Details

sample33.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify808.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	35
1	33	35
2	110	35
3	489	35
4	2430	35
done	5001	35

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 2.4b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ alpha beta) (* beta alpha))
0.0b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.2b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
584×	`*-un-lft-identity`
340×	`add-sqr-sqrt` `add-cube-cbrt`
122×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
29×	`flip3-+` `flip-+`
27×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp` `associate-/r*`
9×	`add-log-exp`
4×	`pow1` `associate-/l/`
3×	`frac-2neg` `clear-num` `sum-log`
1×	`+-commutative` `associate-+l+`

Counts

4 → 463

Calls

4 calls:

7.0ms	(+ (+ alpha beta) (* beta alpha))
22.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
40.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
22.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series70.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ (+ alpha beta) (* beta alpha))
27.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
25.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify482.0ms

Counts

475 → 475

Iterations

Useful iterations: done (452.0ms)

Iter	Nodes	Cost
0	605	25900
1	1530	25129
done	5000	24972

prune1.3s

Filtered

283 candidates to 475 candidates (-67.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	466	9	475
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	467	9	476

Merged error: 0.5b

Counts

476 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.0b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
2.2b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

243×	`times-frac`
191×	`*-un-lft-identity`
154×	`add-sqr-sqrt`
124×	`add-cube-cbrt`
60×	`associate-l`
54×	`add-exp-log`
34×	`add-cbrt-cube`
32×	`distribute-lft-out`
25×	`associate-/l*`
24×	`div-exp` `associate-/r/`
18×	`associate-r`
14×	`cbrt-undiv`
13×	`flip3-+` `flip-+`
12×	`prod-exp` `div-inv`
10×	`associate-/r*`
9×	`unswap-sqr`
7×	`pow1`
6×	`cbrt-unprod`
4×	`rec-exp` `1-exp` `add-log-exp`
3×	`frac-2neg` `clear-num` `associate-/l/`
1×	`frac-times` `pow-flip` `associate-r/` `pow-prod-down` `associate-l/` `un-div-inv` `*-commutative` `inv-pow`

Counts

4 → 282

Calls

4 calls:

13.0ms	(/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
22.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
51.0ms	(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
16.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series71.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
27.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
26.0ms	(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
13.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify923.0ms

Counts

294 → 294

Iterations

Useful iterations: 2 (375.0ms)

Iter	Nodes	Cost
0	369	11010
1	1144	10550
2	4331	9455
done	5000	9455

prune720.0ms

Filtered

197 candidates to 294 candidates (-49.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	294	0	294
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	294	9	303

Merged error: 0.5b

Counts

303 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
0.2b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
2.1b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.1b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
46×	`times-frac`
45×	`sqrt-prod`
38×	`add-cube-cbrt`
27×	`associate-r`
11×	`add-exp-log` `add-cbrt-cube`
10×	`sqrt-div` `distribute-lft-out`
8×	`pow1`
7×	`flip3-+` `associate-l` `flip-+` `associate-/l*`
6×	`unswap-sqr`
4×	`associate-/r/` `add-log-exp`
3×	`associate-/r*`
2×	`cbrt-undiv` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 137

Calls

4 calls:

29.0ms	(* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
16.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
8.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
8.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series87.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
49.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
10.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
14.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify557.0ms

Counts

149 → 149

Iterations

Useful iterations: 2 (157.0ms)

Iter	Nodes	Cost
0	202	4411
1	535	3917
2	1864	3596
done	5000	3596

prune364.0ms

Filtered

106 candidates to 149 candidates (-40.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	148	1	149
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	149	9	158

Merged error: 0.5b

Counts

158 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
1.0b	(* (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
2.1b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.1b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite708.0ms

Algorithm

rewrite-expression-head

Rules

2292×	`times-frac`
1450×	`*-un-lft-identity`
1111×	`add-sqr-sqrt`
912×	`add-cube-cbrt`
890×	`sqrt-prod`
678×	`associate-r`
269×	`distribute-lft-out`
76×	`associate-/r/`
48×	`associate-l`
41×	`add-exp-log` `add-cbrt-cube`
40×	`flip3-+` `flip-+` `unswap-sqr`
38×	`div-inv`
27×	`associate-/l*`
19×	`cbrt-undiv` `div-exp`
16×	`sqrt-div`
8×	`pow1` `prod-exp` `cbrt-unprod`
6×	`associate-/r*`
4×	`add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `associate-/l/`

Counts

4 → 1038

Calls

4 calls:

26.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
538.0ms	(* (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
8.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
8.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series89.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
33.0ms	(* (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
10.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
10.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify996.0ms

Counts

1050 → 1050

Iterations

Useful iterations: done (919.0ms)

Iter	Nodes	Cost
0	1160	62760
1	4053	58247
done	5000	57879

prune4.2s

Filtered

424 candidates to 1050 candidates (-147.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	1050	0	1050
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	1050	9	1059

Merged error: 0.5b

Counts

1059 → 9

regimes140.0ms

Accuracy

49.7% (1.3b remaining)

Error of 2.3b against oracle of 1.1b and baseline of 3.6b

bsearch19.0ms

Steps

Iters	Range		Point
7	7.177480459497802e+164	8.235032861842214e+166	1.892887342950917e+165

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	70
1	38	70
done	38	70

end0.0ms

sample930.0ms

Algorithm

intervals

Results

542.0ms	8000×	body	80	valid
135.0ms	8000×	pre	80	true

Details

sample33.0ms

simplify808.0ms

prune3.0ms

localize13.0ms

rewrite131.0ms

series70.0ms

simplify482.0ms

prune1.3s

localize17.0ms

rewrite117.0ms

series71.0ms

simplify923.0ms

prune720.0ms

localize15.0ms

rewrite67.0ms

series87.0ms

simplify557.0ms

prune364.0ms

localize18.0ms

rewrite708.0ms

series89.0ms

simplify996.0ms

prune4.2s

regimes140.0ms

bsearch19.0ms

simplify3.0ms

end0.0ms

sample930.0ms

Profiling