Details

sample95.0ms

Algorithm

intervals

Results

37.0ms	190×	body	80	valid
17.0ms	30×	body	1280	valid
12.0ms	256×	pre	80	true
11.0ms	25×	body	640	valid
2.0ms	7×	body	320	valid
1.0ms	4×	body	160	valid

simplify457.0ms

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize33.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.4b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite233.0ms

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:

52.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
177.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series169.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
111.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.2s

Counts

108 → 108

Iterations

Iter	Nodes
3	3331
2	1010
1	340
0	130

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.0b

localize36.0ms

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))
1.4b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite746.0ms

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:

481.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
44.0ms	(/ beta (+ (+ alpha beta) 2.0))
31.0ms	(/ alpha (+ (+ alpha beta) 2.0))
170.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series354.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
70.0ms	(/ beta (+ (+ alpha beta) 2.0))
73.0ms	(/ alpha (+ (+ alpha beta) 2.0))
115.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.4s

Counts

429 → 429

Iterations

Iter	Nodes
2	2435
1	967
0	406

prune5.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.2b

localize44.0ms

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))
1.4b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite229.0ms

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:

13.0ms	(cbrt (+ (+ alpha beta) 2.0))
18.0ms	(cbrt (+ (+ alpha beta) 2.0))
10.0ms	(cbrt (+ (+ alpha beta) 2.0))
185.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series575.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(cbrt (+ (+ alpha beta) 2.0))
160.0ms	(cbrt (+ (+ alpha beta) 2.0))
148.0ms	(cbrt (+ (+ alpha beta) 2.0))
112.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.8s

Counts

168 → 168

Iterations

Iter	Nodes
3	3282
2	1098
1	459
0	206

prune2.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.2b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.5b	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
1.4b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
12.1b	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite913.0ms

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×	`exp-sum` `add-exp-log` `distribute-lft-out--`
6×	`pow1` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
5×	`associate-/r*` `flip3-+` `flip3--` `flip-+` `div-inv` `flip--`
4×	`expm1-log1p-u` `exp-prod` `exp-diff` `frac-sub` `insert-posit16` `log1p-expm1-u`
3×	`associate-/l*`
2×	`log-pow`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `rem-exp-log`

Counts

4 → 191

Calls

4 calls:

40.0ms	(/ alpha (+ (+ alpha beta) 2.0))
344.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
174.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
349.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series541.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ alpha (+ (+ alpha beta) 2.0))
110.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
119.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
227.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify3.6s

Counts

203 → 203

Iterations

Iter	Nodes
3	6558
2	1756
1	634
0	283

prune2.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 2.1b

regimes131.0ms

Accuracy

75.4% (3.3b remaining)

Error of 6.0b against oracle of 2.8b and baseline of 16.0b

bsearch71.0ms

Steps

Iters	Range		Point
6	6.516820230851603e+16	5.585234624323947e+17	7.41319761099139e+16

simplify7.0ms

Iterations

Iter	Nodes
2	37
1	37
0	35

end0.0ms

sample2.4s

Algorithm

intervals

Results

895.0ms	891×	body	1280	valid
609.0ms	5816×	body	80	valid
311.0ms	8000×	pre	80	true
235.0ms	703×	body	640	valid
155.0ms	399×	body	320	valid
31.0ms	191×	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