Details

sample100.0ms

Algorithm

intervals

Results

60.0ms	256×	body	80	valid
14.0ms	256×	pre	80	true

simplify4.2s

Counts

1 → 1

Iterations

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

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 54.5b

localize70.0ms

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))))
36.9b	(/ (/ (* (* 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))
48.2b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

rewrite719.0ms

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` `insert-posit16` `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 → 212

Calls

4 calls:

170.0ms	(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
116.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
284.0ms	(/ (/ (* (* 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))
141.0ms	(/ (* (* 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:

100.0ms	(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
194.0ms	(* (* 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))
228.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

simplify3.0s

Counts

224 → 224

Iterations

Iter	Nodes
2	7473
1	1333
0	368

prune2.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 34.4b

localize63.0ms

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)))
0.2b	(* (/ (/ (* 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))))
34.8b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
35.9b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite1.8s

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` `insert-posit16` `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 → 376

Calls

4 calls:

305.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
817.0ms	(* (/ (/ (* 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))))
63.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
585.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series3.8s

Counts

4 → 12

Calls

4 calls:

471.0ms	(/ (/ (+ (* 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))))
127.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
168.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify3.9s

Counts

388 → 388

Iterations

Iter	Nodes
2	7286
1	1713
0	511

prune6.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 34.3b

localize71.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (+ (+ alpha beta) (* 2 i)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
34.8b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
35.8b	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.8b	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

2499×	`times-frac`
1610×	`add-sqr-sqrt`
1254×	`*-un-lft-identity`
938×	`add-cube-cbrt`
921×	`sqrt-prod`
900×	`associate-r`
298×	`difference-of-squares`
149×	`distribute-lft-out--`
92×	`associate-/r/`
89×	`add-cbrt-cube` `add-exp-log`
76×	`sqrt-div`
49×	`div-inv`
46×	`cbrt-undiv` `div-exp`
45×	`flip3-+` `flip-+`
42×	`associate-l`
21×	`prod-exp` `cbrt-unprod`
16×	`unswap-sqr`
9×	`distribute-lft-out`
8×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-r/`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`frac-times` `clear-num` `frac-2neg` `flip3--` `pow-prod-down` `associate-l/` `-commutative` `flip--` `associate-/l*`

Counts

4 → 1069

Calls

4 calls:

980.0ms	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (+ (+ alpha beta) (* 2 i)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
67.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
13.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
13.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series3.5s

Counts

4 → 12

Calls

4 calls:

3.2s	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (+ (+ alpha beta) (* 2 i)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
143.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
80.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
78.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify6.3s

Counts

1081 → 1081

Iterations

Iter	Nodes
1	5083
0	1326

prune21.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 34.3b

localize101.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (+ (+ alpha beta) (* 2 i)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))))
0.2b	(* (/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (+ (+ alpha beta) (* 2 i)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
35.8b	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.8b	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

rewrite913.0ms

Algorithm

rewrite-expression-head

Rules

2697×	`times-frac`
1692×	`add-sqr-sqrt`
1361×	`*-un-lft-identity`
1061×	`add-cube-cbrt`
1054×	`sqrt-prod`
900×	`associate-r`
298×	`difference-of-squares`
149×	`distribute-lft-out--`
97×	`associate-/r/`
92×	`sqrt-div`
89×	`add-cbrt-cube` `add-exp-log`
52×	`div-inv`
47×	`flip3-+` `flip-+`
43×	`cbrt-undiv` `div-exp`
24×	`associate-/r*` `prod-exp` `cbrt-unprod`
10×	`associate-l`
8×	`pow1` `unswap-sqr`
6×	`associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`frac-times` `clear-num` `frac-2neg` `flip3--` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip--` `distribute-lft-out`

Counts

4 → 1195

Calls

4 calls:

79.0ms	(/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (+ (+ alpha beta) (* 2 i)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))))
740.0ms	(* (/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (+ (+ alpha beta) (* 2 i)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
10.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
11.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series3.4s

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (+ (+ alpha beta) (* 2 i)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))))
3.1s	(* (/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (+ (+ alpha beta) (* 2 i)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
59.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
87.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify6.7s

Counts

1207 → 1207

Iterations

Iter	Nodes
1	5058
0	1351

prune23.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.7b

regimes255.0ms

Accuracy

39% (9.9b remaining)

Error of 11.9b against oracle of 2.0b and baseline of 18.3b

bsearch146.0ms

Steps

Iters	Range		Point
2	2.4109334146406695e+156	2.7040324079547275e+156	2.4475707888049268e+156
7	2.2202875547313246e+133	4.3817389628174314e+135	4.295970830004288e+135

simplify21.0ms

Iterations

Iter	Nodes
2	51
1	51
0	38

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.8s	8000×	body	80	valid
398.0ms	8000×	pre	80	true