Details

sample71.0ms

Algorithm

intervals

Results

30.0ms	256×	body	80	valid
8.0ms	256×	pre	80	true

simplify1.5s

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.5b

localize31.0ms

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))))
32.9b	(/ (/ (* (* 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))
44.2b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite693.0ms

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)))
161.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
309.0ms	(/ (/ (* (* 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))
198.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.6s

Counts

4 → 12

Calls

4 calls:

52.0ms	(+ (* beta alpha) (* i (+ (+ alpha beta) i)))
151.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
1.2s	(/ (/ (* (* 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))
241.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify1.9s

Counts

190 → 190

Iterations

Iter	Nodes
done	5001
1	1197
0	339

prune1.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 30.8b

localize46.0ms

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))))
31.1b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
31.1b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.5s

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:

293.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
950.0ms	(* (/ (/ (* 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))))
170.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
106.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

series3.7s

Counts

4 → 12

Calls

4 calls:

375.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
3.1s	(* (/ (/ (* 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))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
169.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
107.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

simplify2.0s

Counts

376 → 376

Iterations

Iter	Nodes
done	5003
1	1731
0	501

prune2.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 30.7b

localize81.0ms

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))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))))
31.1b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
31.1b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
31.1b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

223×	`times-frac`
185×	`add-sqr-sqrt`
147×	`*-un-lft-identity`
117×	`sqrt-prod`
99×	`associate-r` `add-cube-cbrt`
42×	`associate-l`
30×	`associate-/r/` `difference-of-squares`
27×	`add-cbrt-cube` `add-exp-log`
17×	`flip3-+` `flip-+`
15×	`div-inv` `distribute-lft-out--`
9×	`cbrt-undiv` `associate-/r*` `div-exp` `distribute-lft-out`
8×	`unswap-sqr`
7×	`associate-/l*`
6×	`pow1` `prod-exp` `cbrt-unprod` `associate-/l/`
4×	`add-log-exp`
3×	`clear-num` `frac-2neg` `associate-*r/`
2×	`sqrt-div`
1×	`frac-times` `flip3--` `pow-prod-down` `associate-l/` `-commutative` `flip--`

Counts

4 → 256

Calls

4 calls:

926.0ms	(* (/ (/ (* 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))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))))
136.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
137.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
86.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

series3.4s

Counts

4 → 12

Calls

4 calls:

2.6s	(* (/ (/ (* 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))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))))
168.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
435.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
129.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

simplify2.4s

Counts

268 → 268

Iterations

Iter	Nodes
done	5000
1	1316
0	477

prune2.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 30.7b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (/ (/ (* 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)))) 1)) (/ (sqrt (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
31.1b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
31.1b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
31.1b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

183×	`times-frac`
161×	`add-sqr-sqrt`
146×	`add-exp-log`
125×	`*-un-lft-identity`
114×	`associate-r`
108×	`sqrt-prod`
106×	`add-cbrt-cube`
89×	`add-cube-cbrt`
63×	`div-exp`
57×	`prod-exp`
41×	`cbrt-undiv`
39×	`cbrt-unprod`
36×	`difference-of-squares`
20×	`associate-/r/`
18×	`distribute-lft-out--`
12×	`flip3-+` `flip-+`
10×	`div-inv`
9×	`pow1` `associate-/r*`
8×	`1-exp`
7×	`associate-/l*`
6×	`associate-/l/`
5×	`frac-times` `associate-l/` `associate-r/`
4×	`add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down`
1×	`flip3--` `associate-l` `*-commutative` `flip--`

Counts

4 → 263

Calls

4 calls:

1.2s	(* (* (/ (/ (* 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)))) 1)) (/ (sqrt (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
179.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
154.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
80.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

series3.8s

Counts

4 → 12

Calls

4 calls:

3.4s	(* (* (/ (/ (* 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)))) 1)) (/ (sqrt (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
186.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
170.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
120.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

simplify2.6s

Counts

275 → 275

Iterations

Iter	Nodes
done	5000
1	1438
0	439

prune2.3s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 30.7b

regimes255.0ms

Accuracy

36.3% (2.3b remaining)

Error of 36.6b against oracle of 34.2b and baseline of 37.9b

bsearch100.0ms

Steps

Iters	Range		Point
10	1.2190787993314528e+188	2.8840481999635833e+200	4.524890541013964e+196

simplify6.0ms

Iterations

Iter	Nodes
done	33
1	33
0	24

end0.0ms

sample2.0s

Algorithm

intervals

Results

986.0ms	8000×	body	80	valid
600.0ms	8000×	pre	80	true