ (sin kx) (/ Om l))))

series609.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
339.0ms
(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (posit16->real (real->posit16 (/ (sin kx) (/ Om l)))))) 1))
92.0ms
(posit16->real (real->posit16 (/ (sin kx) (/ Om l))))
92.0ms
(posit16->real (real->posit16 (/ (sin kx) (/ Om l))))
86.0ms
(posit16->real (real->posit16 (/ (sin kx) (/ Om l))))

simplify1.1s

Counts
61 → 61

prune2.3s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.3b

regimes458.0ms

Accuracy

0% (0.0b remaining)

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

bsearch5.0ms

end0.0ms

sample4.2s

Algorithm
intervals
Results
3.9s8000×body80valid