Details

sample23.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	35
1	33	35
2	110	35
3	487	35
4	2435	35
done	5001	35

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ 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))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
5.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite677.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 465

Calls

4 calls:

57.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
174.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
261.0ms	(/ (/ (/ (+ (+ (+ 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))
147.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
139.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
151.0ms	(/ (/ (/ (+ (+ (+ 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))
79.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify516.0ms

Counts

477 → 477

Iterations

Useful iterations: done (479.0ms)

Iter	Nodes	Cost
0	603	25954
1	1501	25182
done	5001	25025

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
0.1b	(/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
0.1b	(/ (/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
5.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

18109×	`times-frac`
9724×	`*-un-lft-identity`
6724×	`add-sqr-sqrt` `add-cube-cbrt`
1500×	`distribute-lft-out`
792×	`associate-/l*`
684×	`div-inv`
572×	`associate-/r/`
245×	`flip3-+` `flip-+`
154×	`add-exp-log`
134×	`div-exp`
84×	`associate-/r*`
61×	`add-cbrt-cube`
41×	`cbrt-undiv`
30×	`1-exp`
12×	`rec-exp`
6×	`associate-/l/`
4×	`pow1` `frac-2neg` `clear-num` `add-log-exp`

Counts

4 → 4911

Calls

4 calls:

116.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
123.0ms	(/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
410.0ms	(/ (/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
147.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series530.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
147.0ms	(/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
153.0ms	(/ (/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
82.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify2.0s

Counts

4923 → 4923

Iterations

Useful iterations: 0 (664.0ms)

Iter	Nodes	Cost
0	5274	351082
done	5274	351082

prune15.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))))
0.1b	(/ (/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
5.2b	(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))

rewrite800.0ms

Algorithm

rewrite-expression-head

Rules

2678×	`times-frac`
1264×	`*-un-lft-identity`
918×	`add-sqr-sqrt`
911×	`add-cube-cbrt`
486×	`associate-/r/`
357×	`add-exp-log`
277×	`div-exp`
190×	`associate-/l*`
176×	`distribute-lft-out`
167×	`div-inv`
163×	`flip3-+` `flip-+`
160×	`frac-times` `associate-*l/`
85×	`add-cbrt-cube`
80×	`associate-*r/` `un-div-inv`
76×	`1-exp`
60×	`prod-exp`
51×	`cbrt-undiv`
40×	`rec-exp`
20×	`associate-/r*`
15×	`associate-r`
10×	`cbrt-unprod`
7×	`pow1`
4×	`associate-l` `add-log-exp`
3×	`frac-2neg` `clear-num` `unswap-sqr`
2×	`associate-/l/`
1×	`pow-flip` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 1272

Calls

4 calls:

216.0ms	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
72.0ms	(/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))))
180.0ms	(/ (/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
199.0ms	(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))

series406.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
140.0ms	(/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))))
149.0ms	(/ (/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
79.0ms	(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))

simplify1.4s

Counts

1284 → 1284

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	1633	76611
1	4313	66213
done	5001	63787

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
5.0b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
5.0b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
11.7b	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))))

rewrite809.0ms

Algorithm

rewrite-expression-head

Rules

7742×	`times-frac`
4062×	`*-un-lft-identity`
3062×	`add-sqr-sqrt`
3060×	`add-cube-cbrt`
2004×	`sqrt-prod`
501×	`distribute-lft-out`
193×	`div-inv`
185×	`associate-/r/`
89×	`associate-/r*`
82×	`flip3-+` `flip-+`
36×	`add-exp-log`
32×	`associate-/l*`
27×	`add-cbrt-cube`
25×	`div-exp`
16×	`cbrt-undiv`
6×	`pow1` `sqrt-div`
4×	`add-log-exp`
3×	`1-exp` `associate-/l/`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`

Counts

4 → 2367

Calls

4 calls:

111.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
60.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
62.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
251.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))))

series447.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
53.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
52.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
144.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))))

simplify1.0s

Counts

2379 → 2379

Iterations

Useful iterations: done (790.0ms)

Iter	Nodes	Cost
0	2510	189842
done	5000	189830

prune7.6s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes72.0ms

Accuracy

59.6% (1.5b remaining)

Error of 1.5b against oracle of 0.0b and baseline of 3.6b

bsearch41.0ms

Steps

Iters	Range		Point
5	8.188588653842435e+143	1.9357116286454127e+144	1.790487552627059e+144

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	28	68
1	40	64
done	40	64

end0.0ms

sample541.0ms

Algorithm

intervals

Results

296.0ms	8000×	body	80	valid
103.0ms	8000×	pre	80	true