Details

sample53.0ms

Algorithm

intervals

Results

12.0ms	178×	body	80	valid
11.0ms	35×	body	1280	valid
8.0ms	31×	body	640	valid
8.0ms	256×	pre	80	true
2.0ms	10×	body	320	valid
0.0ms	2×	body	160	valid

simplify437.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.6b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.1b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite198.0ms

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:

35.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
161.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series151.0ms

Counts

2 → 6

Calls

2 calls:

74.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
77.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.1s

Counts

108 → 108

Iterations

Iter	Nodes
3	3320
2	1012
1	342
0	130

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 17.8b

localize40.0ms

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))
1.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite862.0ms

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:

527.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
49.0ms	(/ alpha (+ (+ alpha beta) 2.0))
48.0ms	(/ beta (+ (+ alpha beta) 2.0))
221.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series354.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
55.0ms	(/ alpha (+ (+ alpha beta) 2.0))
55.0ms	(/ beta (+ (+ alpha beta) 2.0))
146.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify987.0ms

Counts

429 → 429

Iterations

Iter	Nodes
2	2419
1	972
0	406

prune5.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ 1 (+ (+ alpha beta) 2.0))
0.1b	(* beta (/ 1 (+ (+ alpha beta) 2.0)))
1.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite314.0ms

Algorithm

rewrite-expression-head

Rules

209×	`*-un-lft-identity`
108×	`times-frac`
103×	`add-sqr-sqrt`
91×	`add-cube-cbrt`
69×	`distribute-lft-out`
63×	`prod-diff`
21×	`fma-neg` `associate-r`
19×	`add-exp-log`
14×	`associate-/r/`
13×	`add-cbrt-cube`
10×	`associate-/r*`
7×	`pow1` `flip3-+` `flip-+` `div-inv`
6×	`associate-/l*` `add-log-exp`
5×	`div-exp`
4×	`expm1-log1p-u` `prod-exp` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-l` `unswap-sqr`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `cbrt-unprod` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `flip--` `distribute-lft-out--` `inv-pow`

Counts

4 → 233

Calls

4 calls:

24.0ms	(/ alpha (+ (+ alpha beta) 2.0))
44.0ms	(/ 1 (+ (+ alpha beta) 2.0))
95.0ms	(* beta (/ 1 (+ (+ alpha beta) 2.0)))
146.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series254.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ alpha (+ (+ alpha beta) 2.0))
51.0ms	(/ 1 (+ (+ alpha beta) 2.0))
57.0ms	(* beta (/ 1 (+ (+ alpha beta) 2.0)))
92.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.3s

Counts

245 → 245

Iterations

Iter	Nodes
3	4724
2	1585
1	612
0	267

prune2.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.7b	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
1.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
12.2b	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite933.0ms

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:

41.0ms	(/ beta (+ (+ alpha beta) 2.0))
247.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
219.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
417.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series407.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ beta (+ (+ alpha beta) 2.0))
87.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
95.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
165.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify3.2s

Counts

203 → 203

Iterations

Iter	Nodes
3	6636
2	1819
1	672
0	303

prune2.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.2b

regimes172.0ms

Accuracy

74% (3.3b remaining)

Error of 6.4b against oracle of 3.0b and baseline of 15.9b

bsearch126.0ms

Steps

Iters	Range		Point
8	2.0198517632767668e+31	2.8356818473805023e+35	9.97332166790088e+32

simplify12.0ms

Iterations

Iter	Nodes
2	39
1	39
0	33

end0.0ms

sample2.7s

Algorithm

intervals

Results

922.0ms	852×	body	1280	valid
706.0ms	5818×	body	80	valid
376.0ms	8000×	pre	80	true
322.0ms	712×	body	640	valid
163.0ms	430×	body	320	valid
38.0ms	188×	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