Details

sample91.0ms

Algorithm

intervals

Results

29.0ms	189×	body	80	valid
17.0ms	30×	body	1280	valid
12.0ms	256×	pre	80	true
8.0ms	17×	body	640	valid
5.0ms	15×	body	320	valid
1.0ms	5×	body	160	valid

simplify535.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.7b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.7b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite173.0ms

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:

33.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
136.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series167.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
94.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.0s

Counts

108 → 108

Iterations

Iter	Nodes
3	3320
2	1012
1	342
0	130

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 15.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
1.7b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite737.0ms

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-cbrt-cube` `add-exp-log`
6×	`associate-/l*`
4×	`expm1-log1p-u` `pow1` `diff-log` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `frac-sub`
1×	`associate--r-`

Counts

4 → 417

Calls

4 calls:

468.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
37.0ms	(/ beta (+ (+ alpha beta) 2.0))
27.0ms	(/ alpha (+ (+ alpha beta) 2.0))
183.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series331.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
59.0ms	(/ beta (+ (+ alpha beta) 2.0))
84.0ms	(/ alpha (+ (+ alpha beta) 2.0))
114.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.0s

Counts

429 → 429

Iterations

Iter	Nodes
2	2417
1	972
0	406

prune5.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.7b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (+ alpha beta) 2.0) beta)
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.2b	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
1.7b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite316.0ms

Algorithm

rewrite-expression-head

Rules

299×	`*-un-lft-identity`
208×	`times-frac`
142×	`add-sqr-sqrt`
137×	`add-cube-cbrt`
96×	`distribute-lft-out`
63×	`prod-diff`
27×	`associate-/r*`
21×	`fma-neg`
19×	`add-exp-log`
13×	`add-cbrt-cube`
11×	`associate-/r/` `div-inv` `associate-/l*`
9×	`div-exp`
6×	`flip3-+` `flip-+` `add-log-exp`
5×	`pow1` `cbrt-undiv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`clear-num` `frac-2neg`
2×	`rec-exp` `1-exp` `difference-of-squares` `associate-/l/`
1×	`sub-neg` `flip3--` `diff-log` `pow-flip` `flip--` `distribute-lft-out--` `inv-pow`

Counts

4 → 285

Calls

4 calls:

64.0ms	(/ (+ (+ alpha beta) 2.0) beta)
34.0ms	(/ alpha (+ (+ alpha beta) 2.0))
23.0ms	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
189.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series319.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (+ (+ alpha beta) 2.0) beta)
71.0ms	(/ alpha (+ (+ alpha beta) 2.0))
79.0ms	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
133.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify3.4s

Counts

297 → 297

Iterations

Iter	Nodes
3	5758
2	1961
1	776
0	329

prune3.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.7b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.2b	(/ (/ 1 (+ (+ alpha beta) 2.0)) (/ 1 beta))
1.7b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite359.0ms

Algorithm

rewrite-expression-head

Rules

772×	`times-frac`
673×	`*-un-lft-identity`
366×	`add-sqr-sqrt`
361×	`add-cube-cbrt`
186×	`distribute-lft-out`
63×	`prod-diff`
50×	`add-exp-log`
43×	`div-inv`
41×	`associate-/r/`
35×	`div-exp`
27×	`associate-/l*`
23×	`associate-/r*`
21×	`fma-neg`
20×	`flip3-+` `add-cbrt-cube` `flip-+`
10×	`cbrt-undiv`
9×	`rec-exp` `1-exp`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`clear-num` `frac-2neg`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `pow-flip` `flip--` `distribute-lft-out--` `inv-pow` `associate-/l/`

Counts

4 → 528

Calls

4 calls:

47.0ms	(/ 1 (+ (+ alpha beta) 2.0))
46.0ms	(/ alpha (+ (+ alpha beta) 2.0))
67.0ms	(/ (/ 1 (+ (+ alpha beta) 2.0)) (/ 1 beta))
172.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series326.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ 1 (+ (+ alpha beta) 2.0))
55.0ms	(/ alpha (+ (+ alpha beta) 2.0))
106.0ms	(/ (/ 1 (+ (+ alpha beta) 2.0)) (/ 1 beta))
120.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.0s

Counts

540 → 540

Iterations

Iter	Nodes
2	4140
1	1761
0	612

prune6.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.7b

regimes187.0ms

Accuracy

69.9% (3.8b remaining)

Error of 7.1b against oracle of 3.3b and baseline of 16.0b

bsearch292.0ms

Steps

Iters	Range		Point
6	1.2346170352287679e+116	7.39392051422293e+116	2.9789869640725355e+116
8	1.9106561100264417e+94	2.3669127127924407e+98	1.8715997178975197e+96
8	9.965811406389288e+16	2.9212720720479702e+20	9.40148130873499e+18

simplify10.0ms

Iterations

Iter	Nodes
2	50
1	50
0	42

end0.0ms

sample2.1s

Algorithm

intervals

Results

518.0ms	5797×	body	80	valid
451.0ms	8000×	pre	80	true
424.0ms	873×	body	1280	valid
344.0ms	717×	body	640	valid
98.0ms	380×	body	320	valid
39.0ms	233×	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