Details

sample47.0ms

Algorithm

intervals

Results

11.0ms	202×	body	80	valid
6.0ms	22×	body	1280	valid
5.0ms	256×	pre	80	true
3.0ms	13×	body	640	valid
2.0ms	14×	body	320	valid
0.0ms	5×	body	160	valid

simplify7.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
26	4760
25	4506
24	4255
23	4020
22	3732
21	3431
20	3171
19	2906
18	2472
17	2125
16	1848
15	1561
14	1275
13	993
12	805
11	679
10	588
9	473
8	355
7	292
6	210
5	124
4	69
3	50
2	33
1	20
0	10

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.6b

localize28.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.2b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite498.0ms

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:

104.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
384.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series219.0ms

Counts

2 → 6

Calls

2 calls:

98.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
121.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.9s

Counts

106 → 106

Iterations

Iter	Nodes
done	5012
2	1163
1	341
0	128

prune788.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 12.1b

localize43.0ms

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))
1.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite3.0s

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:

2.4s	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
110.0ms	(/ alpha (+ (+ alpha beta) 2.0))
68.0ms	(/ beta (+ (+ alpha beta) 2.0))
423.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series431.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
87.0ms	(/ alpha (+ (+ alpha beta) 2.0))
86.0ms	(/ beta (+ (+ alpha beta) 2.0))
142.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify3.3s

Counts

241 → 241

Iterations

Iter	Nodes
done	5006
2	2279
1	741
0	308

prune1.9s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.9b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.5b	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
1.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
7.1b	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

rewrite1.8s

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:

80.0ms	(/ beta (+ (+ alpha beta) 2.0))
646.0ms	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
388.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
622.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ beta (+ (+ alpha beta) 2.0))
129.0ms	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
661.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
247.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

simplify2.7s

Counts

230 → 230

Iterations

Iter	Nodes
done	5001
2	1886
1	769
0	357

prune1.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.9b

localize70.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.6b	(pow E (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
1.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
7.1b	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

207×	`*-un-lft-identity`
130×	`add-sqr-sqrt`
124×	`times-frac`
95×	`add-cube-cbrt`
63×	`prod-diff`
50×	`log-prod`
48×	`distribute-lft-out`
25×	`unpow-prod-up`
21×	`fma-neg`
19×	`distribute-lft-out--`
14×	`difference-of-squares`
10×	`add-exp-log` `associate-/r/`
7×	`pow1` `div-inv`
6×	`add-cbrt-cube` `add-log-exp`
5×	`flip3-+` `associate-/r*` `flip-+`
4×	`expm1-log1p-u` `pow-unpow` `log1p-expm1-u`
3×	`unpow-prod-down` `associate-/l*`
2×	`log-div` `div-exp` `rem-log-exp` `pow-exp` `log-pow`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `e-exp-1` `flip3--` `pow-pow` `frac-2neg` `diff-log` `clear-num` `flip--` `pow-sub` `sqr-pow`

Counts

4 → 225

Calls

4 calls:

75.0ms	(/ beta (+ (+ alpha beta) 2.0))
655.0ms	(pow E (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
451.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
652.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

series844.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ beta (+ (+ alpha beta) 2.0))
321.0ms	(pow E (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
159.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
254.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

simplify3.7s

Counts

237 → 237

Iterations

Iter	Nodes
done	5007
2	2376
1	923
0	371

prune1.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.9b

regimes306.0ms

Accuracy

57.2% (5.4b remaining)

Error of 8.5b against oracle of 3.0b and baseline of 15.7b

bsearch276.0ms

Steps

Iters	Range		Point
7	3.9227933197023594e+166	7.439987087167839e+167	1.1437212734780832e+167
5	7.445604319051971e+112	1.5393751381298674e+113	1.5264500717710571e+113
8	4.6091985256205887e+33	6.133200959176609e+37	7.863989155318433e+36

simplify25.0ms

Iterations

Iter	Nodes
done	51
3	51
2	48
1	45
0	36

end0.0ms

sample1.8s

Algorithm

intervals

Results

442.0ms	5842×	body	80	valid
358.0ms	8000×	pre	80	true
328.0ms	719×	body	640	valid
291.0ms	874×	body	1280	valid
73.0ms	381×	body	320	valid
23.0ms	184×	body	160	valid