Details

sample38.0ms

Algorithm

intervals

Results

7.0ms	179×	body	80	valid
5.0ms	29×	body	1280	valid
4.0ms	256×	pre	80	true
4.0ms	27×	body	640	valid
1.0ms	11×	body	320	valid
1.0ms	10×	body	160	valid

simplify4.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
25	4885
24	4583
23	4303
22	3954
21	3572
20	3229
19	2829
18	2315
17	1985
16	1722
15	1474
14	1236
13	995
12	795
11	669
10	582
9	467
8	348
7	290
6	209
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: 18.0b

localize32.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.5b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite306.0ms

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:

43.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
255.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series156.0ms

Counts

2 → 6

Calls

2 calls:

69.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
86.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.2s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	1160
1	340
0	128

prune581.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 17.1b

localize18.0ms

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))
2.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite1.1s

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:

702.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
48.0ms	(/ alpha (+ (+ alpha beta) 2.0))
51.0ms	(/ beta (+ (+ alpha beta) 2.0))
286.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series347.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
84.0ms	(/ alpha (+ (+ alpha beta) 2.0))
68.0ms	(/ beta (+ (+ alpha beta) 2.0))
115.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.4s

Counts

425 → 425

Iterations

Iter	Nodes
done	5011
2	2690
1	991
0	402

prune2.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.1b

localize26.0ms

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))))
2.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
12.0b	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite1.2s

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×	`exp-sum` `add-exp-log` `distribute-lft-out--`
6×	`pow1` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
5×	`associate-/r*` `flip3-+` `flip3--` `flip-+` `div-inv` `flip--`
4×	`expm1-log1p-u` `exp-prod` `exp-diff` `frac-sub` `log1p-expm1-u`
3×	`associate-/l*`
2×	`log-pow`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `rem-exp-log`

Counts

4 → 187

Calls

4 calls:

54.0ms	(/ beta (+ (+ alpha beta) 2.0))
355.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
208.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
529.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series474.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(/ beta (+ (+ alpha beta) 2.0))
94.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
130.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
180.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify2.0s

Counts

199 → 199

Iterations

Iter	Nodes
done	5005
2	2117
1	684
0	299

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.1b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (log1p (/ beta (+ (+ alpha beta) 2.0))))
0.8b	(exp (log (- (expm1 (log1p (/ beta (+ (+ alpha beta) 2.0)))) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
2.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
12.0b	(log (- (expm1 (log1p (/ beta (+ (+ alpha beta) 2.0)))) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite879.0ms

Algorithm

rewrite-expression-head

Rules

136×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
64×	`add-cube-cbrt`
63×	`prod-diff`
61×	`times-frac`
36×	`distribute-lft-out`
21×	`fma-neg`
12×	`log-prod`
8×	`associate-/r/`
7×	`distribute-lft-out--`
6×	`pow1` `exp-sum` `add-log-exp`
5×	`add-exp-log`
4×	`expm1-log1p-u` `log-div` `exp-prod` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `div-inv` `difference-of-squares`
3×	`flip3--` `flip--`
2×	`exp-diff` `log-pow`
1×	`expm1-log1p` `sub-neg` `diff-log` `rem-log-exp` `expm1-udef` `rem-exp-log`

Counts

4 → 153

Calls

4 calls:

0.0ms	(expm1 (log1p (/ beta (+ (+ alpha beta) 2.0))))
278.0ms	(exp (log (- (expm1 (log1p (/ beta (+ (+ alpha beta) 2.0)))) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
227.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
359.0ms	(log (- (expm1 (log1p (/ beta (+ (+ alpha beta) 2.0)))) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series589.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(expm1 (log1p (/ beta (+ (+ alpha beta) 2.0))))
123.0ms	(exp (log (- (expm1 (log1p (/ beta (+ (+ alpha beta) 2.0)))) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
122.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
253.0ms	(log (- (expm1 (log1p (/ beta (+ (+ alpha beta) 2.0)))) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify1.8s

Counts

165 → 165

Iterations

Iter	Nodes
done	5000
2	1431
1	547
0	248

prune797.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.1b

regimes213.0ms

Accuracy

75.5% (3.1b remaining)

Error of 6.2b against oracle of 3.1b and baseline of 15.9b

bsearch77.0ms

Steps

Iters	Range		Point
9	2.639466206032711e+22	3.0454442621983687e+28	3.1452846425823926e+24

simplify6.0ms

Iterations

Iter	Nodes
done	32
1	32
0	29

end0.0ms

sample1.7s

Algorithm

intervals

Results

617.0ms	729×	body	640	valid
359.0ms	5834×	body	80	valid
199.0ms	830×	body	1280	valid
173.0ms	8000×	pre	80	true
54.0ms	396×	body	320	valid
20.0ms	211×	body	160	valid