Details

sample69.0ms

Algorithm

intervals

Results

15.0ms	178×	body	80	valid
13.0ms	29×	body	640	valid
13.0ms	31×	body	1280	valid
10.0ms	256×	pre	80	true
2.0ms	11×	body	320	valid
1.0ms	7×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	2002
18	2002
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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.5b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.8b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite211.0ms

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:

47.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
160.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series153.0ms

Counts

2 → 6

Calls

2 calls:

61.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
91.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.1s

Counts

108 → 108

Iterations

Iter	Nodes
done	2016
3	2016
2	1170
1	342
0	130

prune400.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 17.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.8b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite1.4s

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:

43.0ms	(/ alpha (+ (+ alpha beta) 2.0))
1.1s	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
33.0ms	(/ beta (+ (+ alpha beta) 2.0))
222.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series355.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ alpha (+ (+ alpha beta) 2.0))
95.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
74.0ms	(/ beta (+ (+ alpha beta) 2.0))
119.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.1s

Counts

245 → 245

Iterations

Iter	Nodes
done	2000
2	2000
1	744
0	312

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.2b

localize60.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
1.8b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

141×	`*-un-lft-identity`
69×	`add-sqr-sqrt`
64×	`add-cube-cbrt`
63×	`prod-diff`
61×	`times-frac`
45×	`distribute-lft-out`
21×	`fma-neg`
15×	`cbrt-prod`
8×	`associate-/r/`
7×	`flip3-+` `flip-+`
6×	`cbrt-div` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`pow1/3`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 156

Calls

4 calls:

10.0ms	(cbrt (+ (+ alpha beta) 2.0))
10.0ms	(cbrt (+ (+ alpha beta) 2.0))
10.0ms	(cbrt (+ (+ alpha beta) 2.0))
193.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series456.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(cbrt (+ (+ alpha beta) 2.0))
150.0ms	(cbrt (+ (+ alpha beta) 2.0))
109.0ms	(cbrt (+ (+ alpha beta) 2.0))
82.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.3s

Counts

168 → 168

Iterations

Iter	Nodes
done	2003
3	2003
2	1186
1	472
0	206

prune1.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.2b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.9b	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
1.8b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
7.8b	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

rewrite706.0ms

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:

36.0ms	(/ beta (+ (+ alpha beta) 2.0))
248.0ms	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
197.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
220.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

series507.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ beta (+ (+ alpha beta) 2.0))
97.0ms	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
113.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
224.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

simplify1.6s

Counts

234 → 234

Iterations

Iter	Nodes
done	2003
3	2003
2	1916
1	771
0	361

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.2b

regimes233.0ms

Accuracy

76.3% (3.0b remaining)

Error of 6.0b against oracle of 3.0b and baseline of 15.6b

bsearch122.0ms

Steps

Iters	Range		Point
9	2224838044.2478166	1531887432751931.0	139510554198006.0

simplify14.0ms

Iterations

Iter	Nodes
done	43
2	43
1	41
0	35

end0.0ms

sample2.1s

Algorithm

intervals

Results

567.0ms	5866×	body	80	valid
415.0ms	385×	body	320	valid
324.0ms	816×	body	1280	valid
305.0ms	8000×	pre	80	true
257.0ms	734×	body	640	valid
63.0ms	199×	body	160	valid