Details

sample66.0ms

Algorithm

intervals

Results

32.0ms	256×	body	80	valid
13.0ms	256×	pre	80	true

simplify4.1s

Counts

1 → 1

Iterations

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

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 51.8b

localize46.0ms

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))))
38.9b	(/ (/ (* (* 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))
45.4b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

rewrite618.0ms

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×	`expm1-log1p-u` `associate-l` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `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 → 201

Calls

4 calls:

81.0ms	(* i (+ (+ alpha beta) i))
87.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
259.0ms	(/ (/ (* (* 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))
179.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

series1.5s

Counts

4 → 12

Calls

4 calls:

30.0ms	(* i (+ (+ alpha beta) i))
157.0ms	(* (* 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))))

simplify3.4s

Counts

213 → 213

Iterations

Iter	Nodes
2	7137
1	1272
0	359

prune3.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 35.7b

localize84.0ms

Local error

Found 4 expressions with local error:

0.0b	(* i (+ (+ alpha beta) i))
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))))
35.5b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
36.7b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite1.1s

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `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 → 272

Calls

4 calls:

72.0ms	(* i (+ (+ alpha beta) i))
823.0ms	(* (/ (/ (* 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))))
72.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
158.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series3.4s

Counts

4 → 12

Calls

4 calls:

39.0ms	(* i (+ (+ alpha beta) i))
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))))
143.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
174.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify2.8s

Counts

284 → 284

Iterations

Iter	Nodes
2	6523
1	1543
0	452

prune4.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 35.7b

localize87.0ms

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))) (/ (+ (* 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))))
35.5b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
36.7b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite1.0s

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/` `insert-posit16` `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 → 203

Calls

4 calls:

285.0ms	(/ (* (/ (/ (* 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)))
511.0ms	(* (/ (/ (* 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))))
77.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
166.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series4.2s

Counts

4 → 12

Calls

4 calls:

3.2s	(/ (* (/ (/ (* 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)))
781.0ms	(* (/ (/ (* 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))))
149.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
166.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify2.1s

Counts

215 → 215

Iterations

Iter	Nodes
2	5165
1	1168
0	349

prune3.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 35.7b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(* i (+ (+ alpha beta) i))
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)))
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))))
36.7b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite964.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-cbrt-cube` `add-exp-log`
40×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
34×	`cbrt-undiv` `div-exp`
29×	`times-frac`
25×	`prod-exp` `add-cube-cbrt` `cbrt-unprod`
20×	`associate-r`
13×	`associate-l`
9×	`associate-/r*`
8×	`pow1` `associate-/r/`
5×	`flip3-+` `flip-+` `associate-/l/`
4×	`expm1-log1p-u` `associate-r/` `insert-posit16` `log1p-expm1-u` `div-inv` `distribute-lft-out` `associate-/l` `add-log-exp` `difference-of-squares`
3×	`unswap-sqr`
2×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `-commutative` `sqrt-prod` `distribute-lft-out--`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3--` `flip--`

Counts

4 → 168

Calls

4 calls:

75.0ms	(* i (+ (+ alpha beta) i))
264.0ms	(/ (* (/ (* 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)))
482.0ms	(* (/ (* 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))))
141.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series4.3s

Counts

4 → 12

Calls

4 calls:

27.0ms	(* i (+ (+ alpha beta) i))
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)))
1.2s	(* (/ (* 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	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify1.8s

Counts

180 → 180

Iterations

Iter	Nodes
2	4665
1	992
0	306

prune2.7s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 2.0b

regimes199.0ms

Accuracy

45.3% (8.7b remaining)

Error of 10.8b against oracle of 2.1b and baseline of 18.0b

bsearch132.0ms

Steps

Iters	Range		Point
8	8.076566236415723e+137	3.1021573281508808e+140	6.711396437353354e+139

simplify8.0ms

Iterations

Iter	Nodes
2	43
1	43
0	32

end0.0ms

sample2.7s

Algorithm

intervals

Results

2.0s	8000×	body	80	valid
393.0ms	8000×	pre	80	true