Details

sample49.0ms

Algorithm

intervals

Results

11.0ms	183×	body	80	valid
9.0ms	25×	body	640	valid
7.0ms	256×	pre	80	true
7.0ms	23×	body	1280	valid
4.0ms	19×	body	320	valid
1.0ms	6×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	2002
18	2002
17	1763
16	1558
15	1364
14	1138
13	931
12	742
11	607
10	526
9	431
8	318
7	267
6	197
5	124
4	69
3	50
2	33
1	20
0	10

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.3b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.3b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
25×	`times-frac`
19×	`distribute-lft-out`
14×	`add-cube-cbrt`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
2×	`pow1` `flip3-+` `div-sub` `associate-/r/` `flip-+` `insert-posit16` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3--` `div-exp` `associate-+l-` `div-inv` `flip--`

Counts

2 → 67

Calls

2 calls:

29.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
90.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series130.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
79.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.1s

Counts

73 → 73

Iterations

Iter	Nodes
done	2000
3	2000
2	1126
1	328
0	126

prune621.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
2.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

73×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
42×	`times-frac`
26×	`add-cube-cbrt`
16×	`distribute-lft-out--`
12×	`distribute-lft-out` `difference-of-squares`
11×	`add-log-exp`
10×	`associate-/l*`
8×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
5×	`flip3--` `flip--`
4×	`pow1` `diff-log` `frac-sub` `insert-posit16` `associate-/l/`
3×	`sub-neg`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate-/r/` `div-inv` `associate--r+`
1×	`flip3-+` `div-sub` `flip-+` `associate--r-`

Counts

4 → 126

Calls

4 calls:

895.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
35.0ms	(/ alpha (+ (+ alpha beta) 2.0))
358.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
157.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series378.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
61.0ms	(/ alpha (+ (+ alpha beta) 2.0))
76.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
124.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.5s

Counts

138 → 138

Iterations

Iter	Nodes
done	2001
3	2001
2	1961
1	567
0	229

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.9b

localize95.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
0.1b	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
0.1b	(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* 2.0 (* (+ (+ alpha beta) 2.0) (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))))
2.3b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite923.0ms

Algorithm

rewrite-expression-head

Rules

245×	`*-un-lft-identity`
141×	`times-frac`
137×	`associate-*r/`
131×	`add-sqr-sqrt`
90×	`distribute-lft-out`
83×	`flip3-+` `flip-+`
73×	`add-cube-cbrt`
71×	`frac-times`
66×	`frac-add` `associate-/l/`
64×	`frac-sub`
41×	`associate-*l/`
39×	`unpow-prod-down` `cube-prod` `swap-sqr`
38×	`associate-/r/`
28×	`add-cbrt-cube` `add-exp-log`
26×	`flip3--` `flip--`
24×	`difference-of-squares`
21×	`associate-r` `associate-l`
12×	`pow1`
11×	`sqr-pow`
8×	`cbrt-undiv` `div-exp`
7×	`prod-exp` `cbrt-unprod` `div-inv`
6×	`add-log-exp`
5×	`distribute-lft-out--`
4×	`insert-posit16` `unswap-sqr`
3×	`pow-unpow` `associate-/l*`
2×	`pow-exp` `rem-cube-cbrt`
1×	`cube-div` `pow2` `cube-mult` `pow-to-exp` `difference-cubes` `clear-num` `associate-/r` `sub-neg` `pow-pow` `frac-2neg` `pow-plus` `diff-log` `unpow3` `div-sub` `pow-prod-down` `pow-sqr` `-commutative` `pow-prod-up`

Counts

4 → 333

Calls

4 calls:

118.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
42.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
375.0ms	(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* 2.0 (* (+ (+ alpha beta) 2.0) (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))))
379.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series1.3s

Counts

4 → 12

Calls

4 calls:

469.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
102.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
605.0ms	(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* 2.0 (* (+ (+ alpha beta) 2.0) (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))))
149.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify1.8s

Counts

345 → 345

Iterations

Iter	Nodes
done	2000
1	2000
0	554

prune6.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 2.8b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.6b	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
2.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
12.6b	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
14×	`log-prod`
11×	`add-log-exp`
10×	`distribute-lft-out--`
8×	`log-div` `difference-of-squares`
7×	`flip3--` `exp-sum` `add-cube-cbrt` `flip--`
6×	`pow1` `frac-sub`
5×	`add-exp-log`
4×	`exp-prod` `times-frac` `add-cbrt-cube` `exp-diff` `diff-log` `insert-posit16`
3×	`sub-neg`
2×	`log-pow` `associate--r+`
1×	`rem-log-exp` `associate--r-` `rem-exp-log`

Counts

4 → 84

Calls

4 calls:

343.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
236.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
142.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
303.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series465.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
63.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
118.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
176.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify1.1s

Counts

96 → 96

Iterations

Iter	Nodes
done	2001
3	2001
2	1127
1	366
0	169

prune1.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 2.8b

regimes139.0ms

Accuracy

72.8% (3.5b remaining)

Error of 6.4b against oracle of 2.9b and baseline of 15.8b

bsearch43.0ms

Steps

Iters	Range		Point
6	2.0302490555836575e+26	1.0361079584824738e+27	2.1159100932126255e+26

simplify5.0ms

Iterations

Iter	Nodes
done	30
1	30
0	27

end0.0ms

sample2.1s

Algorithm

intervals

Results

589.0ms	5837×	body	80	valid
430.0ms	873×	body	1280	valid
372.0ms	8000×	pre	80	true
335.0ms	679×	body	640	valid
110.0ms	384×	body	320	valid
72.0ms	227×	body	160	valid