Details

sample360.0ms

Algorithm

intervals

Results

184.0ms	202×	body	80	valid
22.0ms	256×	pre	80	true
9.0ms	22×	body	1280	valid
4.0ms	13×	body	640	valid
3.0ms	14×	body	320	valid
1.0ms	5×	body	160	valid

simplify22.2s

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.6b

localize29.0ms

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)

rewrite537.0ms

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:

100.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
427.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series294.0ms

Counts

2 → 6

Calls

2 calls:

129.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
163.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify2.2s

Counts

106 → 106

Iterations

Iter	Nodes
done	5012
2	1163
1	341
0	128

prune1.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 12.1b

localize38.0ms

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)

rewrite3.7s

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:

2.9s	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
74.0ms	(/ alpha (+ (+ alpha beta) 2.0))
72.0ms	(/ beta (+ (+ alpha beta) 2.0))
664.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series814.0ms

Counts

4 → 12

Calls

4 calls:

307.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
124.0ms	(/ alpha (+ (+ alpha beta) 2.0))
113.0ms	(/ beta (+ (+ alpha beta) 2.0))
251.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify6.4s

Counts

241 → 241

Iterations

Iter	Nodes
done	5006
2	2279
1	741
0	308

prune4.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.9b

localize85.0ms

Local error

Found 4 expressions with local error:

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

rewrite2.4s

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:

70.0ms	(/ beta (+ (+ beta alpha) 2.0))
684.0ms	(exp (log (/ (- (/ beta (+ (+ beta alpha) 2.0)) (- (/ alpha (+ (+ beta alpha) 2.0)) 1.0)) 2.0)))
604.0ms	(- (/ alpha (+ (+ beta alpha) 2.0)) 1.0)
980.0ms	(log (/ (- (/ beta (+ (+ beta alpha) 2.0)) (- (/ alpha (+ (+ beta alpha) 2.0)) 1.0)) 2.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ beta (+ (+ beta alpha) 2.0))
176.0ms	(exp (log (/ (- (/ beta (+ (+ beta alpha) 2.0)) (- (/ alpha (+ (+ beta alpha) 2.0)) 1.0)) 2.0)))
499.0ms	(- (/ alpha (+ (+ beta alpha) 2.0)) 1.0)
447.0ms	(log (/ (- (/ beta (+ (+ beta alpha) 2.0)) (- (/ alpha (+ (+ beta alpha) 2.0)) 1.0)) 2.0))

simplify3.9s

Counts

230 → 230

Iterations

Iter	Nodes
done	5001
2	1889
1	769
0	357

prune2.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.9b

localize120.0ms

Local error

Found 4 expressions with local error:

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

rewrite2.0s

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:

72.0ms	(/ beta (+ (+ beta alpha) 2.0))
714.0ms	(pow E (log (/ (- (/ beta (+ (+ beta alpha) 2.0)) (- (/ alpha (+ (+ beta alpha) 2.0)) 1.0)) 2.0)))
444.0ms	(- (/ alpha (+ (+ beta alpha) 2.0)) 1.0)
677.0ms	(log (/ (- (/ beta (+ (+ beta alpha) 2.0)) (- (/ alpha (+ (+ beta alpha) 2.0)) 1.0)) 2.0))

series842.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ beta (+ (+ beta alpha) 2.0))
296.0ms	(pow E (log (/ (- (/ beta (+ (+ beta alpha) 2.0)) (- (/ alpha (+ (+ beta alpha) 2.0)) 1.0)) 2.0)))
144.0ms	(- (/ alpha (+ (+ beta alpha) 2.0)) 1.0)
300.0ms	(log (/ (- (/ beta (+ (+ beta alpha) 2.0)) (- (/ alpha (+ (+ beta alpha) 2.0)) 1.0)) 2.0))

simplify5.7s

Counts

237 → 237

Iterations

Iter	Nodes
done	5013
2	2377
1	923
0	371

prune1.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.9b

regimes320.0ms

Accuracy

55.5% (5.9b remaining)

Error of 8.9b against oracle of 3.0b and baseline of 16.3b

bsearch358.0ms

Steps

Iters	Range		Point
7	3.9227933197023594e+166	7.439987087167839e+167	5.5368067149460316e+166
5	7.445604319051971e+112	1.5393751381298674e+113	1.5264500717710571e+113
8	4.6091985256205887e+33	6.133200959176609e+37	7.863989155318433e+36

simplify30.0ms

Iterations

Iter	Nodes
done	56
2	56
1	54
0	45

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.0s	874×	body	1280	valid
932.0ms	5842×	body	80	valid
740.0ms	381×	body	320	valid
447.0ms	719×	body	640	valid
331.0ms	8000×	pre	80	true
99.0ms	184×	body	160	valid