Details

sample25.0ms

Algorithm

intervals

Results

5.0ms	192×	body	80	valid
4.0ms	32×	body	1280	valid
3.0ms	256×	pre	80	true
2.0ms	17×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	7×	body	160	valid

simplify80.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	6
1	34	6
2	52	6
3	73	6
4	123	6
5	184	6
6	250	6
7	287	6
8	349	6
9	437	6
10	574	6
11	654	6
12	712	6
13	785	6
14	1075	6
15	1150	6
16	1193	6
17	1213	6
18	1221	6
19	1221	6
done	1221	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.5b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite223.0ms

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-exp-log` `associate-/r/` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow1` `expm1-log1p-u` `div-sub` `log1p-expm1-u` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `flip3--` `frac-2neg` `div-exp` `clear-num` `sum-log` `flip--`

Counts

2 → 100

Calls

2 calls:

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

series112.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
62.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify38.0ms

Counts

106 → 106

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	335	555
1	1087	529
2	5002	525
done	5002	525

prune215.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.1b

localize9.0ms

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))
2.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite817.0ms

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

Counts

4 → 413

Calls

4 calls:

517.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
34.0ms	(/ alpha (+ (+ alpha beta) 2.0))
33.0ms	(/ beta (+ (+ alpha beta) 2.0))
206.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series238.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
49.0ms	(/ alpha (+ (+ alpha beta) 2.0))
46.0ms	(/ beta (+ (+ alpha beta) 2.0))
80.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify128.0ms

Counts

425 → 425

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	977	8429
1	3143	6259
2	5002	6131
done	5002	6131

prune780.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.1b	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
2.5b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite608.0ms

Algorithm

rewrite-expression-head

Rules

874×	`*-un-lft-identity`
576×	`prod-diff`
470×	`add-sqr-sqrt`
456×	`unpow-prod-down` `cube-prod`
443×	`times-frac`
424×	`add-cube-cbrt`
264×	`distribute-lft-out`
72×	`sqr-pow`
62×	`cube-mult` `unpow3`
58×	`associate-/r/`
48×	`fma-neg`
29×	`flip3-+` `flip-+` `div-inv`
24×	`difference-of-squares`
9×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1` `associate-/r*` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `pow-exp` `rem-cube-cbrt`
1×	`difference-cubes` `cube-div` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `frac-2neg` `diff-log` `clear-num` `flip--` `fma-udef`

Counts

4 → 781

Calls

4 calls:

0.0ms	(fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
33.0ms	(/ beta (+ (+ alpha beta) 2.0))
38.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
471.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series295.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
52.0ms	(/ beta (+ (+ alpha beta) 2.0))
70.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
121.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify246.0ms

Counts

793 → 793

Iterations

Useful iterations: 2 (125.0ms)

Iter	Nodes	Cost
0	1164	12586
1	4058	8872
2	5001	8727
done	5001	8727

prune665.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
0.1b	(pow (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) 3)
0.1b	(pow (/ alpha (+ (+ alpha beta) 2.0)) 6)
2.5b	(- (pow (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) 3) (pow (pow 1.0 3) 3))

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

4978×	`unpow-prod-down`
4957×	`cube-prod`
4002×	`*-un-lft-identity`
3060×	`prod-diff`
2243×	`add-sqr-sqrt`
2005×	`times-frac`
1995×	`add-cube-cbrt`
1179×	`distribute-lft-out`
476×	`sqr-pow`
403×	`cube-mult` `unpow3`
262×	`associate-/r/`
140×	`difference-of-squares`
131×	`flip3-+` `flip-+` `div-inv`
102×	`fma-neg`
21×	`distribute-lft-out--`
14×	`add-exp-log`
10×	`pow-exp`
9×	`pow-unpow`
8×	`add-cbrt-cube`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `pow-to-exp` `log1p-expm1-u`
3×	`cube-div` `pow-pow` `div-exp` `rem-cube-cbrt`
1×	`difference-cubes` `cbrt-undiv` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 3559

Calls

4 calls:

37.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
76.0ms	(pow (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) 3)
38.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 6)
1.1s	(- (pow (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) 3) (pow (pow 1.0 3) 3))

series431.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
133.0ms	(pow (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) 3)
99.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 6)
122.0ms	(- (pow (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) 3) (pow (pow 1.0 3) 3))

simplify849.0ms

Counts

3571 → 3571

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	2022	82464
1	5002	61259
done	5002	61259

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.4b

regimes170.0ms

Accuracy

97.5% (0.3b remaining)

Error of 3.4b against oracle of 3.1b and baseline of 15.2b

bsearch2.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	29
1	39	29
done	39	29

end0.0ms

sample615.0ms

Algorithm

intervals

Results

141.0ms	5909×	body	80	valid
94.0ms	8000×	pre	80	true
89.0ms	775×	body	1280	valid
67.0ms	713×	body	640	valid
27.0ms	399×	body	320	valid
10.0ms	204×	body	160	valid