Details

sample72.0ms

Algorithm

intervals

Results

43.0ms	256×	body	80	valid
12.0ms	256×	pre	80	true

simplify4.9s

Counts

1 → 1

Iterations

Iter	Nodes
4	11139
3	1615
2	280
1	60
0	17

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 52.7b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
0.1b	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
37.5b	(/ (/ (* (* 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))
45.9b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

rewrite652.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-cbrt-cube` `add-exp-log`
58×	`times-frac`
54×	`flip3-+` `flip-+`
50×	`associate-/r/`
44×	`add-sqr-sqrt`
36×	`frac-times`
30×	`associate-*r/`
28×	`*-un-lft-identity` `add-cube-cbrt`
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×	`expm1-log1p-u` `associate-l` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`swap-sqr`
2×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `*-commutative`
1×	`pow2` `pow-plus` `flip3--` `pow-sqr` `pow-prod-up` `flip--` `unswap-sqr`

Counts

4 → 208

Calls

4 calls:

173.0ms	(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
98.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
208.0ms	(/ (/ (* (* 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))
165.0ms	(/ (* (* 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:

75.0ms	(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
165.0ms	(* (* 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))
241.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

simplify3.4s

Counts

220 → 220

Iterations

Iter	Nodes
2	7480
1	1358
0	364

prune3.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 35.9b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
0.1b	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
36.4b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
37.1b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite1.1s

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-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×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-*r/`
2×	`flip3--` `flip--`
1×	`frac-times` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 372

Calls

4 calls:

248.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
623.0ms	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
50.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
158.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series3.9s

Counts

4 → 12

Calls

4 calls:

474.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
3.1s	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
158.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
196.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify3.6s

Counts

384 → 384

Iterations

Iter	Nodes
2	7224
1	1713
0	507

prune6.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 35.9b

localize63.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (* (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2 i)))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
36.4b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
37.0b	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
37.0b	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

rewrite756.0ms

Algorithm

rewrite-expression-head

Rules

193×	`add-exp-log`
145×	`add-cbrt-cube`
98×	`div-exp`
68×	`cbrt-undiv`
65×	`prod-exp`
58×	`times-frac`
48×	`*-un-lft-identity`
47×	`cbrt-unprod`
42×	`associate-l`
39×	`add-sqr-sqrt`
28×	`add-cube-cbrt`
14×	`associate-/r/`
12×	`associate-r`
9×	`flip3-+` `flip-+` `distribute-lft-out`
8×	`pow1` `1-exp`
7×	`sqrt-prod` `div-inv`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-r/`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `difference-of-squares` `unswap-sqr` `associate-/l/`
1×	`frac-times` `clear-num` `frac-2neg` `flip3--` `pow-prod-down` `associate-l/` `-commutative` `flip--` `associate-/l*` `distribute-lft-out--`

Counts

4 → 187

Calls

4 calls:

646.0ms	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (* (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2 i)))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
88.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
11.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
7.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series3.5s

Counts

4 → 12

Calls

4 calls:

3.3s	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (* (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2 i)))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
116.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
60.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
65.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify2.2s

Counts

199 → 199

Iterations

Iter	Nodes
2	5009
1	1235
0	365

prune3.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 35.9b

localize64.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
0.1b	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))))
36.4b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
37.1b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite874.0ms

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×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u` `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 → 199

Calls

4 calls:

318.0ms	(/ (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
355.0ms	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))))
49.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
145.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series4.2s

Counts

4 → 12

Calls

4 calls:

3.0s	(/ (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
874.0ms	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))))
151.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
190.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify2.3s

Counts

211 → 211

Iterations

Iter	Nodes
2	5269
1	1162
0	345

prune3.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 35.9b

regimes266.0ms

Accuracy

-49.9% (3.8b remaining)

Error of 38.4b against oracle of 34.6b and baseline of 37.1b

bsearch120.0ms

Steps

Iters	Range		Point
9	1.1761167343346087e+85	5.239453151611833e+90	5.675791616953813e+89

simplify13.0ms

Iterations

Iter	Nodes
2	38
1	38
0	28

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.9s	8000×	body	80	valid
367.0ms	8000×	pre	80	true