Details

sample24.0ms

Algorithm

intervals

Results

5.0ms	192×	body	80	valid
4.0ms	30×	body	1280	valid
4.0ms	256×	pre	80	true
2.0ms	23×	body	640	valid
0.0ms	5×	body	320	valid
0.0ms	6×	body	160	valid

simplify337.0ms

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	201	13
8	234	13
9	285	13
10	325	13
11	335	13
12	347	13
13	359	13
done	359	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.9b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite131.0ms

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)

series112.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
60.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.2s

Counts

106 → 106

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	128	1178
1	334	1110
2	875	1056
3	2687	1048
done	5001	1047

prune218.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.6b

localize9.0ms

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))
1.9b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite493.0ms

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:

307.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
18.0ms	(/ alpha (+ (+ alpha beta) 2.0))
18.0ms	(/ beta (+ (+ alpha beta) 2.0))
120.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series427.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
237.0ms	(/ alpha (+ (+ alpha beta) 2.0))
45.0ms	(/ beta (+ (+ alpha beta) 2.0))
83.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.0s

Counts

425 → 425

Iterations

Useful iterations: done (990.0ms)

Iter	Nodes	Cost
0	402	16706
1	966	13361
2	2508	11385
done	5000	11298

prune772.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
1.9b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
1.9b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite267.0ms

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:

8.0ms	(cbrt (+ (+ alpha beta) 2.0))
8.0ms	(cbrt (+ (+ alpha beta) 2.0))
117.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
118.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series356.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(cbrt (+ (+ alpha beta) 2.0))
100.0ms	(cbrt (+ (+ alpha beta) 2.0))
79.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
78.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.6s

Counts

248 → 248

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	204	5724
1	460	4422
2	1081	3854
3	3189	3292
done	5000	3058

prune573.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.4b	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
1.9b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
10.7b	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite551.0ms

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:

18.0ms	(/ beta (+ (+ alpha beta) 2.0))
173.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
119.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
232.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series326.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ beta (+ (+ alpha beta) 2.0))
66.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
81.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
128.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify699.0ms

Counts

199 → 199

Iterations

Useful iterations: done (692.0ms)

Iter	Nodes	Cost
0	299	4746
1	663	3934
2	1703	3535
done	5001	3417

prune422.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.1b

regimes104.0ms

Accuracy

76.3% (3.1b remaining)

Error of 6.2b against oracle of 3.1b and baseline of 16.1b

bsearch31.0ms

Steps

Iters	Range		Point
5	6.313757509671862e+29	2.4877244354034998e+30	6.48438097382689e+29

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	52
1	34	52
done	34	52

end0.0ms

sample617.0ms

Algorithm

intervals

Results

146.0ms	5812×	body	80	valid
106.0ms	807×	body	1280	valid
105.0ms	8000×	pre	80	true
76.0ms	765×	body	640	valid
33.0ms	395×	body	320	valid
11.0ms	221×	body	160	valid