Details

sample88.0ms

Algorithm

intervals

Results

22.0ms	25×	body	1280	valid
21.0ms	186×	body	80	valid
12.0ms	256×	pre	80	true
11.0ms	24×	body	640	valid
4.0ms	13×	body	320	valid
2.0ms	8×	body	160	valid

simplify4.7s

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.1b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.3b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite218.0ms

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:

46.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
169.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series150.0ms

Counts

2 → 6

Calls

2 calls:

78.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
72.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.1s

Counts

108 → 108

Iterations

Iter	Nodes
done	5004
2	1170
1	342
0	130

prune383.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 15.3b

localize21.0ms

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))
2.3b	(- (/ 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:

1.2s	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
26.0ms	(/ alpha (+ (+ alpha beta) 2.0))
33.0ms	(/ beta (+ (+ alpha beta) 2.0))
155.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series343.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
62.0ms	(/ alpha (+ (+ alpha beta) 2.0))
80.0ms	(/ beta (+ (+ alpha beta) 2.0))
119.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.2s

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: 3.2b

localize68.0ms

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))
2.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite244.0ms

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:

20.0ms	(cbrt (+ (+ alpha beta) 2.0))
20.0ms	(cbrt (+ (+ alpha beta) 2.0))
19.0ms	(cbrt (+ (+ alpha beta) 2.0))
179.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series540.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(cbrt (+ (+ alpha beta) 2.0))
143.0ms	(cbrt (+ (+ alpha beta) 2.0))
138.0ms	(cbrt (+ (+ alpha beta) 2.0))
111.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.4s

Counts

168 → 168

Iterations

Iter	Nodes
done	5000
3	3887
2	1186
1	472
0	206

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.2b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.8b	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
2.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
8.8b	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

rewrite803.0ms

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))
254.0ms	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
233.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
270.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

series437.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ beta (+ (+ alpha beta) 2.0))
97.0ms	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
91.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
186.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

simplify1.7s

Counts

234 → 234

Iterations

Iter	Nodes
done	5000
2	1916
1	771
0	361

prune972.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.2b

regimes180.0ms

Accuracy

77.4% (2.9b remaining)

Error of 5.9b against oracle of 3.0b and baseline of 15.9b

bsearch443.0ms

Steps

Iters	Range		Point
10	0.06193883622199307	464811167.6258734	460518623.3564523

simplify6.0ms

Iterations

Iter	Nodes
done	35
1	35
0	30

end0.0ms

sample2.0s

Algorithm

intervals

Results

637.0ms	5820×	body	80	valid
375.0ms	851×	body	1280	valid
320.0ms	713×	body	640	valid
288.0ms	8000×	pre	80	true
133.0ms	418×	body	320	valid
31.0ms	198×	body	160	valid