Details

sample24.0ms

Algorithm

intervals

Results

4.0ms	178×	body	80	valid
4.0ms	34×	body	1280	valid
3.0ms	256×	pre	80	true
2.0ms	19×	body	640	valid
1.0ms	15×	body	320	valid
1.0ms	10×	body	160	valid

simplify1.1s

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	119	13
6	155	13
7	194	13
8	229	13
9	280	13
10	319	13
11	352	13
12	399	13
13	450	13
14	520	13
15	582	13
16	623	13
17	666	13
18	698	13
19	706	13
done	706	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.6b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite137.0ms

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:

25.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
106.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series105.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
61.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.7s

Counts

106 → 106

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	128	1178
1	334	1110
2	931	1056
3	3995	1048
done	5001	1047

prune208.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 17.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
2.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite515.0ms

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:

19.0ms	(/ alpha (+ (+ alpha beta) 2.0))
319.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
19.0ms	(/ beta (+ (+ alpha beta) 2.0))
126.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series226.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ alpha (+ (+ alpha beta) 2.0))
56.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
47.0ms	(/ beta (+ (+ alpha beta) 2.0))
78.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify931.0ms

Counts

425 → 425

Iterations

Useful iterations: done (913.0ms)

Iter	Nodes	Cost
0	402	16706
1	936	13361
2	2688	11298
done	5001	11286

prune764.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
2.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
2.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite283.0ms

Algorithm

rewrite-expression-head

Rules

254×	`*-un-lft-identity`
130×	`add-sqr-sqrt`
126×	`prod-diff`
122×	`times-frac`
120×	`add-cube-cbrt`
78×	`distribute-lft-out`
42×	`fma-neg`
16×	`associate-/r/`
10×	`cbrt-prod` `flip3-+` `flip-+`
8×	`div-inv` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `log1p-expm1-u` `difference-of-squares`
2×	`sub-neg` `flip3--` `pow1/3` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 236

Calls

4 calls:

11.0ms	(cbrt (+ (+ alpha beta) 2.0))
9.0ms	(cbrt (+ (+ alpha beta) 2.0))
123.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
125.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series343.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(cbrt (+ (+ alpha beta) 2.0))
93.0ms	(cbrt (+ (+ alpha beta) 2.0))
73.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
78.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify813.0ms

Counts

248 → 248

Iterations

Useful iterations: done (803.0ms)

Iter	Nodes	Cost
0	204	5724
1	445	4422
2	1196	3728
done	5000	3292

prune565.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.6b	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
2.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
10.6b	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite580.0ms

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

Counts

4 → 187

Calls

4 calls:

19.0ms	(/ beta (+ (+ alpha beta) 2.0))
181.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
125.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
244.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series513.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ beta (+ (+ alpha beta) 2.0))
59.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
278.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
128.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify723.0ms

Counts

199 → 199

Iterations

Useful iterations: done (715.0ms)

Iter	Nodes	Cost
0	299	4746
1	648	3934
2	1908	3472
done	5000	3466

prune382.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.6b

regimes128.0ms

Accuracy

78.1% (2.8b remaining)

Error of 6.0b against oracle of 3.3b and baseline of 15.9b

bsearch32.0ms

Steps

Iters	Range		Point
5	391248603.19673574	1027443772.3458656	1015227874.2528594

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	98
1	39	98
done	39	98

end0.0ms

sample598.0ms

Algorithm

intervals

Results

154.0ms	5870×	body	80	valid
99.0ms	828×	body	1280	valid
96.0ms	8000×	pre	80	true
68.0ms	692×	body	640	valid
29.0ms	409×	body	320	valid
10.0ms	201×	body	160	valid