Details

sample65.0ms

Algorithm

intervals

Results

29.0ms	256×	body	80	valid
8.0ms	256×	pre	80	true

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5013
3	1566
2	267
1	58
0	17

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* beta alpha) (* i (+ (+ alpha beta) i)))
0.1b	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.2b	(/ (/ (* (* 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))
45.5b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite652.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-cbrt-cube` `add-exp-log`
58×	`times-frac`
50×	`associate-/r/`
49×	`flip3-+` `flip-+`
38×	`add-sqr-sqrt`
32×	`frac-times`
28×	`associate-*r/`
24×	`*-un-lft-identity` `add-cube-cbrt`
21×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
16×	`associate-*l/`
14×	`associate-/l*` `difference-of-squares`
9×	`pow1` `associate-/l/`
7×	`div-inv`
6×	`add-log-exp`
5×	`associate-/r*`
3×	`associate-r` `pow-prod-down`
2×	`distribute-rgt-in` `associate-+r+` `clear-num` `frac-2neg` `distribute-lft-in`
1×	`+-commutative` `sum-log` `flip3--` `associate-l` `*-commutative` `flip--`

Counts

4 → 178

Calls

4 calls:

17.0ms	(+ (* beta alpha) (* i (+ (+ alpha beta) i)))
125.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
304.0ms	(/ (/ (* (* 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))
191.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.8s

Counts

4 → 12

Calls

4 calls:

58.0ms	(+ (* beta alpha) (* i (+ (+ alpha beta) i)))
159.0ms	(* (* 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))
285.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify1.8s

Counts

190 → 190

Iterations

Iter	Nodes
done	5001
1	1197
0	339

prune1.4s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 32.3b

localize48.0ms

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)))
0.2b	(* (/ (/ (* 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))))
32.6b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
33.1b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.6s

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-cbrt-cube` `add-exp-log`
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×	`clear-num` `frac-2neg` `associate-*r/`
2×	`flip3--` `flip--`
1×	`frac-times` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 364

Calls

4 calls:

334.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
995.0ms	(* (/ (/ (* 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))))
75.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
138.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series4.1s

Counts

4 → 12

Calls

4 calls:

417.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
3.4s	(* (/ (/ (* 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))))
136.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
195.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify2.2s

Counts

376 → 376

Iterations

Iter	Nodes
done	5002
1	1721
0	501

prune2.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 32.2b

localize66.0ms

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))))
0.2b	(* (* (/ (/ (* 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)))) (/ 1 (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
32.6b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
33.1b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite2.0s

Algorithm

rewrite-expression-head

Rules

220×	`add-exp-log`
136×	`add-cbrt-cube`
91×	`times-frac` `div-exp`
87×	`prod-exp`
73×	`add-sqr-sqrt` `*-un-lft-identity`
54×	`cbrt-undiv`
49×	`add-cube-cbrt` `cbrt-unprod`
43×	`associate-l`
39×	`associate-r`
18×	`associate-/r/`
11×	`pow1`
10×	`flip3-+` `flip-+`
9×	`rec-exp` `1-exp` `div-inv` `distribute-lft-out`
6×	`frac-times` `associate-/r` `associate-l/` `associate-*r/` `difference-of-squares`
4×	`pow-prod-down` `associate-/l*` `add-log-exp` `unswap-sqr` `associate-/l/`
3×	`sqrt-prod` `distribute-lft-out--`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`flip3--` `un-div-inv` `flip--`

Counts

4 → 242

Calls

4 calls:

613.0ms	(* (/ (/ (* 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))))
1.1s	(* (* (/ (/ (* 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)))) (/ 1 (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
65.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
170.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series5.1s

Counts

4 → 12

Calls

4 calls:

885.0ms	(* (/ (/ (* 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))))
3.5s	(* (* (/ (/ (* 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)))) (/ 1 (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
520.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
201.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify3.1s

Counts

254 → 254

Iterations

Iter	Nodes
done	5001
1	1373
0	409

prune1.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 32.2b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (* (/ (* 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))) (/ 1 (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
28.6b	(/ (* (/ (* 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)))
32.6b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
33.1b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

200×	`add-exp-log`
124×	`add-cbrt-cube`
89×	`div-exp`
73×	`prod-exp`
53×	`cbrt-undiv`
47×	`add-sqr-sqrt`
41×	`*-un-lft-identity` `cbrt-unprod`
40×	`times-frac`
28×	`add-cube-cbrt`
24×	`associate-r`
10×	`associate-/r` `associate-l*` `associate-/r/`
8×	`rec-exp` `1-exp`
7×	`associate-/l/`
6×	`pow1` `flip3-+` `flip-+` `difference-of-squares`
5×	`div-inv` `associate-/l*`
4×	`associate-*r/` `add-log-exp`
3×	`clear-num` `frac-2neg` `sqrt-prod` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`
2×	`frac-times` `associate-*l/`
1×	`flip3--` `pow-prod-down` `un-div-inv` `*-commutative` `flip--`

Counts

4 → 192

Calls

4 calls:

1.2s	(* (/ (* (/ (* 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))) (/ 1 (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
265.0ms	(/ (* (/ (* 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)))
94.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
155.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series4.5s

Counts

4 → 12

Calls

4 calls:

3.3s	(* (/ (* (/ (* 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))) (/ 1 (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
840.0ms	(/ (* (/ (* 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)))
148.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
202.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify2.3s

Counts

204 → 204

Iterations

Iter	Nodes
done	5000
1	1086
0	345

prune1.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 32.2b

regimes307.0ms

Accuracy

36.9% (2.3b remaining)

Error of 36.1b against oracle of 33.8b and baseline of 37.5b

bsearch116.0ms

Steps

Iters	Range		Point
8	1.5761988857549511e+195	9.744806586651462e+197	6.52967490975705e+195

simplify5.0ms

Iterations

Iter	Nodes
done	37
1	37
0	26

end0.0ms

sample1.6s

Algorithm

intervals

Results

902.0ms	8000×	body	80	valid
366.0ms	8000×	pre	80	true