Details

sample87.0ms

Algorithm

intervals

Results

54.0ms	256×	body	80	valid
13.0ms	256×	pre	80	true

simplify1.0s

Counts

1 → 1

Iterations

Iter	Nodes
4	2384
3	459
2	104
1	33
0	15

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ 2 (+ beta alpha)) 1.0)
0.0b	(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b	(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
3.2b	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite443.0ms

Algorithm

rewrite-expression-head

Rules

4338×	`*-un-lft-identity`
2696×	`times-frac`
2176×	`distribute-lft-out`
779×	`add-sqr-sqrt` `add-cube-cbrt`
166×	`associate-/l*`
102×	`associate-/r/`
53×	`flip3-+` `flip-+`
51×	`div-inv`
20×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/r*`
13×	`add-log-exp`
10×	`cbrt-undiv` `div-exp`
6×	`sum-log`
5×	`fma-def`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `associate-/l/`
3×	`clear-num` `frac-2neg`
1×	`+-commutative` `associate-+l+`

Counts

4 → 1234

Calls

4 calls:

121.0ms	(+ (+ 2 (+ beta alpha)) 1.0)
54.0ms	(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
162.0ms	(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
28.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

series582.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+ (+ 2 (+ beta alpha)) 1.0)
199.0ms	(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
207.0ms	(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
152.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify2.6s

Counts

1246 → 1246

Iterations

Iter	Nodes
2	4034
1	1422
0	612

prune14.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (+ 2 (+ beta alpha)))
0.0b	(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b	(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 1.0 (+ 2 (+ beta alpha))))
3.2b	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite472.0ms

Algorithm

rewrite-expression-head

Rules

4333×	`*-un-lft-identity`
2696×	`times-frac`
2173×	`distribute-lft-out`
779×	`add-sqr-sqrt` `add-cube-cbrt`
166×	`associate-/l*`
102×	`associate-/r/`
53×	`flip3-+` `flip-+`
51×	`div-inv`
20×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/r*`
13×	`add-log-exp`
10×	`cbrt-undiv` `div-exp`
6×	`sum-log`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `associate-/l/`
3×	`clear-num` `fma-def` `frac-2neg`
1×	`+-commutative` `associate-+r+`

Counts

4 → 1232

Calls

4 calls:

46.0ms	(+ 1.0 (+ 2 (+ beta alpha)))
91.0ms	(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
206.0ms	(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 1.0 (+ 2 (+ beta alpha))))
56.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

series542.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ 1.0 (+ 2 (+ beta alpha)))
201.0ms	(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
197.0ms	(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 1.0 (+ 2 (+ beta alpha))))
128.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify2.5s

Counts

1244 → 1244

Iterations

Iter	Nodes
2	4047
1	1426
0	612

prune14.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
0.1b	(/ (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ 1.0 (+ 2 (+ beta alpha))))
3.2b	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
3.2b	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite463.0ms

Algorithm

rewrite-expression-head

Rules

4363×	`*-un-lft-identity`
2717×	`times-frac`
2186×	`distribute-lft-out`
1088×	`sqrt-prod`
795×	`add-sqr-sqrt`
789×	`add-cube-cbrt`
147×	`associate-/l*`
102×	`associate-/r/`
53×	`flip3-+` `flip-+`
51×	`div-inv`
16×	`associate-/r*`
10×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/l/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `div-exp`
2×	`sqrt-div`
1×	`sqrt-pow1` `pow1/2`

Counts

4 → 1245

Calls

4 calls:

80.0ms	(sqrt (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
178.0ms	(/ (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ 1.0 (+ 2 (+ beta alpha))))
46.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
70.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

series750.0ms

Counts

4 → 12

Calls

4 calls:

274.0ms	(sqrt (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
184.0ms	(/ (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ 1.0 (+ 2 (+ beta alpha))))
139.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
153.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify2.5s

Counts

1257 → 1257

Iterations

Iter	Nodes
2	2691
1	1205
0	695

prune19.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
0.3b	(* (/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))))
3.2b	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
3.2b	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite691.0ms

Algorithm

rewrite-expression-head

Rules

10303×	`*-un-lft-identity`
5924×	`times-frac`
5372×	`sqrt-prod`
4549×	`distribute-lft-out`
1979×	`add-sqr-sqrt`
1397×	`add-cube-cbrt`
1238×	`swap-sqr`
238×	`associate-r` `associate-l`
128×	`associate-/r/`
66×	`flip3-+` `flip-+`
64×	`div-inv`
49×	`unswap-sqr`
37×	`associate-/l*`
22×	`add-cbrt-cube` `add-exp-log`
18×	`associate-/r*`
11×	`pow1` `sqrt-div`
7×	`cbrt-undiv` `div-exp`
5×	`sqrt-undiv` `associate-/l/`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`pow2` `frac-times` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 2176

Calls

4 calls:

90.0ms	(/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
298.0ms	(* (/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))))
27.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
42.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

series737.0ms

Counts

4 → 12

Calls

4 calls:

288.0ms	(/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
192.0ms	(* (/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (/ (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))))
130.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
126.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify2.4s

Counts

2188 → 2188

Iterations

Iter	Nodes
1	2358
0	676

prune33.1s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 1.0b

regimes145.0ms

Accuracy

34.2% (1.5b remaining)

Error of 2.7b against oracle of 1.2b and baseline of 3.5b

bsearch91.0ms

Steps

Iters	Range		Point
10	1.0616118620208224e+130	9.907476369181602e+146	9.687684579379148e+146

simplify3.0ms

Iterations

Iter	Nodes
2	20
1	20
0	16

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.4s	8000×	body	80	valid
790.0ms	8000×	pre	80	true