Details

sample50.0ms

Algorithm

intervals

Results

22.0ms	256×	body	80	valid
9.0ms	256×	pre	80	true

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5011
3	1567
2	267
1	58
0	17

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.5b

localize32.0ms

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))))
38.7b	(/ (/ (* (* 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))
47.8b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

rewrite732.0ms

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×	`associate-l` `pow-prod-down` `insert-posit16` `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 → 204

Calls

4 calls:

160.0ms	(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
142.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
279.0ms	(/ (/ (* (* 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))
142.0ms	(/ (* (* 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:

73.0ms	(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
159.0ms	(* (* 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))
260.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

simplify1.5s

Counts

216 → 216

Iterations

Iter	Nodes
done	5001
1	1313
0	360

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 34.7b

localize43.0ms

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

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

264×	`times-frac`
191×	`add-sqr-sqrt`
178×	`*-un-lft-identity`
110×	`add-cube-cbrt`
96×	`associate-r`
74×	`add-cbrt-cube` `add-exp-log`
42×	`associate-l`
40×	`associate-/r/`
35×	`cbrt-undiv` `div-exp`
30×	`difference-of-squares`
21×	`flip3-+` `flip-+`
20×	`div-inv`
19×	`distribute-lft-out`
17×	`prod-exp` `cbrt-unprod`
15×	`sqrt-prod` `distribute-lft-out--`
13×	`associate-/l*`
10×	`associate-/r*`
6×	`pow1` `unswap-sqr`
5×	`associate-/l/`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-*r/`
1×	`frac-times` `flip3--` `pow-prod-down` `associate-l/` `-commutative` `flip--`

Counts

4 → 308

Calls

4 calls:

333.0ms	(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
967.0ms	(* (/ (/ (* 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))))
64.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
134.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series3.6s

Counts

4 → 12

Calls

4 calls:

329.0ms	(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
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))))
119.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
166.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify2.0s

Counts

320 → 320

Iterations

Iter	Nodes
done	5000
1	1621
0	465

prune2.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 34.7b

localize80.0ms

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))))
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)))
34.8b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
35.5b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite1.4s

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/` `insert-posit16` `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 → 195

Calls

4 calls:

696.0ms	(* (/ (/ (* 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))))
432.0ms	(/ (* (/ (/ (* 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)))
97.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
185.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series4.7s

Counts

4 → 12

Calls

4 calls:

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))))
3.6s	(/ (* (/ (/ (* 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)))
129.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
169.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify2.4s

Counts

207 → 207

Iterations

Iter	Nodes
done	5000
1	1165
0	341

prune1.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 34.7b

localize73.0ms

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))))
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)))) (/ 1 (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
34.8b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
35.5b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 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` `insert-posit16` `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 → 246

Calls

4 calls:

722.0ms	(* (/ (/ (* 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))))
1.1s	(* (* (/ (/ (* 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)))) (/ 1 (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
95.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
213.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series4.3s

Counts

4 → 12

Calls

4 calls:

803.0ms	(* (/ (/ (* 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))))
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)))) (/ 1 (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
134.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
153.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify2.1s

Counts

258 → 258

Iterations

Iter	Nodes
done	5000
1	1372
0	411

prune1.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 34.7b

regimes197.0ms

Accuracy

38.1% (1.5b remaining)

Error of 35.5b against oracle of 34.0b and baseline of 36.4b

bsearch58.0ms

Steps

Iters	Range		Point
7	5.0302074637835405e+203	9.008549611356897e+205	9.866752982876504e+203

simplify10.0ms

Iterations

Iter	Nodes
done	33
1	33
0	24

end0.0ms

sample2.0s

Algorithm

intervals

Results

921.0ms	8000×	body	80	valid
839.0ms	8000×	pre	80	true