Details

Time bar (total: 27.3s)

sample112.0ms

Algorithm
intervals
Results
92.0ms256×body80valid

simplify4.2s

Counts
1 → 1
Iterations
IterNodes
57379
41765
3524
2164
157
022

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.9b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1/2 (sqrt (fma (* (* (/ l Om) (/ l Om)) 4) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))
0.3b
(* (sin ky) (sin ky))
2.2b
(fma (* (* (/ l Om) (/ l Om)) 4) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)
7.5b
(sqrt (fma (* (* (/ l Om) (/ l Om)) 4) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

rewrite33.0ms

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:
5.0ms
(/ 1/2 (sqrt (fma (* (* (/ l Om) (/ l Om)) 4) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))
13.0ms
(* (sin ky) (sin ky))
0.0ms
(fma (* (* (/ l Om) (/ l Om)) 4) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)
3.0ms
(sqrt (fma (* (* (/ l Om) (/ l Om)) 4) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

series1.0s

Counts
4 → 12
Calls
4 calls:
470.0ms
(/ 1/2 (sqrt (fma (* (* (/ l Om) (/ l Om)) 4) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))
24.0ms
(* (sin ky) (sin ky))
182.0ms
(fma (* (* (/ l Om) (/ l Om)) 4) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)
326.0ms
(sqrt (fma (* (* (/ l Om) (/ l Om)) 4) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

simplify902.0ms

Counts
111 → 111
Iterations
IterNodes
32222
2758
1317
0158

prune2.5s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize89.0ms

Local error

Found 4 expressions with local error:

3.0b
(/ l (/ Om (sin ky)))
3.6b
(/ (* (sin kx) l) Om)
3.6b
(/ (* (sin kx) l) Om)
7.5b
(sqrt (fma 4 (+ (* (/ (* (sin kx) l) Om) (/ (* (sin kx) l) Om)) (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky))))) 1))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
81×times-frac
52×add-sqr-sqrt
51×*-un-lft-identity add-cube-cbrt
19×associate-/r* add-cbrt-cube add-exp-log
7×cbrt-undiv div-exp div-inv
5×pow1 associate-/l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg sqrt-prod
2×prod-exp cbrt-unprod
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
Counts
4 → 137
Calls
4 calls:
15.0ms
(/ l (/ Om (sin ky)))
21.0ms
(/ (* (sin kx) l) Om)
13.0ms
(/ (* (sin kx) l) Om)
1.0ms
(sqrt (fma 4 (+ (* (/ (* (sin kx) l) Om) (/ (* (sin kx) l) Om)) (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky))))) 1))

series609.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(/ l (/ Om (sin ky)))
80.0ms
(/ (* (sin kx) l) Om)
90.0ms
(/ (* (sin kx) l) Om)
344.0ms
(sqrt (fma 4 (+ (* (/ (* (sin kx) l) Om) (/ (* (sin kx) l) Om)) (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky))))) 1))

simplify1.8s

Counts
149 → 149
Iterations
IterNodes
35422
21659
1559
0236

prune2.7s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize93.0ms

Local error

Found 4 expressions with local error:

3.6b
(/ (* (sin kx) l) Om)
3.6b
(/ (* (sin kx) l) Om)
7.5b
(sqrt (fma 4 (+ (* (/ (* (sin kx) l) Om) (/ (* (sin kx) l) Om)) (* (/ l (/ Om (sin ky))) (posit16->real (real->posit16 (/ l (/ Om (sin ky))))))) 1))
47.7b
(posit16->real (real->posit16 (/ l (/ Om (sin ky)))))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
14×add-cbrt-cube add-exp-log
10×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt
6×associate-/r* times-frac
5×pow1
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-prod
2×clear-num frac-2neg prod-exp cbrt-unprod div-inv associate-/l*
1×rem-sqrt-square sqrt-pow1 pow1/2 remove-posit16
Counts
4 → 75
Calls
4 calls:
24.0ms
(/ (* (sin kx) l) Om)
35.0ms
(/ (* (sin kx) l) Om)
3.0ms
(sqrt (fma 4 (+ (* (/ (* (sin kx) l) Om) (/ (* (sin kx) l) Om)) (* (/ l (/ Om (sin ky))) (posit16->real (real->posit16 (/ l (/ Om (sin ky))))))) 1))
1.0ms
(posit16->real (real->posit16 (/ l (/ Om (sin ky)))))

series632.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(/ (* (sin kx) l) Om)
74.0ms
(/ (* (sin kx) l) Om)
337.0ms
(sqrt (fma 4 (+ (* (/ (* (sin kx) l) Om) (/ (* (sin kx) l) Om)) (* (/ l (/ Om (sin ky))) (posit16->real (real->posit16 (/ l (/ Om (sin ky))))))) 1))
116.0ms
(posit16->real (real->posit16 (/ l (/ Om (sin ky)))))

simplify1.1s

Counts
87 → 87
Iterations
IterNodes
32904
2799
1248
0115

prune2.6s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize126.0ms

Local error

Found 4 expressions with local error:

3.6b
(/ (* (sin kx) l) Om)
7.5b
(sqrt (fma 4 (+ (* (posit16->real (real->posit16 (/ (* (sin kx) l) Om))) (/ (* (sin kx) l) Om)) (* (/ l (/ Om (sin ky))) (posit16->real (real->posit16 (/ l (/ Om (sin ky))))))) 1))
47.7b
(posit16->real (real->posit16 (/ l (/ Om (sin ky)))))
49.2b
(posit16->real (real->posit16 (/ (* (sin kx) l) Om)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
9×add-cbrt-cube add-exp-log
8×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* times-frac sqrt-prod
2×cbrt-undiv div-exp remove-posit16
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 prod-exp cbrt-unprod div-inv associate-/l*
Counts
4 → 62
Calls
4 calls:
25.0ms
(/ (* (sin kx) l) Om)
2.0ms
(sqrt (fma 4 (+ (* (posit16->real (real->posit16 (/ (* (sin kx) l) Om))) (/ (* (sin kx) l) Om)) (* (/ l (/ Om (sin ky))) (posit16->real (real->posit16 (/ l (/ Om (sin ky))))))) 1))
0.0ms
(posit16->real (real->posit16 (/ l (/ Om (sin ky)))))
1.0ms
(posit16->real (real->posit16 (/ (* (sin kx) l) Om)))

series680.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(/ (* (sin kx) l) Om)
402.0ms
(sqrt (fma 4 (+ (* (posit16->real (real->posit16 (/ (* (sin kx) l) Om))) (/ (* (sin kx) l) Om)) (* (/ l (/ Om (sin ky))) (posit16->real (real->posit16 (/ l (/ Om (sin ky))))))) 1))
92.0ms
(posit16->real (real->posit16 (/ l (/ Om (sin ky)))))
97.0ms
(posit16->real (real->posit16 (/ (* (sin kx) l) Om)))

simplify887.0ms

Counts
74 → 74
Iterations
IterNodes
32922
2820
1263
0127

prune2.9s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

regimes349.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
226
126
021

end0.0ms

sample3.9s

Algorithm
intervals
Results
3.6s8000×body80valid