Details

sample43.0ms

Algorithm

intervals

Results

7.0ms	185×	body	80	valid
5.0ms	31×	body	1280	valid
5.0ms	256×	pre	80	true
3.0ms	25×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	5×	body	160	valid

simplify4.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
25	4885
24	4583
23	4303
22	3954
21	3572
20	3229
19	2829
18	2315
17	1985
16	1722
15	1474
14	1236
13	995
12	795
11	669
10	582
9	467
8	348
7	290
6	209
5	124
4	69
3	50
2	33
1	20
0	10

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.5b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite333.0ms

Algorithm

rewrite-expression-head

Rules

104×	`*-un-lft-identity`
50×	`times-frac`
47×	`add-sqr-sqrt`
34×	`distribute-lft-out`
31×	`fma-def`
25×	`add-cube-cbrt`
11×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-cbrt-cube` `add-exp-log` `associate-/r/` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`expm1-log1p-u` `pow1` `div-sub` `insert-posit16` `log1p-expm1-u` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3--` `div-exp` `associate-+l-` `flip--`

Counts

2 → 102

Calls

2 calls:

64.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
262.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series177.0ms

Counts

2 → 6

Calls

2 calls:

86.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
90.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.3s

Counts

108 → 108

Iterations

Iter	Nodes
done	5004
2	1170
1	342
0	130

prune408.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 15.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite2.1s

Algorithm

rewrite-expression-head

Rules

215×	`*-un-lft-identity`
118×	`add-sqr-sqrt`
116×	`times-frac`
93×	`add-cube-cbrt`
63×	`prod-diff`
60×	`distribute-lft-out`
21×	`fma-neg`
13×	`associate-/r` `associate-/l` `distribute-lft-out--`
12×	`associate-/r/`
10×	`add-cbrt-cube` `add-exp-log` `difference-of-squares`
7×	`div-inv`
6×	`flip3-+` `flip-+` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `associate-/l/`
3×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-exp` `flip--`
2×	`frac-sub`
1×	`sub-neg` `diff-log` `div-sub`

Counts

4 → 233

Calls

4 calls:

1.6s	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
68.0ms	(/ alpha (+ (+ alpha beta) 2.0))
48.0ms	(/ beta (+ (+ alpha beta) 2.0))
315.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series342.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
62.0ms	(/ alpha (+ (+ alpha beta) 2.0))
63.0ms	(/ beta (+ (+ alpha beta) 2.0))
101.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.0s

Counts

245 → 245

Iterations

Iter	Nodes
done	5024
2	2258
1	744
0	312

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (+ (+ alpha beta) 2.0))) (/ beta (sqrt (+ (+ alpha beta) 2.0))))
0.4b	(/ beta (sqrt (+ (+ alpha beta) 2.0)))
0.6b	(/ 1 (sqrt (+ (+ alpha beta) 2.0)))
1.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite662.0ms

Algorithm

rewrite-expression-head

Rules

263×	`*-un-lft-identity`
179×	`times-frac`
176×	`add-sqr-sqrt`
125×	`add-cube-cbrt`
81×	`sqrt-prod`
78×	`distribute-lft-out`
63×	`prod-diff`
32×	`add-exp-log`
30×	`associate-r` `associate-l`
21×	`fma-neg`
20×	`add-cbrt-cube`
16×	`associate-/r*` `associate-/r/`
15×	`unswap-sqr`
11×	`div-exp`
8×	`pow1` `flip3-+` `sqrt-div` `prod-exp` `flip-+` `div-inv`
6×	`cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
3×	`rec-exp` `1-exp` `pow-flip`
2×	`clear-num` `frac-2neg` `difference-of-squares`
1×	`frac-times` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip--` `distribute-lft-out--` `inv-pow`

Counts

4 → 314

Calls

4 calls:

208.0ms	(* (/ 1 (sqrt (+ (+ alpha beta) 2.0))) (/ beta (sqrt (+ (+ alpha beta) 2.0))))
47.0ms	(/ beta (sqrt (+ (+ alpha beta) 2.0)))
64.0ms	(/ 1 (sqrt (+ (+ alpha beta) 2.0)))
316.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series353.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (/ 1 (sqrt (+ (+ alpha beta) 2.0))) (/ beta (sqrt (+ (+ alpha beta) 2.0))))
84.0ms	(/ beta (sqrt (+ (+ alpha beta) 2.0)))
71.0ms	(/ 1 (sqrt (+ (+ alpha beta) 2.0)))
123.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.7s

Counts

326 → 326

Iterations

Iter	Nodes
done	5001
2	2640
1	971
0	378

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.5b

localize43.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ beta (sqrt (+ (+ alpha beta) 2.0)))
0.6b	(/ 1 (sqrt (sqrt (+ (+ alpha beta) 2.0))))
0.6b	(/ 1 (sqrt (sqrt (+ (+ alpha beta) 2.0))))
1.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite512.0ms

Algorithm

rewrite-expression-head

Rules

248×	`*-un-lft-identity`
151×	`times-frac`
131×	`add-sqr-sqrt`
126×	`add-cube-cbrt`
124×	`sqrt-prod`
72×	`distribute-lft-out`
63×	`prod-diff`
30×	`associate-/r*`
21×	`fma-neg`
14×	`add-exp-log` `associate-/r/`
10×	`pow1` `add-cbrt-cube` `sqrt-div` `pow-flip`
9×	`associate-/l*`
8×	`sqrt-pow1`
7×	`flip3-+` `flip-+` `div-inv`
6×	`add-log-exp`
5×	`div-exp`
4×	`expm1-log1p-u` `pow1/2` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `clear-num` `frac-2neg`
2×	`rec-exp` `1-exp` `inv-pow` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 298

Calls

4 calls:

71.0ms	(/ beta (sqrt (+ (+ alpha beta) 2.0)))
76.0ms	(/ 1 (sqrt (sqrt (+ (+ alpha beta) 2.0))))
50.0ms	(/ 1 (sqrt (sqrt (+ (+ alpha beta) 2.0))))
300.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series503.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ beta (sqrt (+ (+ alpha beta) 2.0)))
140.0ms	(/ 1 (sqrt (sqrt (+ (+ alpha beta) 2.0))))
139.0ms	(/ 1 (sqrt (sqrt (+ (+ alpha beta) 2.0))))
113.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.9s

Counts

310 → 310

Iterations

Iter	Nodes
done	5000
2	1924
1	752
0	357

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.5b

regimes163.0ms

Accuracy

72% (3.5b remaining)

Error of 6.5b against oracle of 3.0b and baseline of 15.5b

bsearch61.0ms

Steps

Iters	Range		Point
8	2.5944574887415813e+32	4.736445516336521e+35	6.866680421773357e+32

simplify12.0ms

Iterations

Iter	Nodes
done	35
1	35
0	30

end0.0ms

sample2.0s

Algorithm

intervals

Results

902.0ms	5895×	body	80	valid
350.0ms	8000×	pre	80	true
276.0ms	817×	body	1280	valid
157.0ms	707×	body	640	valid
64.0ms	385×	body	320	valid
20.0ms	196×	body	160	valid