Details

Time bar (total: 27.6s)

sample115.0ms

Algorithm
intervals
Results
59.0ms256×body80valid

simplify1.8s

Counts
1 → 1
Iterations
IterNodes
done5005
41812
3494
2160
157
022

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.8b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin kx) (sin kx))
0.2b
(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1)))
2.9b
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om)))
6.6b
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1))

rewrite324.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
26×add-cbrt-cube add-exp-log
25×*-un-lft-identity add-cube-cbrt
18×times-frac
17×pow1
15×sqrt-prod
13×frac-times
10×prod-exp cbrt-unprod
9×sin-mult
7×associate-*l/ associate-*r/
6×associate-/r* flip3-+ associate-*l* flip-+
5×cbrt-undiv div-exp
4×sqrt-div associate-*r* pow-prod-down frac-add insert-posit16 add-log-exp
3×swap-sqr associate-/l*
2×associate-/r/ *-commutative unswap-sqr
1×pow2 rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow-plus pow1/2 pow-sqr pow-prod-up sqr-sin div-inv
Counts
4 → 127
Calls
4 calls:
19.0ms
(* (sin kx) (sin kx))
116.0ms
(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1)))
84.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om)))
99.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1))

series1.6s

Counts
4 → 12
Calls
4 calls:
30.0ms
(* (sin kx) (sin kx))
855.0ms
(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1)))
288.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om)))
469.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1))

simplify2.5s

Counts
139 → 139
Iterations
IterNodes
done5001
22770
1695
0261

prune969.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize61.0ms

Local error

Found 4 expressions with local error:

3.1b
(* (/ (+ l l) Om) (sin kx))
3.1b
(* (/ (+ l l) Om) (sin kx))
6.6b
(sqrt (+ 1 (+ (* (* (/ (+ l l) Om) (sin ky)) (* (/ (+ l l) Om) (sin ky))) (* (* (/ (+ l l) Om) (sin kx)) (* (/ (+ l l) Om) (sin kx))))))
10.5b
(cbrt (* (sqrt (+ 1 (+ (* (* (/ (+ l l) Om) (sin ky)) (* (/ (+ l l) Om) (sin ky))) (* (* (/ (+ l l) Om) (sin kx)) (* (/ (+ l l) Om) (sin kx)))))) (+ 1 (+ (* (* (/ (+ l l) Om) (sin ky)) (* (/ (+ l l) Om) (sin ky))) (* (* (/ (+ l l) Om) (sin kx)) (* (/ (+ l l) Om) (sin kx)))))))

rewrite858.0ms

Algorithm
rewrite-expression-head
Rules
80×associate-*l*
77×*-un-lft-identity
75×add-sqr-sqrt
74×times-frac
63×add-cube-cbrt
19×distribute-lft-out
18×distribute-rgt-out
14×add-cbrt-cube add-exp-log
9×pow1
8×cbrt-div sqrt-div
7×flip3-+ flip-+
6×distribute-lft1-in count-2 associate-*r* distribute-rgt1-in
4×frac-times associate-*l/ prod-exp sqrt-prod cbrt-unprod insert-posit16 add-log-exp unswap-sqr
2×cbrt-undiv div-exp pow-prod-down associate-*r/ *-commutative div-inv
1×cbrt-prod rem-sqrt-square sqrt-pow1 pow1/2 pow1/3 cube-unmult rem-cbrt-cube
Counts
4 → 156
Calls
4 calls:
44.0ms
(* (/ (+ l l) Om) (sin kx))
42.0ms
(* (/ (+ l l) Om) (sin kx))
370.0ms
(sqrt (+ 1 (+ (* (* (/ (+ l l) Om) (sin ky)) (* (/ (+ l l) Om) (sin ky))) (* (* (/ (+ l l) Om) (sin kx)) (* (/ (+ l l) Om) (sin kx))))))
396.0ms
(cbrt (* (sqrt (+ 1 (+ (* (* (/ (+ l l) Om) (sin ky)) (* (/ (+ l l) Om) (sin ky))) (* (* (/ (+ l l) Om) (sin kx)) (* (/ (+ l l) Om) (sin kx)))))) (+ 1 (+ (* (* (/ (+ l l) Om) (sin ky)) (* (/ (+ l l) Om) (sin ky))) (* (* (/ (+ l l) Om) (sin kx)) (* (/ (+ l l) Om) (sin kx)))))))

series954.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(* (/ (+ l l) Om) (sin kx))
109.0ms
(* (/ (+ l l) Om) (sin kx))
361.0ms
(sqrt (+ 1 (+ (* (* (/ (+ l l) Om) (sin ky)) (* (/ (+ l l) Om) (sin ky))) (* (* (/ (+ l l) Om) (sin kx)) (* (/ (+ l l) Om) (sin kx))))))
377.0ms
(cbrt (* (sqrt (+ 1 (+ (* (* (/ (+ l l) Om) (sin ky)) (* (/ (+ l l) Om) (sin ky))) (* (* (/ (+ l l) Om) (sin kx)) (* (/ (+ l l) Om) (sin kx)))))) (+ 1 (+ (* (* (/ (+ l l) Om) (sin ky)) (* (/ (+ l l) Om) (sin ky))) (* (* (/ (+ l l) Om) (sin kx)) (* (/ (+ l l) Om) (sin kx)))))))

simplify2.5s

Counts
168 → 168
Iterations
IterNodes
done5001
21593
1488
0201

prune1.5s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize70.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (sin kx) (sin kx))))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1)))
2.9b
(* (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (sin kx) (sin kx))))) (* (/ (+ l l) Om) (/ (+ l l) Om)))
6.6b
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (sin kx) (sin kx))))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1))
36.4b
(posit16->real (real->posit16 (* (sin kx) (sin kx))))

rewrite301.0ms

Algorithm
rewrite-expression-head
Rules
24×add-cbrt-cube add-exp-log
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac
15×sqrt-prod
10×pow1
9×frac-times prod-exp cbrt-unprod
6×associate-/r* flip3-+ associate-*r/ flip-+
5×cbrt-undiv div-exp associate-*l/
4×sqrt-div insert-posit16 add-log-exp
3×associate-*l* pow-prod-down associate-/l*
2×associate-/r/
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-*r* *-commutative div-inv remove-posit16 unswap-sqr
Counts
4 → 104
Calls
4 calls:
83.0ms
(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (sin kx) (sin kx))))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1)))
96.0ms
(* (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (sin kx) (sin kx))))) (* (/ (+ l l) Om) (/ (+ l l) Om)))
119.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (sin kx) (sin kx))))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1))
0.0ms
(posit16->real (real->posit16 (* (sin kx) (sin kx))))

series1.2s

Counts
4 → 12
Calls
4 calls:
359.0ms
(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (sin kx) (sin kx))))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1)))
298.0ms
(* (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (sin kx) (sin kx))))) (* (/ (+ l l) Om) (/ (+ l l) Om)))
473.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (sin kx) (sin kx))))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1))
20.0ms
(posit16->real (real->posit16 (* (sin kx) (sin kx))))

simplify2.2s

Counts
116 → 116
Iterations
IterNodes
done5001
22075
1539
0224

prune1.4s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize117.0ms

Local error

Found 4 expressions with local error:

6.7b
(cbrt (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (sin kx) (sin kx))))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1))))
36.4b
(posit16->real (real->posit16 (* (sin kx) (sin kx))))
36.4b
(posit16->real (real->posit16 (* (sin kx) (sin kx))))
36.4b
(posit16->real (real->posit16 (* (sin kx) (sin kx))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
24×cbrt-prod
18×times-frac
17×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×sqrt-prod
4×pow1 add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×remove-posit16
2×sqrt-div associate-/r/
1×cbrt-div flip3-+ pow1/3 flip-+ div-inv
Counts
4 → 61
Calls
4 calls:
59.0ms
(cbrt (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (sin kx) (sin kx))))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1))))
0.0ms
(posit16->real (real->posit16 (* (sin kx) (sin kx))))
0.0ms
(posit16->real (real->posit16 (* (sin kx) (sin kx))))
1.0ms
(posit16->real (real->posit16 (* (sin kx) (sin kx))))

series554.0ms

Counts
4 → 12
Calls
4 calls:
459.0ms
(cbrt (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (sin kx) (sin kx))))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1))))
21.0ms
(posit16->real (real->posit16 (* (sin kx) (sin kx))))
33.0ms
(posit16->real (real->posit16 (* (sin kx) (sin kx))))
40.0ms
(posit16->real (real->posit16 (* (sin kx) (sin kx))))

simplify2.7s

Counts
73 → 73
Iterations
IterNodes
done5002
32719
2747
1293
0168

prune996.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

regimes493.0ms

Accuracy

-22.2% (2.0b remaining)

Error of 2.6b against oracle of 0.6b and baseline of 2.3b

bsearch556.0ms

Steps
ItersRangePoint
9
3.0402715726570317e+171
7.658297473827752e+180
1.6529205245568764e+178
9
-3.9231825431047055e-236
-6.164355571314205e-243
-5.595436898681083e-237

simplify22.0ms

Iterations
IterNodes
done67
167
051

end0.0ms

sample3.6s

Algorithm
intervals
Results
3.4s8000×body80valid