Details

sample51.0ms

Algorithm

intervals

Results

22.0ms	256×	body	80	valid
6.0ms	256×	pre	80	true

simplify1.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	53
1	58	53
2	282	53
3	1591	53
done	5000	53

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.5b

localize36.0ms

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))))
37.2b	(/ (/ (* (* 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))
46.5b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite932.0ms

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:

237.0ms	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
166.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
312.0ms	(/ (/ (* (* 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))
196.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.9s

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
150.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
1.3s	(/ (/ (* (* 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))
296.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify835.0ms

Counts

212 → 212

Iterations

Useful iterations: done (819.0ms)

Iter	Nodes	Cost
0	358	12169
1	1205	11261
done	5001	10133

prune983.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 34.6b

localize24.0ms

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))))
35.2b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
35.5b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite2.1s

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:

452.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
1.3s	(* (/ (/ (* 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))))
72.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
192.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series4.0s

Counts

4 → 12

Calls

4 calls:

477.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
3.2s	(* (/ (/ (* 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))))
97.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
196.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify1.0s

Counts

376 → 376

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	501	21013
1	1612	20455
done	5000	18795

prune1.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 34.6b

localize57.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.1b	(* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
35.2b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
35.5b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

166×	`times-frac`
145×	`add-sqr-sqrt`
110×	`*-un-lft-identity`
96×	`associate-r`
94×	`add-exp-log` `add-cbrt-cube`
76×	`add-cube-cbrt`
43×	`cbrt-undiv` `div-exp`
30×	`difference-of-squares`
25×	`prod-exp` `cbrt-unprod`
22×	`associate-/r/`
15×	`sqrt-prod` `distribute-lft-out--`
12×	`flip3-+` `flip-+`
11×	`div-inv`
10×	`associate-/r*`
9×	`associate-l`
7×	`associate-/l/`
6×	`pow1`
5×	`associate-/l*`
4×	`associate-*r/` `add-log-exp`
3×	`frac-2neg` `clear-num` `unswap-sqr`
2×	`frac-times` `associate-*l/` `distribute-lft-out`
1×	`flip3--` `pow-prod-down` `*-commutative` `flip--`

Counts

4 → 238

Calls

4 calls:

512.0ms	(/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
816.0ms	(* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
103.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
195.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series4.8s

Counts

4 → 12

Calls

4 calls:

3.5s	(/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
997.0ms	(* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
123.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
217.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify886.0ms

Counts

250 → 250

Iterations

Useful iterations: done (866.0ms)

Iter	Nodes	Cost
0	398	13053
1	1286	12505
done	5000	10313

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 34.6b

localize37.0ms

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))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (+ (+ alpha beta) (* 2.0 i)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
35.2b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
35.3b	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.3b	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

rewrite2.3s

Algorithm

rewrite-expression-head

Rules

2499×	`times-frac`
1610×	`add-sqr-sqrt`
1254×	`*-un-lft-identity`
938×	`add-cube-cbrt`
921×	`sqrt-prod`
900×	`associate-r`
298×	`difference-of-squares`
149×	`distribute-lft-out--`
92×	`associate-/r/`
89×	`add-exp-log` `add-cbrt-cube`
76×	`sqrt-div`
49×	`div-inv`
46×	`cbrt-undiv` `div-exp`
45×	`flip3-+` `flip-+`
42×	`associate-l`
21×	`prod-exp` `cbrt-unprod`
16×	`unswap-sqr`
9×	`distribute-lft-out`
8×	`pow1`
4×	`add-log-exp`
3×	`associate-r/` `associate-/r`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`frac-times` `flip3--` `frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `flip--` `associate-/l*`

Counts

4 → 1057

Calls

4 calls:

1.9s	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (+ (+ alpha beta) (* 2.0 i)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
129.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
12.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
8.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series3.9s

Counts

4 → 12

Calls

4 calls:

3.2s	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (+ (+ alpha beta) (* 2.0 i)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
519.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
105.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
65.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify3.6s

Counts

1069 → 1069

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	1320	79899
1	4458	74031
done	5000	71677

prune3.8s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 34.6b

regimes190.0ms

Accuracy

35.7% (2.4b remaining)

Error of 36.9b against oracle of 34.5b and baseline of 38.2b

bsearch81.0ms

Steps

Iters	Range		Point
6	1.713823017139382e+208	1.2819070550181894e+209	4.670506575327118e+208

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	62
1	33	62
done	33	62

end0.0ms

sample1.6s

Algorithm

intervals

Results

900.0ms	8000×	body	80	valid
288.0ms	8000×	pre	80	true