Details

sample61.0ms

Algorithm

intervals

Results

11.0ms	178×	body	80	valid
10.0ms	30×	body	1280	valid
7.0ms	256×	pre	80	true
6.0ms	25×	body	640	valid
3.0ms	18×	body	320	valid
1.0ms	5×	body	160	valid

simplify804.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	13
1	20	13
2	34	13
3	52	13
4	73	13
5	118	13
6	161	13
7	199	13
8	230	13
9	268	13
10	296	13
11	307	13
12	319	13
13	323	13
done	323	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.4b

localize18.0ms

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)

rewrite408.0ms

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:

78.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
325.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series166.0ms

Counts

2 → 6

Calls

2 calls:

77.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
89.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify2.2s

Counts

106 → 106

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	128	1178
1	335	1110
2	950	1056
3	3094	1048
done	5001	1043

prune358.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 17.5b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.4s

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:

856.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
38.0ms	(/ beta (+ (+ alpha beta) 2.0))
63.0ms	(/ alpha (+ (+ alpha beta) 2.0))
368.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series344.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
76.0ms	(/ beta (+ (+ alpha beta) 2.0))
58.0ms	(/ alpha (+ (+ alpha beta) 2.0))
111.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.1s

Counts

425 → 425

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	402	16706
1	942	13361
2	2393	11385
done	5000	9914

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ 2.0 (+ alpha beta)))
0.4b	(pow (cbrt (/ beta (+ (+ alpha beta) 2.0))) 3)
2.0b	(- (/ alpha (+ 2.0 (+ alpha beta))) 1.0)
8.0b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite425.0ms

Algorithm

rewrite-expression-head

Rules

228×	`*-un-lft-identity`
121×	`times-frac`
106×	`add-sqr-sqrt`
101×	`add-cube-cbrt`
75×	`distribute-lft-out`
63×	`cbrt-prod` `prod-diff`
24×	`unpow-prod-down` `cube-prod`
21×	`fma-neg`
16×	`associate-/r/`
8×	`flip3-+` `flip-+` `div-inv`
7×	`add-exp-log`
6×	`add-cbrt-cube` `add-log-exp`
5×	`pow1` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `associate-/l*`
2×	`cbrt-div` `pow-pow` `pow1/3` `difference-of-squares`
1×	`cbrt-undiv` `cube-div` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `diff-log` `unpow3` `div-exp` `pow-exp` `clear-num` `flip--` `distribute-lft-out--` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 241

Calls

4 calls:

41.0ms	(/ alpha (+ 2.0 (+ alpha beta)))
80.0ms	(pow (cbrt (/ beta (+ (+ alpha beta) 2.0))) 3)
266.0ms	(- (/ alpha (+ 2.0 (+ alpha beta))) 1.0)
24.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series689.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ alpha (+ 2.0 (+ alpha beta)))
320.0ms	(pow (cbrt (/ beta (+ (+ alpha beta) 2.0))) 3)
93.0ms	(- (/ alpha (+ 2.0 (+ alpha beta))) 1.0)
200.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify1.9s

Counts

253 → 253

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	346	5078
1	884	3953
2	2413	3526
done	5000	3237

prune816.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.9b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (log (exp (cbrt (/ beta (+ (+ alpha beta) 2.0))))) 3)
2.0b	(- (/ alpha (+ 2.0 (+ alpha beta))) 1.0)
8.0b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
9.2b	(log (exp (cbrt (/ beta (+ (+ alpha beta) 2.0)))))

rewrite546.0ms

Algorithm

rewrite-expression-head

Rules

226×	`*-un-lft-identity`
121×	`times-frac`
109×	`add-sqr-sqrt`
104×	`add-cube-cbrt`
84×	`cbrt-prod`
75×	`log-pow`
72×	`exp-prod` `distribute-lft-out`
63×	`prod-diff`
28×	`unpow-prod-down` `cube-prod`
21×	`fma-neg`
16×	`associate-/r/`
8×	`pow1` `flip3-+` `flip-+` `div-inv`
6×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `log-prod`
2×	`difference-of-squares`
1×	`cube-mult` `pow-to-exp` `sub-neg` `cbrt-div` `flip3--` `pow-pow` `pow1/3` `diff-log` `unpow3` `rem-log-exp` `pow-exp` `flip--` `distribute-lft-out--` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 246

Calls

4 calls:

156.0ms	(pow (log (exp (cbrt (/ beta (+ (+ alpha beta) 2.0))))) 3)
227.0ms	(- (/ alpha (+ 2.0 (+ alpha beta))) 1.0)
19.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
115.0ms	(log (exp (cbrt (/ beta (+ (+ alpha beta) 2.0)))))

series897.0ms

Counts

4 → 12

Calls

4 calls:

289.0ms	(pow (log (exp (cbrt (/ beta (+ (+ alpha beta) 2.0))))) 3)
112.0ms	(- (/ alpha (+ 2.0 (+ alpha beta))) 1.0)
225.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
271.0ms	(log (exp (cbrt (/ beta (+ (+ alpha beta) 2.0)))))

simplify1.6s

Counts

258 → 258

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	381	5463
1	899	4150
2	2043	3582
done	5000	3411

prune737.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.9b

regimes165.0ms

Accuracy

77.1% (3.1b remaining)

Error of 6.3b against oracle of 3.2b and baseline of 16.6b

bsearch79.0ms

Steps

Iters	Range		Point
8	627164805739635.8	1.0354160951297587e+18	4.39115944925299e+17

simplify4.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	31	48
1	35	46
done	35	46

end0.0ms

sample1.8s

Algorithm

intervals

Results

450.0ms	377×	body	320	valid
355.0ms	5780×	body	80	valid
258.0ms	926×	body	1280	valid
248.0ms	8000×	pre	80	true
201.0ms	718×	body	640	valid
20.0ms	199×	body	160	valid