Details

sample53.0ms

Algorithm

intervals

Results

11.0ms	198×	body	80	valid
8.0ms	27×	body	1280	valid
6.0ms	256×	pre	80	true
4.0ms	16×	body	640	valid
2.0ms	9×	body	320	valid
1.0ms	6×	body	160	valid

simplify10.5s

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

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize71.0ms

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)

rewrite661.0ms

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:

113.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
538.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series169.0ms

Counts

2 → 6

Calls

2 calls:

71.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
98.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify2.8s

Counts

108 → 108

Iterations

Iter	Nodes
done	5000
2	1177
1	342
0	130

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.0b

localize134.0ms

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

rewrite4.3s

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:

3.4s	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
81.0ms	(/ beta (+ (+ alpha beta) 2.0))
117.0ms	(/ alpha (+ (+ alpha beta) 2.0))
661.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series458.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
80.0ms	(/ beta (+ (+ alpha beta) 2.0))
80.0ms	(/ alpha (+ (+ alpha beta) 2.0))
153.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify5.4s

Counts

245 → 245

Iterations

Iter	Nodes
done	5002
2	2313
1	744
0	312

prune2.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.9b

localize203.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.5b	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
1.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
8.2b	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

rewrite2.7s

Algorithm

rewrite-expression-head

Rules

206×	`*-un-lft-identity`
129×	`add-sqr-sqrt`
124×	`times-frac`
94×	`add-cube-cbrt`
63×	`prod-diff`
50×	`log-prod`
48×	`distribute-lft-out`
25×	`exp-sum`
21×	`fma-neg`
19×	`distribute-lft-out--`
14×	`difference-of-squares`
10×	`associate-/r/`
9×	`add-exp-log`
7×	`div-inv`
6×	`pow1` `add-cbrt-cube` `add-log-exp`
5×	`associate-/r*` `flip3-+` `flip-+`
4×	`expm1-log1p-u` `exp-prod` `insert-posit16` `log1p-expm1-u`
3×	`associate-/l*`
2×	`log-div` `div-exp` `rem-log-exp` `log-pow`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3--` `exp-diff` `diff-log` `flip--` `rem-exp-log`

Counts

4 → 222

Calls

4 calls:

116.0ms	(/ alpha (+ (+ alpha beta) 2.0))
1.1s	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
563.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
913.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

series601.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ alpha (+ (+ alpha beta) 2.0))
122.0ms	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
169.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
235.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

simplify4.0s

Counts

234 → 234

Iterations

Iter	Nodes
done	5004
2	1859
1	731
0	340

prune2.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.9b

Details

sample53.0ms

simplify10.5s

prune19.0ms

localize71.0ms

rewrite661.0ms

series169.0ms

simplify2.8s

prune1.1s

localize134.0ms

rewrite4.3s

series458.0ms

simplify5.4s

prune2.5s

localize203.0ms

rewrite2.7s

series601.0ms

simplify4.0s

prune2.5s

localize14.0ms