Details

sample32.0ms

Algorithm

intervals

Results

14.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify431.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	53
1	58	53
2	253	53
3	1282	53
done	5000	53

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
0.1b	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
38.2b	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
45.9b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite310.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-exp-log` `add-cbrt-cube`
58×	`times-frac`
54×	`flip3-+` `flip-+`
50×	`associate-/r/`
44×	`add-sqr-sqrt`
36×	`frac-times`
30×	`associate-*r/`
28×	`add-cube-cbrt` `*-un-lft-identity`
22×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
18×	`associate-*l/`
16×	`pow1`
14×	`associate-/l*` `difference-of-squares`
9×	`associate-/l/`
7×	`div-inv`
6×	`associate-r`
5×	`associate-/r*`
4×	`associate-l` `pow-prod-down` `add-log-exp`
3×	`swap-sqr`
2×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `*-commutative`
1×	`pow2` `flip3--` `pow-plus` `pow-sqr` `pow-prod-up` `flip--` `unswap-sqr`

Counts

4 → 200

Calls

4 calls:

70.0ms	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
48.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
113.0ms	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
68.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.3s

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
103.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
948.0ms	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
174.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify404.0ms

Counts

212 → 212

Iterations

Useful iterations: done (390.0ms)

Iter	Nodes	Cost
0	358	12169
1	1224	11261
done	5000	10999

prune620.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 35.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.1b	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
36.8b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
37.3b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite696.0ms

Algorithm

rewrite-expression-head

Rules

366×	`times-frac`
300×	`add-sqr-sqrt`
235×	`*-un-lft-identity`
155×	`add-cube-cbrt`
96×	`associate-r`
70×	`add-exp-log` `add-cbrt-cube`
62×	`difference-of-squares`
44×	`associate-/r/`
42×	`associate-l`
33×	`cbrt-undiv` `div-exp`
31×	`sqrt-prod` `distribute-lft-out--`
22×	`flip3-+` `flip-+` `div-inv`
19×	`associate-/l*`
16×	`prod-exp` `cbrt-unprod`
12×	`associate-/r*`
9×	`distribute-lft-out`
6×	`pow1` `unswap-sqr`
5×	`associate-/l/`
4×	`add-log-exp`
3×	`frac-2neg` `associate-*r/` `clear-num`
2×	`flip3--` `flip--`
1×	`frac-times` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 364

Calls

4 calls:

134.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
443.0ms	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
31.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
63.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series2.8s

Counts

4 → 12

Calls

4 calls:

336.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
2.3s	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
87.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
118.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify512.0ms

Counts

376 → 376

Iterations

Useful iterations: done (493.0ms)

Iter	Nodes	Cost
0	501	21013
1	1698	20456
done	5000	20076

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 35.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.1b	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))
36.8b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
37.3b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite519.0ms

Algorithm

rewrite-expression-head

Rules

85×	`add-exp-log` `add-cbrt-cube`
79×	`times-frac`
63×	`*-un-lft-identity`
61×	`add-sqr-sqrt`
42×	`associate-l`
41×	`add-cube-cbrt`
40×	`cbrt-undiv` `div-exp`
21×	`prod-exp` `cbrt-unprod`
18×	`associate-/r/`
15×	`associate-r`
12×	`associate-/r*`
10×	`flip3-+` `flip-+`
9×	`div-inv` `distribute-lft-out`
7×	`associate-/l/`
6×	`pow1`
5×	`associate-/l*`
4×	`associate-*r/` `add-log-exp` `difference-of-squares` `unswap-sqr`
3×	`frac-2neg` `clear-num`
2×	`frac-times` `associate-*l/` `sqrt-prod` `distribute-lft-out--`
1×	`flip3--` `pow-prod-down` `*-commutative` `flip--`

Counts

4 → 191

Calls

4 calls:

158.0ms	(/ (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
256.0ms	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))
31.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
64.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series3.1s

Counts

4 → 12

Calls

4 calls:

2.3s	(/ (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
615.0ms	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))
88.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
119.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify395.0ms

Counts

203 → 203

Iterations

Useful iterations: done (386.0ms)

Iter	Nodes	Cost
0	339	10534
1	1158	10122
done	5002	9722

prune617.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 35.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i))))
36.8b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
37.2b	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
37.2b	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
25×	`times-frac`
24×	`associate-r`
23×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
14×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `sqrt-div`
7×	`flip3-+` `flip-+`
6×	`associate-l` `unswap-sqr`
4×	`associate-/r/` `add-log-exp`
3×	`cbrt-undiv` `associate-r/` `div-exp` `prod-exp` `associate-/r` `cbrt-unprod`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*l/` `div-inv` `associate-/l/`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `associate-/l`

Counts

4 → 109

Calls

4 calls:

56.0ms	(* (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i))))
31.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
3.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
3.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series333.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(* (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i))))
90.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
53.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
60.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify702.0ms

Counts

121 → 121

Iterations

Useful iterations: done (698.0ms)

Iter	Nodes	Cost
0	190	3629
1	558	3127
2	2267	2755
done	5000	2751

prune446.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 35.8b

regimes170.0ms

Accuracy

13% (3.1b remaining)

Error of 37.2b against oracle of 34.1b and baseline of 37.7b

bsearch97.0ms

Steps

Iters	Range		Point
8	8.825925470648207e+152	6.737979593258544e+156	6.726192858084654e+153
6	1.2216694781712944e+87	1.3335934448459098e+88	3.7225611126883413e+87

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	89
1	44	89
done	44	89

end0.0ms

sample673.0ms

Algorithm

intervals

Results

355.0ms	8000×	body	80	valid
134.0ms	8000×	pre	80	true