Details

sample70.0ms

Algorithm

intervals

Results

41.0ms	256×	body	80	valid
11.0ms	256×	pre	80	true

simplify936.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	5070
3	783
2	127
1	36
0	15

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.6b

localize49.0ms

Local error

Found 3 expressions with local error:

0.0b

(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))

0.1b

(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))

3.4b

(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite817.0ms

Algorithm

rewrite-expression-head

Rules

4322×	`*-un-lft-identity`
2696×	`times-frac`
2167×	`distribute-lft-out`
777×	`add-sqr-sqrt` `add-cube-cbrt`
166×	`associate-/l*`
102×	`associate-/r/`
52×	`flip3-+` `flip-+`
51×	`div-inv`
19×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/r*`
10×	`cbrt-undiv` `div-exp`
4×	`associate-/l/`
3×	`pow1` `clear-num` `frac-2neg` `insert-posit16` `add-log-exp`

Counts

3 → 1203

Calls

3 calls:

203.0ms

(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))

358.0ms

(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))

191.0ms

(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

series541.0ms

Counts

3 → 9

Calls

3 calls:

184.0ms

(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))

237.0ms

(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))

119.0ms

(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify3.5s

Counts

1212 → 1212

Iterations

Iter	Nodes
done	5015
2	4829
1	1400
0	582

prune2.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.7b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ 2 (+ beta alpha)))
0.0b	(* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha))))
0.1b	(/ (* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ (+ 2 (+ beta alpha)) 1.0))
3.4b	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite623.0ms

Algorithm

rewrite-expression-head

Rules

168×	`*-un-lft-identity`
83×	`times-frac`
71×	`distribute-lft-out`
64×	`add-exp-log`
63×	`add-sqr-sqrt`
46×	`add-cube-cbrt`
38×	`add-cbrt-cube`
28×	`div-exp`
26×	`associate-l`
21×	`associate-r`
16×	`associate-/r*` `prod-exp`
15×	`cbrt-undiv`
10×	`associate-/r/`
8×	`cbrt-unprod` `associate-/l*`
7×	`pow1`
6×	`flip3-+` `flip-+` `unswap-sqr` `associate-/l/`
5×	`rec-exp` `1-exp` `div-inv`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`frac-times` `associate-l/` `associate-r/` `un-div-inv`
1×	`pow-prod-down` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 211

Calls

4 calls:

22.0ms	(/ 1 (+ 2 (+ beta alpha)))
267.0ms	(* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha))))
166.0ms	(/ (* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ (+ 2 (+ beta alpha)) 1.0))
164.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

series609.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ 1 (+ 2 (+ beta alpha)))
192.0ms	(* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha))))
219.0ms	(/ (* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ (+ 2 (+ beta alpha)) 1.0))
136.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify2.1s

Counts

223 → 223

Iterations

Iter	Nodes
done	5004
2	3727
1	783
0	255

prune827.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.7b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
0.1b	(/ (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ (+ 2 (+ beta alpha)) 1.0))
3.4b	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
3.4b	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite717.0ms

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×	`insert-posit16` `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 → 1237

Calls

4 calls:

114.0ms	(sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
232.0ms	(/ (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ (+ 2 (+ beta alpha)) 1.0))
154.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
144.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

series683.0ms

Counts

4 → 12

Calls

4 calls:

264.0ms	(sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
180.0ms	(/ (sqrt (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (+ (+ 2 (+ beta alpha)) 1.0))
132.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
108.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify2.8s

Counts

1249 → 1249

Iterations

Iter	Nodes
done	5005
2	2993
1	1210
0	690

prune3.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.7b

localize92.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 2 (+ beta alpha)))
3.4b	(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
3.4b	(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
3.4b	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite468.0ms

Algorithm

rewrite-expression-head

Rules

130×	`*-un-lft-identity`
55×	`times-frac`
53×	`distribute-lft-out`
39×	`add-sqr-sqrt`
37×	`add-cube-cbrt`
32×	`sqrt-prod`
11×	`associate-/l*`
10×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `flip3-+` `sqrt-div` `flip-+`
4×	`associate-/r/` `insert-posit16` `add-log-exp` `associate-/l/`
2×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

4 → 144

Calls

4 calls:

130.0ms	(/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 2 (+ beta alpha)))
65.0ms	(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
76.0ms	(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
195.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

series473.0ms

Counts

4 → 12

Calls

4 calls:

250.0ms	(/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 2 (+ beta alpha)))
65.0ms	(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
66.0ms	(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
92.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify1.6s

Counts

156 → 156

Iterations

Iter	Nodes
done	5002
2	1690
1	456
0	184

prune953.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.7b

regimes137.0ms

Accuracy

0% (2.5b remaining)

Error of 3.5b against oracle of 1.0b and baseline of 3.5b

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	33
1	33
0	23

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.3s	8000×	body	80	valid
364.0ms	8000×	pre	80	true