Details

sample24.0ms

Algorithm

intervals

Results

4.0ms	178×	body	80	valid
4.0ms	34×	body	1280	valid
3.0ms	256×	pre	80	true
2.0ms	19×	body	640	valid
1.0ms	15×	body	320	valid
1.0ms	10×	body	160	valid

simplify320.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	13
1	20	13
2	33	13
3	51	13
4	70	13
5	119	13
6	155	13
7	201	13
8	234	13
9	285	13
10	325	13
11	335	13
12	347	13
13	359	13
done	359	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.6b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite128.0ms

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:

26.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
97.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series107.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
61.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.2s

Counts

106 → 106

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	128	1178
1	334	1110
2	875	1056
3	2687	1048
done	5000	1047

prune215.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 17.3b

localize9.0ms

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))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
2.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite482.0ms

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-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`pow1` `expm1-log1p-u` `diff-log` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub`
1×	`associate--r-`

Counts

4 → 413

Calls

4 calls:

18.0ms	(/ alpha (+ (+ alpha beta) 2.0))
296.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
19.0ms	(/ beta (+ (+ alpha beta) 2.0))
116.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series228.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ alpha (+ (+ alpha beta) 2.0))
60.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
46.0ms	(/ beta (+ (+ alpha beta) 2.0))
76.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify891.0ms

Counts

425 → 425

Iterations

Useful iterations: done (873.0ms)

Iter	Nodes	Cost
0	402	16706
1	936	13361
2	2472	11385
done	5001	11298

prune755.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
2.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
2.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite262.0ms

Algorithm

rewrite-expression-head

Rules

254×	`*-un-lft-identity`
130×	`add-sqr-sqrt`
126×	`prod-diff`
122×	`times-frac`
120×	`add-cube-cbrt`
78×	`distribute-lft-out`
42×	`fma-neg`
16×	`associate-/r/`
10×	`cbrt-prod` `flip3-+` `flip-+`
8×	`div-inv` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `log1p-expm1-u` `difference-of-squares`
2×	`sub-neg` `flip3--` `pow1/3` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 236

Calls

4 calls:

8.0ms	(cbrt (+ (+ alpha beta) 2.0))
8.0ms	(cbrt (+ (+ alpha beta) 2.0))
115.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
117.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series354.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(cbrt (+ (+ alpha beta) 2.0))
98.0ms	(cbrt (+ (+ alpha beta) 2.0))
78.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
80.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.3s

Counts

248 → 248

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	204	5724
1	445	4422
2	1065	3854
3	3143	3292
done	5000	3058

prune533.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.6b	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
2.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
10.6b	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite532.0ms

Algorithm

rewrite-expression-head

Rules

166×	`*-un-lft-identity`
89×	`add-sqr-sqrt`
78×	`times-frac`
74×	`add-cube-cbrt`
63×	`prod-diff`
48×	`distribute-lft-out`
21×	`fma-neg`
14×	`log-prod`
10×	`associate-/r/`
8×	`log-div`
7×	`add-exp-log` `exp-sum` `distribute-lft-out--`
6×	`pow1` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
5×	`flip3--` `flip3-+` `associate-/r*` `flip--` `flip-+` `div-inv`
4×	`expm1-log1p-u` `exp-prod` `exp-diff` `frac-sub` `log1p-expm1-u`
3×	`associate-/l*`
2×	`log-pow`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 187

Calls

4 calls:

18.0ms	(/ beta (+ (+ alpha beta) 2.0))
167.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
114.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
223.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series316.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ beta (+ (+ alpha beta) 2.0))
65.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
71.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
130.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify629.0ms

Counts

199 → 199

Iterations

Useful iterations: done (622.0ms)

Iter	Nodes	Cost
0	299	4746
1	648	3934
2	1687	3535
done	5000	3417

prune371.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.6b

regimes128.0ms

Accuracy

78.1% (2.8b remaining)

Error of 6.0b against oracle of 3.3b and baseline of 15.9b

bsearch36.0ms

Steps

Iters	Range		Point
5	391248603.19673574	1027443772.3458656	1015227874.2528594

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	98
1	39	98
done	39	98

end0.0ms

sample609.0ms

Algorithm

intervals

Results

147.0ms	5870×	body	80	valid
104.0ms	828×	body	1280	valid
100.0ms	8000×	pre	80	true
67.0ms	692×	body	640	valid
34.0ms	409×	body	320	valid
10.0ms	201×	body	160	valid