Details

Time bar (total: 46.7s)

sample181.0ms

Algorithm
intervals
Results
143.0ms256×body80valid

simplify4.2s

Counts
1 → 1
Iterations
IterNodes
57482
41754
3519
2162
155
022

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ l (/ Om 2)) (/ l (/ Om 2)))
0.6b
(/ 1/2 (sqrt (fma (* (/ l (/ Om 2)) (/ l (/ Om 2))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
1.2b
(fma (* (/ l (/ Om 2)) (/ l (/ Om 2))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
9.0b
(sqrt (fma (* (/ l (/ Om 2)) (/ l (/ Om 2))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
300×times-frac
197×add-sqr-sqrt
160×*-un-lft-identity add-cube-cbrt
44×swap-sqr associate-*r* associate-*l*
42×add-cbrt-cube add-exp-log
19×cbrt-undiv div-exp
17×div-inv
15×sqrt-prod
12×pow1
9×prod-exp cbrt-unprod unswap-sqr
6×associate-/r*
4×expm1-log1p-u associate-/r/ insert-posit16 log1p-expm1-u add-log-exp
3×associate-/l*
1×pow2 frac-times rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow-plus pow1/2 pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up fma-udef
Counts
4 → 247
Calls
4 calls:
42.0ms
(* (/ l (/ Om 2)) (/ l (/ Om 2)))
9.0ms
(/ 1/2 (sqrt (fma (* (/ l (/ Om 2)) (/ l (/ Om 2))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
0.0ms
(fma (* (/ l (/ Om 2)) (/ l (/ Om 2))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
5.0ms
(sqrt (fma (* (/ l (/ Om 2)) (/ l (/ Om 2))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))

series952.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (/ l (/ Om 2)) (/ l (/ Om 2)))
417.0ms
(/ 1/2 (sqrt (fma (* (/ l (/ Om 2)) (/ l (/ Om 2))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
182.0ms
(fma (* (/ l (/ Om 2)) (/ l (/ Om 2))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
303.0ms
(sqrt (fma (* (/ l (/ Om 2)) (/ l (/ Om 2))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))

simplify7.5s

Counts
259 → 259
Iterations
IterNodes
26119
11455
0435

prune4.7s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

localize80.0ms

Local error

Found 4 expressions with local error:

1.2b
(fma (* (* (/ l Om) (/ l Om)) 4) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
1.2b
(fma (* (* (/ l Om) (/ l Om)) 4) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
9.0b
(sqrt (fma (* (* (/ l Om) (/ l Om)) 4) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
10.4b
(cbrt (* (sqrt (fma (* (* (/ l Om) (/ l Om)) 4) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)) (fma (* (* (/ l Om) (/ l Om)) 4) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
7×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
2×fma-udef
1×cbrt-prod rem-sqrt-square sqrt-pow1 pow1/2 pow1/3 cube-unmult rem-cbrt-cube
Counts
4 → 51
Calls
4 calls:
0.0ms
(fma (* (* (/ l Om) (/ l Om)) 4) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
0.0ms
(fma (* (* (/ l Om) (/ l Om)) 4) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
3.0ms
(sqrt (fma (* (* (/ l Om) (/ l Om)) 4) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
8.0ms
(cbrt (* (sqrt (fma (* (* (/ l Om) (/ l Om)) 4) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)) (fma (* (* (/ l Om) (/ l Om)) 4) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))

series988.0ms

Counts
4 → 12
Calls
4 calls:
207.0ms
(fma (* (* (/ l Om) (/ l Om)) 4) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
174.0ms
(fma (* (* (/ l Om) (/ l Om)) 4) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
337.0ms
(sqrt (fma (* (* (/ l Om) (/ l Om)) 4) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
269.0ms
(cbrt (* (sqrt (fma (* (* (/ l Om) (/ l Om)) 4) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)) (fma (* (* (/ l Om) (/ l Om)) 4) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))

simplify5.3s

Counts
63 → 63
Iterations
IterNodes
48332
31371
2330
1122
069

prune1.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize77.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1/2 (sqrt (fma (* (/ l (/ Om 2)) (/ l (/ Om 2))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
1.2b
(fma (* (/ l (/ Om 2)) (/ l (/ Om 2))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
2.2b
(log (exp (/ 1/2 (sqrt (fma (* (/ l (/ Om 2)) (/ l (/ Om 2))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))))
9.0b
(sqrt (fma (* (/ l (/ Om 2)) (/ l (/ Om 2))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
35×add-sqr-sqrt
34×*-un-lft-identity add-cube-cbrt
24×sqrt-prod
23×log-pow
22×exp-prod
6×pow1 associate-/r* add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×log-prod associate-/l*
2×div-inv
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp rem-log-exp fma-udef
Counts
4 → 106
Calls
4 calls:
8.0ms
(/ 1/2 (sqrt (fma (* (/ l (/ Om 2)) (/ l (/ Om 2))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
0.0ms
(fma (* (/ l (/ Om 2)) (/ l (/ Om 2))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
10.0ms
(log (exp (/ 1/2 (sqrt (fma (* (/ l (/ Om 2)) (/ l (/ Om 2))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))))
1.0ms
(sqrt (fma (* (/ l (/ Om 2)) (/ l (/ Om 2))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))

series1.3s

Counts
4 → 12
Calls
4 calls:
440.0ms
(/ 1/2 (sqrt (fma (* (/ l (/ Om 2)) (/ l (/ Om 2))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
179.0ms
(fma (* (/ l (/ Om 2)) (/ l (/ Om 2))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
391.0ms
(log (exp (/ 1/2 (sqrt (fma (* (/ l (/ Om 2)) (/ l (/ Om 2))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))))
328.0ms
(sqrt (fma (* (/ l (/ Om 2)) (/ l (/ Om 2))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))

simplify5.2s

Counts
118 → 118
Iterations
IterNodes
46975
31701
2562
1265
0170

prune2.4s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

localize84.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ l Om) (/ l Om))
0.2b
(log (exp (fma (* (* (/ l Om) (/ l Om)) 4) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
1.2b
(fma (* (* (/ l Om) (/ l Om)) 4) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
1.2b
(fma (* (* (/ l Om) (/ l Om)) 4) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
40×times-frac
34×*-un-lft-identity add-cube-cbrt
16×add-cbrt-cube add-exp-log
13×swap-sqr associate-*r* associate-*l*
12×pow1
4×expm1-log1p-u cbrt-undiv log-prod div-exp prod-exp log-pow cbrt-unprod insert-posit16 log1p-expm1-u div-inv add-log-exp unswap-sqr
3×exp-prod fma-udef
1×pow2 frac-times pow-plus rem-log-exp exp-sum pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
Counts
4 → 111
Calls
4 calls:
21.0ms
(* (/ l Om) (/ l Om))
2.0ms
(log (exp (fma (* (* (/ l Om) (/ l Om)) 4) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
0.0ms
(fma (* (* (/ l Om) (/ l Om)) 4) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
0.0ms
(fma (* (* (/ l Om) (/ l Om)) 4) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)

series619.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (/ l Om) (/ l Om))
186.0ms
(log (exp (fma (* (* (/ l Om) (/ l Om)) 4) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
211.0ms
(fma (* (* (/ l Om) (/ l Om)) 4) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
171.0ms
(fma (* (* (/ l Om) (/ l Om)) 4) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)

simplify4.7s

Counts
123 → 123
Iterations
IterNodes
35408
21473
1466
0168

prune2.9s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.6b

regimes608.0ms

Accuracy

0% (0.8b remaining)

Error of 1.6b against oracle of 0.8b and baseline of 1.6b

bsearch0.0ms

simplify8.0ms

Iterations
IterNodes
222
122
021

end0.0ms

sample3.4s

Algorithm
intervals
Results
3.2s8000×body80valid