Details

sample69.0ms

Algorithm

intervals

Results

23.0ms	182×	body	80	valid
9.0ms	256×	pre	80	true
9.0ms	26×	body	1280	valid
7.0ms	26×	body	640	valid
3.0ms	14×	body	320	valid
1.0ms	8×	body	160	valid

simplify4.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
25	4885
24	4583
23	4303
22	3954
21	3572
20	3229
19	2829
18	2315
17	1985
16	1722
15	1474
14	1236
13	995
12	795
11	669
10	582
9	467
8	348
7	290
6	209
5	124
4	69
3	50
2	33
1	20
0	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.5b

localize20.0ms

Local error

Found 2 expressions with local error:

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

rewrite199.0ms

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:

46.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
149.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series155.0ms

Counts

2 → 6

Calls

2 calls:

60.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
95.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.1s

Counts

108 → 108

Iterations

Iter	Nodes
done	5004
2	1170
1	342
0	130

prune378.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.7b

localize22.0ms

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

rewrite625.0ms

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:

369.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
36.0ms	(/ alpha (+ (+ alpha beta) 2.0))
28.0ms	(/ beta (+ (+ alpha beta) 2.0))
182.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series302.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
62.0ms	(/ alpha (+ (+ alpha beta) 2.0))
55.0ms	(/ beta (+ (+ alpha beta) 2.0))
97.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.6s

Counts

429 → 429

Iterations

Iter	Nodes
done	5003
2	2686
1	995
0	406

prune2.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.1b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite597.0ms

Algorithm

rewrite-expression-head

Rules

280×	`*-un-lft-identity`
141×	`add-sqr-sqrt`
137×	`times-frac`
131×	`add-cube-cbrt`
126×	`prod-diff`
87×	`distribute-lft-out`
68×	`log-prod`
65×	`exp-sum`
21×	`fma-neg`
18×	`associate-/r/`
10×	`associate-/r*`
9×	`flip3-+` `flip-+` `div-inv`
8×	`add-cbrt-cube` `add-exp-log`
7×	`log-pow`
6×	`exp-prod` `associate-/l*` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
2×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `div-exp` `distribute-lft-out--`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 269

Calls

4 calls:

22.0ms	(/ alpha (+ (+ alpha beta) 2.0))
44.0ms	(/ beta (+ (+ alpha beta) 2.0))
191.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
333.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series399.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ alpha (+ (+ alpha beta) 2.0))
87.0ms	(/ beta (+ (+ alpha beta) 2.0))
137.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
114.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify1.6s

Counts

281 → 281

Iterations

Iter	Nodes
done	5001
2	1748
1	664
0	352

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.1b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite720.0ms

Algorithm

rewrite-expression-head

Rules

276×	`*-un-lft-identity`
148×	`add-sqr-sqrt`
139×	`times-frac`
131×	`add-cube-cbrt`
126×	`prod-diff`
84×	`distribute-lft-out`
68×	`log-prod`
65×	`exp-sum`
21×	`fma-neg` `associate-r`
18×	`associate-/r/`
17×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`flip3-+` `flip-+` `div-inv`
8×	`pow1`
7×	`log-pow`
6×	`exp-prod` `add-log-exp`
5×	`associate-/r*`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `sub-neg` `1-exp` `cbrt-unprod` `distribute-lft-out--`
1×	`log-div` `clear-num` `frac-2neg` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `flip--` `inv-pow`

Counts

4 → 280

Calls

4 calls:

49.0ms	(/ 1 (+ (+ alpha beta) 2.0))
97.0ms	(* beta (/ 1 (+ (+ alpha beta) 2.0)))
196.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
366.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series350.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ 1 (+ (+ alpha beta) 2.0))
66.0ms	(* beta (/ 1 (+ (+ alpha beta) 2.0)))
93.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
143.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify1.6s

Counts

292 → 292

Iterations

Iter	Nodes
done	5010
2	1959
1	748
0	376

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.1b

regimes124.0ms

Accuracy

75.9% (3.0b remaining)

Error of 6.0b against oracle of 3.0b and baseline of 15.4b

bsearch94.0ms

Steps

Iters	Range		Point
8	28342861701.492744	542402004696104.94	11629067263522.379

simplify6.0ms

Iterations

Iter	Nodes
done	36
1	36
0	31

end0.0ms

sample1.9s

Algorithm

intervals

Results

713.0ms	817×	body	1280	valid
507.0ms	5886×	body	80	valid
247.0ms	8000×	pre	80	true
163.0ms	732×	body	640	valid
64.0ms	373×	body	320	valid
21.0ms	192×	body	160	valid