Details

sample52.0ms

Algorithm

intervals

Results

12.0ms	200×	body	80	valid
6.0ms	22×	body	1280	valid
6.0ms	256×	pre	80	true
4.0ms	22×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	6×	body	160	valid

simplify2.6s

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: 13.1b

localize25.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.4b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite310.0ms

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:

72.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
234.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series163.0ms

Counts

2 → 6

Calls

2 calls:

74.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
89.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.3s

Counts

106 → 106

Iterations

Iter	Nodes
done	5002
2	1431
1	340
0	128

prune618.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.5b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

512×	`*-un-lft-identity`
328×	`add-sqr-sqrt`
263×	`times-frac`
252×	`prod-diff`
213×	`add-cube-cbrt`
150×	`distribute-lft-out`
65×	`associate--r+`
46×	`difference-of-squares`
42×	`fma-neg`
32×	`associate-/r/`
25×	`distribute-lft-out--`
16×	`flip3-+` `flip-+` `div-inv`
11×	`add-log-exp`
10×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/l*`
4×	`expm1-log1p-u` `pow1` `diff-log` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `frac-sub`
1×	`associate--r-`

Counts

4 → 413

Calls

4 calls:

601.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
33.0ms	(/ alpha (+ (+ alpha beta) 2.0))
58.0ms	(/ beta (+ (+ alpha beta) 2.0))
268.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series368.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
78.0ms	(/ alpha (+ (+ alpha beta) 2.0))
65.0ms	(/ beta (+ (+ alpha beta) 2.0))
137.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.4s

Counts

425 → 425

Iterations

Iter	Nodes
done	5000
2	3885
1	992
0	402

prune2.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.6b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.5b	(- (log (exp (/ alpha (+ (+ alpha beta) 2.0)))) 1.0)
2.3b	(log (exp (/ alpha (+ (+ alpha beta) 2.0))))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

218×	`*-un-lft-identity`
111×	`log-pow`
105×	`exp-prod` `times-frac`
102×	`add-sqr-sqrt`
100×	`add-cube-cbrt`
75×	`prod-diff`
69×	`distribute-lft-out`
25×	`fma-neg`
14×	`associate-/r/`
10×	`pow1` `associate-/r*`
8×	`add-cbrt-cube` `add-exp-log`
7×	`flip3-+` `flip-+` `div-inv`
6×	`log-prod` `associate-/l*`
5×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate--l+`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

4 → 233

Calls

4 calls:

54.0ms	(/ alpha (+ (+ alpha beta) 2.0))
55.0ms	(/ beta (+ (+ alpha beta) 2.0))
898.0ms	(- (log (exp (/ alpha (+ (+ alpha beta) 2.0)))) 1.0)
89.0ms	(log (exp (/ alpha (+ (+ alpha beta) 2.0))))

series343.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ alpha (+ (+ alpha beta) 2.0))
81.0ms	(/ beta (+ (+ alpha beta) 2.0))
118.0ms	(- (log (exp (/ alpha (+ (+ alpha beta) 2.0)))) 1.0)
61.0ms	(log (exp (/ alpha (+ (+ alpha beta) 2.0))))

simplify1.5s

Counts

245 → 245

Iterations

Iter	Nodes
done	5000
2	2021
1	594
0	277

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.6b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.5b	(+ (log (sqrt (exp (/ alpha (+ (+ alpha beta) 2.0))))) (- (log (sqrt (exp (/ alpha (+ (+ alpha beta) 2.0))))) 1.0))
2.3b	(log (sqrt (exp (/ alpha (+ (+ alpha beta) 2.0)))))
2.3b	(log (sqrt (exp (/ alpha (+ (+ alpha beta) 2.0)))))

rewrite2.0s

Algorithm

rewrite-expression-head

Rules

228×	`*-un-lft-identity`
149×	`log-pow`
132×	`sqrt-pow1`
126×	`exp-prod`
107×	`add-sqr-sqrt` `add-cube-cbrt`
105×	`times-frac`
89×	`associate-+r+`
81×	`prod-diff`
72×	`distribute-lft-out`
27×	`fma-def`
24×	`log-prod`
21×	`pow1`
14×	`associate-/r/`
12×	`sqrt-prod`
8×	`flip3-+` `add-exp-log` `flip-+`
7×	`div-inv`
6×	`associate-+l+` `add-cbrt-cube` `pow1/2` `associate--l+` `add-log-exp`
5×	`associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--`
3×	`associate-/l*`
2×	`sum-log` `rem-log-exp`
1×	`cbrt-undiv` `+-commutative` `clear-num` `associate-+r-` `sub-neg` `frac-2neg` `diff-log` `div-exp`

Counts

4 → 262

Calls

4 calls:

47.0ms	(/ beta (+ (+ alpha beta) 2.0))
1.7s	(+ (log (sqrt (exp (/ alpha (+ (+ alpha beta) 2.0))))) (- (log (sqrt (exp (/ alpha (+ (+ alpha beta) 2.0))))) 1.0))
87.0ms	(log (sqrt (exp (/ alpha (+ (+ alpha beta) 2.0)))))
76.0ms	(log (sqrt (exp (/ alpha (+ (+ alpha beta) 2.0)))))

series487.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ beta (+ (+ alpha beta) 2.0))
149.0ms	(+ (log (sqrt (exp (/ alpha (+ (+ alpha beta) 2.0))))) (- (log (sqrt (exp (/ alpha (+ (+ alpha beta) 2.0))))) 1.0))
120.0ms	(log (sqrt (exp (/ alpha (+ (+ alpha beta) 2.0)))))
129.0ms	(log (sqrt (exp (/ alpha (+ (+ alpha beta) 2.0)))))

simplify1.9s

Counts

274 → 274

Iterations

Iter	Nodes
done	5000
2	2482
1	763
0	365

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.6b

regimes249.0ms

Accuracy

73% (3.3b remaining)

Error of 6.2b against oracle of 2.9b and baseline of 15.2b

bsearch90.0ms

Steps

Iters	Range		Point
9	7.141495025384564e+25	1.1524881963593713e+31	1.6348256570929846e+27

simplify7.0ms

Iterations

Iter	Nodes
done	41
1	41
0	35

end0.0ms

sample1.6s

Algorithm

intervals

Results

499.0ms	8000×	pre	80	true
340.0ms	5915×	body	80	valid
216.0ms	810×	body	1280	valid
203.0ms	715×	body	640	valid
45.0ms	364×	body	320	valid
18.0ms	196×	body	160	valid