Details

sample22.0ms

Algorithm

intervals

Results

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

simplify877.0ms

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

prune3.0ms

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)))

rewrite717.0ms

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:

58.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
185.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
278.0ms	(/ (/ (/ (+ (+ (+ 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))
159.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series391.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
140.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
152.0ms	(/ (/ (/ (+ (+ (+ 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))
82.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify506.0ms

Counts

477 → 477

Iterations

Useful iterations: done (479.0ms)

Iter	Nodes	Cost
0	603	25954
1	1501	25182
done	5000	25056

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.8b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite591.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-exp-log`
58×	`*-un-lft-identity`
55×	`add-sqr-sqrt`
53×	`times-frac`
38×	`add-cube-cbrt` `add-cbrt-cube`
28×	`div-exp`
18×	`associate-l`
16×	`prod-exp`
15×	`cbrt-undiv` `associate-r`
10×	`associate-/r*` `associate-/r/`
9×	`distribute-lft-out`
8×	`cbrt-unprod` `associate-/l*`
7×	`pow1`
6×	`flip3-+` `flip-+` `associate-/l/` `unswap-sqr`
5×	`rec-exp` `1-exp` `div-inv`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`frac-times` `associate-r/` `associate-l/` `un-div-inv`
1×	`pow-flip` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 171

Calls

4 calls:

18.0ms	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
161.0ms	(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
250.0ms	(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))
155.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series409.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
152.0ms	(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
143.0ms	(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))
77.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.5s

Counts

183 → 183

Iterations

Useful iterations: 2 (295.0ms)

Iter	Nodes	Cost
0	248	5651
1	770	5243
2	3596	4499
done	5000	4499

prune384.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.5b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
5.0b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
5.0b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite377.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 176

Calls

4 calls:

119.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
118.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
66.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
66.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series303.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
103.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
50.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
47.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify1.2s

Counts

188 → 188

Iterations

Useful iterations: 3 (325.0ms)

Iter	Nodes	Cost
0	160	5606
1	329	5122
2	930	4954
3	3127	4918
done	5000	4918

prune504.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
0.0b	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
2.4b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
5.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite637.0ms

Algorithm

rewrite-expression-head

Rules

55×	`*-un-lft-identity`
54×	`times-frac`
33×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
22×	`associate-/l*`
20×	`add-exp-log` `add-cbrt-cube`
17×	`flip3-+` `flip-+`
14×	`associate-/r/`
13×	`add-log-exp`
12×	`distribute-lft-out`
8×	`frac-times`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `sum-log`
4×	`associate-r/` `associate-l` `associate-l/` `associate-/r*` `div-inv`
3×	`associate-r` `prod-exp` `cbrt-unprod` `associate-/l/`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `distribute-rgt-in` `associate-+l+` `distribute-lft-in` `pow-prod-down` `*-commutative` `unswap-sqr`

Counts

4 → 143

Calls

4 calls:

204.0ms	(* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
60.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
212.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
155.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series274.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
18.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
149.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
78.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.1s

Counts

155 → 155

Iterations

Useful iterations: 2 (243.0ms)

Iter	Nodes	Cost
0	248	5148
1	734	5002
2	3621	4543
done	5000	4543

prune371.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.8b

regimes72.0ms

Accuracy

56% (1.1b remaining)

Error of 2.2b against oracle of 1.1b and baseline of 3.6b

bsearch67.0ms

Steps

Iters	Range		Point
9	1.68690722297182e+158	2.212909629018009e+163	6.329269688592064e+161

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	68
1	42	68
done	42	68

end0.0ms

sample517.0ms

Algorithm

intervals

Results

282.0ms	8000×	body	80	valid
96.0ms	8000×	pre	80	true