Details

sample26.0ms

Algorithm

intervals

Results

6.0ms	29×	body	1280	valid
5.0ms	190×	body	80	valid
3.0ms	256×	pre	80	true
1.0ms	15×	body	640	valid
1.0ms	14×	body	320	valid
0.0ms	8×	body	160	valid

simplify1.9s

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	121	13
6	166	13
7	208	13
8	243	13
9	306	13
10	413	13
11	475	13
12	522	13
13	575	13
14	730	13
15	889	13
16	928	13
17	971	13
18	1003	13
19	1011	13
done	1011	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.1b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite130.0ms

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))
99.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series107.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
62.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify2.1s

Counts

106 → 106

Iterations

Useful iterations: 3 (419.0ms)

Iter	Nodes	Cost
0	128	1178
1	336	1110
2	1021	1056
3	4786	1048
done	5000	1048

prune219.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.8b

localize9.0ms

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))
2.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite845.0ms

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:

676.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
18.0ms	(/ alpha (+ (+ alpha beta) 2.0))
18.0ms	(/ beta (+ (+ alpha beta) 2.0))
120.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series240.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
45.0ms	(/ alpha (+ (+ alpha beta) 2.0))
48.0ms	(/ beta (+ (+ alpha beta) 2.0))
79.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify853.0ms

Counts

241 → 241

Iterations

Useful iterations: 2 (227.0ms)

Iter	Nodes	Cost
0	308	5116
1	726	4369
2	2453	3909
done	5001	3909

prune449.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.9b

localize15.0ms

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)))
2.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
8.7b	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

rewrite493.0ms

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:

18.0ms	(/ beta (+ (+ alpha beta) 2.0))
172.0ms	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
118.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
171.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

series323.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ beta (+ (+ alpha beta) 2.0))
68.0ms	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
78.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
131.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

simplify725.0ms

Counts

230 → 230

Iterations

Useful iterations: done (716.0ms)

Iter	Nodes	Cost
0	357	5840
1	751	4992
2	2187	4491
done	5000	4485

prune478.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3)
0.5b	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (cbrt (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))) 2.0)))
2.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
8.7b	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (cbrt (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))) 2.0))

rewrite852.0ms

Algorithm

rewrite-expression-head

Rules

254×	`add-sqr-sqrt`
179×	`*-un-lft-identity`
177×	`times-frac`
101×	`add-cube-cbrt`
92×	`log-prod`
66×	`difference-of-squares`
63×	`prod-diff`
48×	`cbrt-prod`
46×	`exp-sum`
36×	`distribute-lft-out`
21×	`fma-neg`
18×	`unpow-prod-down` `cube-prod`
13×	`sqr-pow`
9×	`distribute-lft-out--`
8×	`add-exp-log` `associate-/r/`
7×	`pow1`
6×	`div-inv` `add-log-exp`
5×	`add-cbrt-cube`
4×	`expm1-log1p-u` `exp-prod` `flip3-+` `flip-+` `log1p-expm1-u`
3×	`pow-unpow`
2×	`cube-div` `log-div` `flip3--` `rem-log-exp` `log-pow` `flip--`
1×	`cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `exp-diff` `diff-log` `unpow3` `div-exp` `pow-exp` `rem-exp-log` `rem-cube-cbrt`

Counts

4 → 254

Calls

4 calls:

104.0ms	(pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3)
306.0ms	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (cbrt (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))) 2.0)))
117.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
308.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (cbrt (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))) 2.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

211.0ms	(pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3)
111.0ms	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (cbrt (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))) 2.0)))
74.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
800.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (cbrt (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))) 2.0))

simplify1.1s

Counts

266 → 266

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	508	8883
1	1108	7352
2	3311	6835
done	5000	6829

prune609.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.9b

regimes110.0ms

Accuracy

73.8% (3.3b remaining)

Error of 6.3b against oracle of 3.0b and baseline of 15.5b

bsearch21.0ms

Steps

Iters	Range		Point
3	3.641538013012944e+29	5.083548469405937e+29	3.731663666537506e+29

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	67
1	43	67
done	43	67

end0.0ms

sample590.0ms

Algorithm

intervals

Results

144.0ms	5892×	body	80	valid
103.0ms	807×	body	1280	valid
91.0ms	8000×	pre	80	true
76.0ms	727×	body	640	valid
28.0ms	383×	body	320	valid
9.0ms	191×	body	160	valid