Details

sample41.0ms

Algorithm

intervals

Results

7.0ms	169×	body	80	valid
6.0ms	33×	body	1280	valid
5.0ms	33×	body	640	valid
5.0ms	256×	pre	80	true
1.0ms	12×	body	320	valid
1.0ms	9×	body	160	valid

simplify2.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
9	4691
8	1531
7	665
6	318
5	164
4	74
3	53
2	34
1	20
0	10

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.1b

localize25.0ms

Local error

Found 2 expressions with local error:

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

rewrite233.0ms

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` `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 → 100

Calls

2 calls:

46.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
182.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series154.0ms

Counts

2 → 6

Calls

2 calls:

63.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
91.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.2s

Counts

106 → 106

Iterations

Iter	Nodes
done	5002
2	1431
1	340
0	128

prune482.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 19.2b

localize28.0ms

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

rewrite1.8s

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` `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 → 229

Calls

4 calls:

1.4s	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
44.0ms	(/ alpha (+ (+ alpha beta) 2.0))
29.0ms	(/ beta (+ (+ alpha beta) 2.0))
254.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series320.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
64.0ms	(/ alpha (+ (+ alpha beta) 2.0))
68.0ms	(/ beta (+ (+ alpha beta) 2.0))
106.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.9s

Counts

241 → 241

Iterations

Iter	Nodes
done	5000
2	2982
1	741
0	308

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.2b

localize59.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
9.1b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
9.1b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
9.1b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite365.0ms

Algorithm

rewrite-expression-head

Rules

195×	`*-un-lft-identity`
106×	`times-frac`
93×	`add-sqr-sqrt`
88×	`add-cube-cbrt`
63×	`cbrt-prod` `prod-diff` `distribute-lft-out`
21×	`fma-neg`
14×	`associate-/r/`
7×	`flip3-+` `flip-+` `div-inv`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`cbrt-div` `pow1/3`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 197

Calls

4 calls:

282.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
18.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
20.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
27.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series744.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
213.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
214.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
200.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify1.4s

Counts

209 → 209

Iterations

Iter	Nodes
done	5001
2	1591
1	522
0	241

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.2b

localize31.0ms

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)))
2.0b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
10.8b	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

rewrite1.0s

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` `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 → 218

Calls

4 calls:

54.0ms	(/ beta (+ (+ alpha beta) 2.0))
337.0ms	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
209.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
398.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

series444.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ beta (+ (+ alpha beta) 2.0))
87.0ms	(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)
188.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

simplify1.9s

Counts

230 → 230

Iterations

Iter	Nodes
done	5000
2	2440
1	768
0	357

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.2b

regimes345.0ms

Accuracy

75.5% (3.2b remaining)

Error of 6.0b against oracle of 2.8b and baseline of 15.7b

bsearch52.0ms

Steps

Iters	Range		Point
7	46374.558514477714	3809480.5813382245	234711.65091804432

simplify7.0ms

Iterations

Iter	Nodes
done	38
1	38
0	32

end0.0ms

sample1.4s

Algorithm

intervals

Results

444.0ms	5858×	body	80	valid
239.0ms	864×	body	1280	valid
180.0ms	8000×	pre	80	true
170.0ms	666×	body	640	valid
58.0ms	392×	body	320	valid
19.0ms	220×	body	160	valid