Details

sample32.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
3	589
2	119
1	33
0	14

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (fma 2.0 1.0 (+ beta alpha)))
0.0b	(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
0.1b	(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
4.8b	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

736×	`times-frac`
551×	`*-un-lft-identity`
321×	`add-sqr-sqrt` `add-cube-cbrt`
115×	`distribute-lft-out`
72×	`associate-/l*`
27×	`div-inv`
20×	`add-cbrt-cube` `add-exp-log`
10×	`cbrt-undiv` `associate-/r*` `div-exp`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `associate-/l/`
3×	`clear-num` `fma-def` `frac-2neg` `flip3-+` `flip-+`
2×	`associate-/r/`
1×	`+-commutative` `associate-+r+` `sum-log` `fma-udef`

Counts

4 → 422

Calls

4 calls:

9.0ms	(+ 1.0 (fma 2.0 1.0 (+ beta alpha)))
30.0ms	(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
64.0ms	(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
17.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

series546.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+ 1.0 (fma 2.0 1.0 (+ beta alpha)))
208.0ms	(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
193.0ms	(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
126.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

simplify1.6s

Counts

434 → 434

Iterations

Iter	Nodes
done	5001
1	1328
0	516

prune2.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.5b

localize74.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
0.5b	(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
4.8b	(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
4.8b	(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

112×	`sqrt-prod`
98×	`*-un-lft-identity`
84×	`times-frac`
72×	`add-sqr-sqrt`
66×	`add-cube-cbrt`
16×	`distribute-lft-out`
14×	`associate-/l*`
12×	`associate-/r*`
8×	`add-cbrt-cube` `sqrt-div` `add-exp-log`
6×	`pow1`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp` `associate-/l/`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `hypot-def` `div-inv`

Counts

4 → 182

Calls

4 calls:

29.0ms	(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
29.0ms	(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
21.0ms	(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
12.0ms	(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

series474.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
153.0ms	(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
65.0ms	(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
93.0ms	(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

simplify1.9s

Counts

194 → 194

Iterations

Iter	Nodes
done	5000
3	3891
2	879
1	296
0	153

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 1.5b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha)))
0.1b	(/ (/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
1.5b	(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
3.9b	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha))))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

11464×	`times-frac`
7044×	`*-un-lft-identity`
4536×	`add-sqr-sqrt` `add-cube-cbrt`
3150×	`sqrt-prod`
1254×	`distribute-lft-out`
724×	`associate-/l*`
149×	`div-inv`
34×	`add-cbrt-cube` `add-exp-log`
20×	`cbrt-undiv` `div-exp`
19×	`associate-/r*`
5×	`associate-/l/`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `log1p-expm1-u` `add-log-exp`
2×	`flip3-+` `associate-/r/` `flip-+`

Counts

4 → 3606

Calls

4 calls:

87.0ms	(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha)))
324.0ms	(/ (/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
44.0ms	(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
19.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha))))

series701.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha)))
211.0ms	(/ (/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
107.0ms	(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
163.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha))))

simplify3.7s

Counts

3618 → 3618

Iterations

Iter	Nodes
done	5000
0	2560

prune17.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 1.5b

localize55.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (+ 1.0 (fma 2.0 1.0 (+ beta alpha)))))
0.6b	(/ (/ (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha))) (sqrt (+ 1.0 (fma 2.0 1.0 (+ beta alpha)))))
4.8b	(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
4.8b	(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

rewrite408.0ms

Algorithm

rewrite-expression-head

Rules

3764×	`times-frac`
2394×	`*-un-lft-identity`
2208×	`sqrt-prod`
1632×	`add-sqr-sqrt`
1626×	`add-cube-cbrt`
384×	`distribute-lft-out`
188×	`associate-/l*`
42×	`div-inv`
18×	`add-cbrt-cube` `add-exp-log`
14×	`associate-/r*`
9×	`cbrt-undiv` `div-exp`
8×	`sqrt-div`
6×	`pow1`
4×	`expm1-log1p-u` `flip3-+` `associate-/r/` `flip-+` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `hypot-def` `associate-/l/`

Counts

4 → 1597

Calls

4 calls:

72.0ms	(/ (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (+ 1.0 (fma 2.0 1.0 (+ beta alpha)))))
121.0ms	(/ (/ (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha))) (sqrt (+ 1.0 (fma 2.0 1.0 (+ beta alpha)))))
10.0ms	(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
6.0ms	(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

series759.0ms

Counts

4 → 12

Calls

4 calls:

318.0ms	(/ (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (+ 1.0 (fma 2.0 1.0 (+ beta alpha)))))
271.0ms	(/ (/ (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha))) (sqrt (+ 1.0 (fma 2.0 1.0 (+ beta alpha)))))
84.0ms	(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
85.0ms	(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

simplify3.0s

Counts

1609 → 1609

Iterations

Iter	Nodes
done	5000
1	3345
0	1311

prune6.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.5b

regimes296.0ms

Accuracy

52.7% (1.2b remaining)

Error of 2.4b against oracle of 1.2b and baseline of 3.8b

bsearch128.0ms

Steps

Iters	Range		Point
8	1.842274828350243e+215	1.0430713603340258e+218	1.8729540195851578e+215

simplify17.0ms

Iterations

Iter	Nodes
done	39
1	39
0	33

end0.0ms

sample1.3s

Algorithm

intervals

Results

709.0ms	8000×	body	80	valid
287.0ms	8000×	pre	80	true