Details

sample44.0ms

Algorithm

intervals

Results

8.0ms	175×	body	80	valid
6.0ms	29×	body	1280	valid
6.0ms	31×	body	640	valid
5.0ms	256×	pre	80	true
2.0ms	14×	body	320	valid
1.0ms	7×	body	160	valid

simplify4.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	20	13
2	34	13
3	53	13
4	74	13
5	163	13
6	314	13
7	647	13
8	1463	13
9	4388	13
done	5001	13

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.3b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.2b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite396.0ms

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-exp-log` `associate-/r/` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow1` `expm1-log1p-u` `div-sub` `log1p-expm1-u` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `flip3--` `frac-2neg` `div-exp` `clear-num` `sum-log` `flip--`

Counts

2 → 100

Calls

2 calls:

90.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
297.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series156.0ms

Counts

2 → 6

Calls

2 calls:

71.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
85.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.1s

Counts

106 → 106

Iterations

Useful iterations: 2 (271.0ms)

Iter	Nodes	Cost
0	128	1178
1	341	1110
2	1440	1056
done	5000	1056

prune318.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 18.3b

localize16.0ms

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))
2.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite2.2s

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-exp-log` `add-cbrt-cube` `difference-of-squares`
7×	`div-inv`
6×	`flip3-+` `flip-+` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/`
3×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--`
2×	`frac-sub`
1×	`sub-neg` `diff-log` `div-sub`

Counts

4 → 229

Calls

4 calls:

1.8s	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
43.0ms	(/ beta (+ (+ alpha beta) 2.0))
46.0ms	(/ alpha (+ (+ alpha beta) 2.0))
290.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series346.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
86.0ms	(/ beta (+ (+ alpha beta) 2.0))
66.0ms	(/ alpha (+ (+ alpha beta) 2.0))
103.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.9s

Counts

241 → 241

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	308	5116
1	742	4394
2	2989	3980
done	5001	3842

prune691.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.6b

localize23.0ms

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))
2.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite436.0ms

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×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `div-inv`
3×	`pow1/3`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 152

Calls

4 calls:

31.0ms	(cbrt (+ (+ alpha beta) 2.0))
17.0ms	(cbrt (+ (+ alpha beta) 2.0))
24.0ms	(cbrt (+ (+ alpha beta) 2.0))
349.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series561.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(cbrt (+ (+ alpha beta) 2.0))
133.0ms	(cbrt (+ (+ alpha beta) 2.0))
153.0ms	(cbrt (+ (+ alpha beta) 2.0))
126.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify975.0ms

Counts

164 → 164

Iterations

Useful iterations: done (969.0ms)

Iter	Nodes	Cost
0	204	3412
1	473	2754
2	1410	2423
done	5001	2209

prune678.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.8b	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
2.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
7.2b	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

rewrite1.3s

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×	`flip3-+` `associate-/r*` `flip-+`
4×	`expm1-log1p-u` `exp-prod` `log1p-expm1-u`
3×	`associate-/l*`
2×	`log-div` `div-exp` `rem-log-exp` `log-pow`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `exp-diff` `diff-log` `clear-num` `flip--` `rem-exp-log`

Counts

4 → 218

Calls

4 calls:

60.0ms	(/ alpha (+ (+ alpha beta) 2.0))
437.0ms	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
279.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
525.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

series451.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(/ alpha (+ (+ alpha beta) 2.0))
84.0ms	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
107.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
183.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

simplify1.5s

Counts

230 → 230

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	336	5840
1	731	5005
2	2370	4554
done	5000	4397

prune623.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.6b

regimes178.0ms

Accuracy

75.8% (3.1b remaining)

Error of 6.1b against oracle of 3.0b and baseline of 15.7b

bsearch55.0ms

Steps

Iters	Range		Point
6	1.1627257238775583e+18	9.659747104654096e+18	1.1900968737058765e+18

simplify12.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	37	73
1	42	73
2	44	73
done	44	73

end0.0ms

sample1.9s

Algorithm

intervals

Results

856.0ms	5853×	body	80	valid
245.0ms	850×	body	1280	valid
169.0ms	8000×	pre	80	true
143.0ms	746×	body	640	valid
109.0ms	363×	body	320	valid
17.0ms	188×	body	160	valid