Details

sample45.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify1.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
3	554
2	111
1	33
0	14

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.9b

localize34.0ms

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))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.6s

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-cbrt-cube` `add-exp-log`
13×	`add-log-exp`
10×	`cbrt-undiv` `associate-/r*` `div-exp`
6×	`sum-log`
4×	`pow1` `associate-/l/`
3×	`clear-num` `frac-2neg`
1×	`+-commutative` `associate-+l+`

Counts

4 → 465

Calls

4 calls:

119.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
388.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
625.0ms	(/ (/ (/ (+ (+ (+ 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))
382.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series546.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
206.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
211.0ms	(/ (/ (/ (+ (+ (+ 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))
107.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.8s

Counts

477 → 477

Iterations

Iter	Nodes
done	5001
1	1609
0	602

prune2.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.3b

localize86.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) 1) (/ (sqrt (/ (/ (+ (+ (+ 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)))
0.1b	(/ (sqrt (/ (/ (+ (+ (+ 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))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite3.6s

Algorithm

rewrite-expression-head

Rules

1930×	`times-frac`
1248×	`*-un-lft-identity`
945×	`add-sqr-sqrt`
777×	`sqrt-prod`
742×	`add-cube-cbrt`
258×	`associate-r`
243×	`distribute-lft-out`
193×	`associate-l`
104×	`associate-/r/`
71×	`associate-/l*`
54×	`flip3-+` `flip-+`
53×	`div-inv`
45×	`unswap-sqr`
27×	`add-exp-log`
22×	`add-cbrt-cube`
10×	`associate-/r*` `div-exp`
7×	`cbrt-undiv`
6×	`pow1` `prod-exp`
5×	`associate-/l/`
4×	`cbrt-unprod` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`1-exp`
1×	`frac-times` `sqrt-div` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 922

Calls

4 calls:

2.2s	(* (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) 1) (/ (sqrt (/ (/ (+ (+ (+ 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)))
532.0ms	(/ (sqrt (/ (/ (+ (+ (+ 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))
389.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
369.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series661.0ms

Counts

4 → 12

Calls

4 calls:

268.0ms	(* (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) 1) (/ (sqrt (/ (/ (+ (+ (+ 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)))
165.0ms	(/ (sqrt (/ (/ (+ (+ (+ 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))
113.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
115.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify4.5s

Counts

934 → 934

Iterations

Iter	Nodes
done	5000
1	3424
0	1180

prune7.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.3b

localize127.0ms

Local error

Found 4 expressions with local error:

1.5b	(/ (/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) 1) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.9b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.9b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.9b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite398.0ms

Algorithm

rewrite-expression-head

Rules

63×	`times-frac`
43×	`*-un-lft-identity`
37×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`sqrt-prod`
18×	`add-exp-log`
12×	`cbrt-prod`
11×	`add-cbrt-cube`
9×	`div-exp`
8×	`div-inv`
7×	`associate-/l*`
6×	`cbrt-div` `associate-/r*`
5×	`cbrt-undiv`
4×	`pow1` `flip3-+` `flip-+` `add-log-exp`
3×	`pow1/3` `distribute-lft-out`
2×	`sqrt-div` `1-exp` `prod-exp` `associate-/r/`
1×	`clear-num` `frac-2neg` `cbrt-unprod` `associate-/l/`

Counts

4 → 118

Calls

4 calls:

157.0ms	(/ (/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) 1) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
64.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
64.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
105.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series697.0ms

Counts

4 → 12

Calls

4 calls:

390.0ms	(/ (/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) 1) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
97.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
119.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
92.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify2.3s

Counts

130 → 130

Iterations

Iter	Nodes
done	5000
2	3117
1	731
0	271

prune1.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.3b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
1.2b	(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

3939×	`times-frac`
2530×	`*-un-lft-identity`
1518×	`add-sqr-sqrt` `add-cube-cbrt`
506×	`distribute-lft-out`
311×	`associate-/r*`
186×	`associate-/r/`
96×	`div-inv`
92×	`flip3-+` `flip-+`
54×	`add-exp-log`
36×	`div-exp`
34×	`add-cbrt-cube`
29×	`associate-/l*`
20×	`cbrt-undiv`
5×	`pow1` `associate-/l/`
4×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `add-log-exp`
1×	`pow-flip` `inv-pow`

Counts

4 → 1462

Calls

4 calls:

428.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
548.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
431.0ms	(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
314.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series867.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
356.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
234.0ms	(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
110.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify5.8s

Counts

1474 → 1474

Iterations

Iter	Nodes
done	5001
1	4710
0	1528

prune8.3s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.3b

regimes190.0ms

Accuracy

49.8% (1.2b remaining)

Error of 2.4b against oracle of 1.2b and baseline of 3.6b

bsearch119.0ms

Steps

Iters	Range		Point
9	1.0979366360005654e+169	8.815064583508274e+175	2.147016907849488e+170

simplify12.0ms

Iterations

Iter	Nodes
done	39
1	39
0	28

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.2s	8000×	body	80	valid
217.0ms	8000×	pre	80	true