Details

sample35.0ms

Algorithm

intervals

Results

15.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
3	1753
2	282
1	58
0	17

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.8b

localize52.0ms

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))))
33.8b	(/ (/ (* (* 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))
45.1b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite566.0ms

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` `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 → 189

Calls

4 calls:

69.0ms	(* i (+ (+ alpha beta) i))
105.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
245.0ms	(/ (/ (* (* 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))
137.0ms	(/ (* (* 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:

32.0ms	(* i (+ (+ alpha beta) i))
138.0ms	(* (* 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))
313.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify1.8s

Counts

201 → 201

Iterations

Iter	Nodes
done	5000
1	1272
0	348

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 31.9b

localize60.0ms

Local error

Found 4 expressions with local error:

0.0b	(* i (+ (+ alpha beta) i))
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))))
32.9b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
32.9b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

213×	`times-frac`
175×	`add-sqr-sqrt`
145×	`*-un-lft-identity`
101×	`associate-r`
92×	`add-cube-cbrt`
67×	`add-cbrt-cube` `add-exp-log`
45×	`associate-l`
30×	`cbrt-undiv` `div-exp` `difference-of-squares`
28×	`associate-/r/`
17×	`prod-exp` `cbrt-unprod`
16×	`flip3-+` `flip-+`
15×	`sqrt-prod` `distribute-lft-out--`
14×	`div-inv`
12×	`distribute-lft-out`
8×	`pow1`
7×	`unswap-sqr`
6×	`associate-/r*`
5×	`associate-*r/`
4×	`associate-/l*` `add-log-exp` `associate-/l/`
2×	`clear-num` `frac-2neg` `pow-prod-down` `*-commutative`
1×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `flip3--` `associate-*l/` `flip--`

Counts

4 → 260

Calls

4 calls:

87.0ms	(* i (+ (+ alpha beta) i))
919.0ms	(* (/ (/ (* 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))))
133.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
88.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

series3.3s

Counts

4 → 12

Calls

4 calls:

33.0ms	(* i (+ (+ alpha beta) i))
3.0s	(* (/ (/ (* 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))))
191.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
105.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

simplify1.8s

Counts

272 → 272

Iterations

Iter	Nodes
done	5001
1	1613
0	442

prune2.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 31.8b

localize90.0ms

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

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 191

Calls

4 calls:

408.0ms	(/ (* (/ (/ (* 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)))
584.0ms	(* (/ (/ (* 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))))
178.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
71.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

series4.5s

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))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
877.0ms	(* (/ (/ (* 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))))
178.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
129.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

simplify2.1s

Counts

203 → 203

Iterations

Iter	Nodes
done	5000
1	1191
0	339

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 31.8b

localize86.0ms

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

rewrite2.2s

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:

687.0ms	(* (/ (/ (* 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))))
1.2s	(* (* (/ (/ (* 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)))) (/ 1 (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
138.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
113.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

series4.9s

Counts

4 → 12

Calls

4 calls:

813.0ms	(* (/ (/ (* 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))))
3.8s	(* (* (/ (/ (* 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))))
148.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
160.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

simplify2.3s

Counts

254 → 254

Iterations

Iter	Nodes
done	5001
1	1493
0	409

prune1.8s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 31.8b

regimes324.0ms

Accuracy

33.8% (2.4b remaining)

Error of 37.1b against oracle of 34.6b and baseline of 38.3b

bsearch145.0ms

Steps

Iters	Range		Point
9	2.633169120176745e+195	3.9600275033090194e+200	1.706379319752007e+196

simplify11.0ms

Iterations

Iter	Nodes
done	37
1	37
0	26

end0.0ms

sample1.6s

Algorithm

intervals

Results

931.0ms	8000×	body	80	valid
350.0ms	8000×	pre	80	true