Details

sample63.0ms

Algorithm

intervals

Results

35.0ms	256×	body	80	valid
10.0ms	256×	pre	80	true

simplify1.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	2093
4	2093
3	1567
2	267
1	58
0	17

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(* i (+ (+ alpha beta) i))
0.1b	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.7b	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
44.8b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

rewrite630.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-cbrt-cube` `add-exp-log`
58×	`times-frac`
50×	`associate-/r/`
49×	`flip3-+` `flip-+`
42×	`add-sqr-sqrt`
32×	`frac-times`
31×	`*-un-lft-identity`
30×	`associate-*r/`
26×	`add-cube-cbrt`
22×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
16×	`associate-*l/`
14×	`associate-/l*` `difference-of-squares`
11×	`pow1`
9×	`associate-/l/`
8×	`associate-r`
7×	`div-inv`
5×	`associate-/r*`
4×	`associate-l` `pow-prod-down` `insert-posit16` `add-log-exp`
3×	`distribute-lft-out`
2×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `*-commutative`
1×	`flip3--` `flip--` `unswap-sqr`

Counts

4 → 193

Calls

4 calls:

68.0ms	(* i (+ (+ alpha beta) i))
100.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
267.0ms	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
187.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

series1.6s

Counts

4 → 12

Calls

4 calls:

24.0ms	(* i (+ (+ alpha beta) i))
145.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
1.1s	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
279.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

simplify1.5s

Counts

205 → 205

Iterations

Iter	Nodes
done	2002
2	2002
1	1251
0	351

prune2.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 33.0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
0.3b	(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
33.6b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
33.6b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

rewrite685.0ms

Algorithm

rewrite-expression-head

Rules

216×	`times-frac`
163×	`add-sqr-sqrt`
151×	`*-un-lft-identity`
99×	`add-cube-cbrt`
32×	`associate-/r/` `difference-of-squares`
28×	`associate-/l*`
25×	`add-cbrt-cube` `add-exp-log`
17×	`flip3-+` `flip-+`
16×	`associate-/r*` `sqrt-prod` `div-inv` `distribute-lft-out--`
11×	`cbrt-undiv` `div-exp`
10×	`distribute-lft-out`
6×	`associate-/l/`
4×	`pow1` `clear-num` `frac-2neg` `insert-posit16` `add-log-exp`
2×	`prod-exp` `associate-*r/` `cbrt-unprod`
1×	`flip3--` `flip--`

Counts

4 → 256

Calls

4 calls:

261.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
175.0ms	(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
165.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
74.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

series1.2s

Counts

4 → 12

Calls

4 calls:

459.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
376.0ms	(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
181.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
148.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

simplify1.3s

Counts

268 → 268

Iterations

Iter	Nodes
done	2004
2	2004
1	1130
0	401

prune3.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 32.9b

localize60.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
0.3b	(/ (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))))
33.6b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
33.6b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

rewrite720.0ms

Algorithm

rewrite-expression-head

Rules

216×	`times-frac`
163×	`add-sqr-sqrt`
151×	`*-un-lft-identity`
99×	`add-cube-cbrt`
32×	`difference-of-squares`
31×	`associate-/r/`
25×	`add-cbrt-cube` `add-exp-log`
23×	`associate-/l*`
21×	`associate-/r*`
17×	`flip3-+` `flip-+`
16×	`sqrt-prod` `div-inv` `distribute-lft-out--`
11×	`cbrt-undiv` `div-exp`
10×	`distribute-lft-out`
7×	`associate-/l/`
4×	`pow1` `clear-num` `frac-2neg` `insert-posit16` `add-log-exp`
2×	`prod-exp` `associate-*r/` `cbrt-unprod`
1×	`flip3--` `flip--`

Counts

4 → 256

Calls

4 calls:

266.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
281.0ms	(/ (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))))
116.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
51.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

series891.0ms

Counts

4 → 12

Calls

4 calls:

397.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
233.0ms	(/ (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))))
149.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
111.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

simplify1.2s

Counts

268 → 268

Iterations

Iter	Nodes
done	2002
2	2002
1	1149
0	404

prune4.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 32.9b

localize75.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))))
33.6b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
33.6b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
33.6b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

rewrite622.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
56×	`*-un-lft-identity`
36×	`add-sqr-sqrt` `add-cube-cbrt`
25×	`add-cbrt-cube` `add-exp-log`
18×	`associate-/r*`
17×	`associate-/r/`
12×	`flip3-+` `flip-+`
10×	`cbrt-undiv` `div-exp` `distribute-lft-out`
9×	`div-inv` `associate-/l*`
8×	`associate-/l/`
4×	`pow1` `clear-num` `frac-2neg` `associate-*r/` `insert-posit16` `add-log-exp`
3×	`prod-exp` `cbrt-unprod`

Counts

4 → 153

Calls

4 calls:

335.0ms	(/ (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))))
143.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
70.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
70.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

series709.0ms

Counts

4 → 12

Calls

4 calls:

256.0ms	(/ (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))))
192.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
135.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
125.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

simplify1.1s

Counts

165 → 165

Iterations

Iter	Nodes
done	2003
2	2003
1	694
0	234

prune3.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 32.9b

regimes297.0ms

Accuracy

45.9% (1.5b remaining)

Error of 35.5b against oracle of 34.0b and baseline of 36.8b

bsearch104.0ms

Steps

Iters	Range		Point
8	4.618004300617091e+214	1.8668567131862295e+218	4.718881236776059e+214

simplify30.0ms

Iterations

Iter	Nodes
done	38
1	38
0	28

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.5s	8000×	body	80	valid
434.0ms	8000×	pre	80	true