Details

sample91.0ms

Algorithm

intervals

Results

34.0ms	183×	body	80	valid
12.0ms	23×	body	1280	valid
11.0ms	256×	pre	80	true
10.0ms	25×	body	640	valid
6.0ms	19×	body	320	valid
1.0ms	6×	body	160	valid

simplify475.0ms

Counts

1 → 1

Iterations

Iter	Nodes
15	445
14	445
13	442
12	437
11	416
10	364
9	276
8	211
7	186
6	152
5	112
4	69
3	50
2	33
1	20
0	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.3b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.3b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite239.0ms

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` `insert-posit16` `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 → 102

Calls

2 calls:

60.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
176.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series138.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
83.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.2s

Counts

108 → 108

Iterations

Iter	Nodes
3	3331
2	1010
1	340
0	130

prune416.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.5b

localize36.0ms

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)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
2.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

514×	`*-un-lft-identity`
350×	`add-sqr-sqrt`
273×	`times-frac`
252×	`prod-diff`
215×	`add-cube-cbrt`
138×	`distribute-lft-out`
65×	`associate--r+`
54×	`difference-of-squares`
42×	`fma-neg`
37×	`distribute-lft-out--`
30×	`associate-/r/`
16×	`div-inv`
15×	`flip3-+` `flip-+`
11×	`add-log-exp`
10×	`associate-/l*`
8×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `pow1` `diff-log` `frac-sub` `insert-posit16` `log1p-expm1-u` `associate-/l/`
3×	`sub-neg`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp`
1×	`div-sub` `associate--r-`

Counts

4 → 428

Calls

4 calls:

963.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
47.0ms	(/ alpha (+ (+ alpha beta) 2.0))
490.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
165.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series382.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
73.0ms	(/ alpha (+ (+ alpha beta) 2.0))
75.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
125.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.3s

Counts

440 → 440

Iterations

Iter	Nodes
2	2886
1	1102
0	456

prune1.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.9b

localize35.0ms

Local error

Found 4 expressions with local error:

2.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
7.8b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.8b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.8b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite275.0ms

Algorithm

rewrite-expression-head

Rules

195×	`*-un-lft-identity`
106×	`times-frac`
93×	`add-sqr-sqrt`
88×	`add-cube-cbrt`
63×	`cbrt-prod` `prod-diff` `distribute-lft-out`
21×	`fma-neg`
14×	`associate-/r/`
7×	`flip3-+` `flip-+` `div-inv`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-div` `pow1/3`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 201

Calls

4 calls:

222.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
11.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
11.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
23.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series743.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
185.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
192.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
235.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify1.9s

Counts

213 → 213

Iterations

Iter	Nodes
3	3616
2	1201
1	510
0	243

prune962.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.9b

localize60.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
2.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite290.0ms

Algorithm

rewrite-expression-head

Rules

141×	`*-un-lft-identity`
69×	`add-sqr-sqrt`
64×	`add-cube-cbrt`
63×	`prod-diff`
61×	`times-frac`
45×	`distribute-lft-out`
21×	`fma-neg`
15×	`cbrt-prod`
8×	`associate-/r/`
7×	`flip3-+` `flip-+`
6×	`cbrt-div` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`pow1/3`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 156

Calls

4 calls:

22.0ms	(cbrt (+ (+ alpha beta) 2.0))
21.0ms	(cbrt (+ (+ alpha beta) 2.0))
21.0ms	(cbrt (+ (+ alpha beta) 2.0))
219.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series528.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(cbrt (+ (+ alpha beta) 2.0))
147.0ms	(cbrt (+ (+ alpha beta) 2.0))
139.0ms	(cbrt (+ (+ alpha beta) 2.0))
121.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.7s

Counts

168 → 168

Iterations

Iter	Nodes
3	3282
2	1098
1	459
0	206

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.9b

regimes178.0ms

Accuracy

73.1% (3.4b remaining)

Error of 6.4b against oracle of 3.0b and baseline of 15.7b

bsearch88.0ms

Steps

Iters	Range		Point
6	2.0302490555836575e+26	1.0361079584824738e+27	2.1159100932126255e+26

simplify20.0ms

Iterations

Iter	Nodes
2	37
1	37
0	35

end0.0ms

sample2.1s

Algorithm

intervals

Results

705.0ms	5837×	body	80	valid
481.0ms	873×	body	1280	valid
325.0ms	8000×	pre	80	true
242.0ms	679×	body	640	valid
135.0ms	384×	body	320	valid
40.0ms	227×	body	160	valid

Iter	Nodes
15	445
14	445
13	442
12	437
11	416
10	364
9	276
8	211
7	186
6	152
5	112
4	69
3	50
2	33
1	20
0	10

Iter	Nodes
15	445
14	445
13	442
12	437
11	416
10	364
9	276
8	211
7	186
6	152
5	112
4	69
3	50
2	33
1	20
0	10

Iter	Nodes
15	445
14	445
13	442
12	437
11	416
10	364
9	276
8	211
7	186
6	152
5	112
4	69
3	50
2	33
1	20
0	10