Details

sample37.0ms

Algorithm

intervals

Results

7.0ms	200×	body	80	valid
6.0ms	6×	body	320	valid
4.0ms	256×	pre	80	true
3.0ms	22×	body	1280	valid
3.0ms	22×	body	640	valid
0.0ms	6×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
9	4613
8	1507
7	644
6	306
5	164
4	74
3	53
2	34
1	20
0	10

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize23.0ms

Local error

Found 2 expressions with local error:

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

rewrite216.0ms

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-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3--` `div-exp` `associate-+l-` `div-inv` `flip--`

Counts

2 → 65

Calls

2 calls:

66.0ms	(/ (- beta alpha) (+ (+ alpha 2.0) beta))
148.0ms	(+ (/ (- beta alpha) (+ (+ alpha 2.0) beta)) 1.0)

series127.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ (- beta alpha) (+ (+ alpha 2.0) beta))
77.0ms	(+ (/ (- beta alpha) (+ (+ alpha 2.0) beta)) 1.0)

simplify640.0ms

Counts

71 → 71

Iterations

Iter	Nodes
done	5002
2	1315
1	326
0	123

prune381.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ beta (+ (+ alpha 2.0) beta)) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0))
0.0b	(/ alpha (+ beta (+ alpha 2.0)))
0.0b	(/ beta (+ (+ alpha 2.0) beta))
1.5b	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

rewrite749.0ms

Algorithm

rewrite-expression-head

Rules

71×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
32×	`times-frac`
24×	`add-cube-cbrt` `distribute-lft-out`
11×	`add-log-exp`
10×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/l*`
4×	`pow1` `diff-log` `associate-/r/` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `frac-sub` `flip-+` `div-inv` `associate--r+`
1×	`associate--r-`

Counts

4 → 111

Calls

4 calls:

433.0ms	(- (/ beta (+ (+ alpha 2.0) beta)) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0))
34.0ms	(/ alpha (+ beta (+ alpha 2.0)))
54.0ms	(/ beta (+ (+ alpha 2.0) beta))
222.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

series364.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(- (/ beta (+ (+ alpha 2.0) beta)) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0))
73.0ms	(/ alpha (+ beta (+ alpha 2.0)))
61.0ms	(/ beta (+ (+ alpha 2.0) beta))
127.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

simplify965.0ms

Counts

123 → 123

Iterations

Iter	Nodes
done	5000
2	2210
1	501
0	205

prune690.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.6b

localize64.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ beta (+ alpha 2.0)))
0.6b	(exp (log (- (/ beta (+ beta (+ alpha 2.0))) (- (/ alpha (+ (+ alpha 2.0) beta)) 1.0))))
1.5b	(- (/ alpha (+ (+ alpha 2.0) beta)) 1.0)
10.3b	(log (- (/ beta (+ beta (+ alpha 2.0))) (- (/ alpha (+ (+ alpha 2.0) beta)) 1.0)))

rewrite953.0ms

Algorithm

rewrite-expression-head

Rules

49×	`*-un-lft-identity`
32×	`add-sqr-sqrt`
18×	`times-frac`
17×	`add-cube-cbrt`
14×	`log-prod`
12×	`distribute-lft-out`
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--` `flip--`
4×	`exp-prod` `exp-diff` `frac-sub`
3×	`associate-/l*`
2×	`associate-/r/` `log-pow`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `rem-log-exp` `flip-+` `div-inv` `rem-exp-log`

Counts

4 → 95

Calls

4 calls:

31.0ms	(/ beta (+ beta (+ alpha 2.0)))
384.0ms	(exp (log (- (/ beta (+ beta (+ alpha 2.0))) (- (/ alpha (+ (+ alpha 2.0) beta)) 1.0))))
214.0ms	(- (/ alpha (+ (+ alpha 2.0) beta)) 1.0)
320.0ms	(log (- (/ beta (+ beta (+ alpha 2.0))) (- (/ alpha (+ (+ alpha 2.0) beta)) 1.0)))

series446.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(/ beta (+ beta (+ alpha 2.0)))
84.0ms	(exp (log (- (/ beta (+ beta (+ alpha 2.0))) (- (/ alpha (+ (+ alpha 2.0) beta)) 1.0))))
112.0ms	(- (/ alpha (+ (+ alpha 2.0) beta)) 1.0)
175.0ms	(log (- (/ beta (+ beta (+ alpha 2.0))) (- (/ alpha (+ (+ alpha 2.0) beta)) 1.0)))

simplify927.0ms

Counts

107 → 107

Iterations

Iter	Nodes
done	5002
2	1941
1	481
0	212

prune698.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.6b

localize66.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (+ alpha (+ 2.0 beta)) beta))
0.6b	(exp (log (- (/ 1 (/ (+ alpha (+ 2.0 beta)) beta)) (- (/ alpha (+ (+ alpha 2.0) beta)) 1.0))))
1.5b	(- (/ alpha (+ (+ alpha 2.0) beta)) 1.0)
10.3b	(log (- (/ 1 (/ (+ alpha (+ 2.0 beta)) beta)) (- (/ alpha (+ (+ alpha 2.0) beta)) 1.0)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

145×	`*-un-lft-identity`
130×	`times-frac`
96×	`add-sqr-sqrt`
63×	`add-cube-cbrt`
36×	`distribute-lft-out`
24×	`log-prod`
19×	`associate-/r*`
16×	`add-exp-log`
13×	`distribute-lft-out--`
12×	`exp-sum` `difference-of-squares`
9×	`add-cbrt-cube` `div-inv`
8×	`log-div`
7×	`pow1` `div-exp`
6×	`add-log-exp`
5×	`flip3--` `flip--`
4×	`exp-prod` `exp-diff` `frac-sub`
3×	`cbrt-undiv` `associate-/l*`
2×	`rec-exp` `1-exp` `log-pow`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `rem-log-exp` `associate-/r/` `pow-flip` `inv-pow` `rem-exp-log`

Counts

4 → 168

Calls

4 calls:

35.0ms	(/ 1 (/ (+ alpha (+ 2.0 beta)) beta))
416.0ms	(exp (log (- (/ 1 (/ (+ alpha (+ 2.0 beta)) beta)) (- (/ alpha (+ (+ alpha 2.0) beta)) 1.0))))
242.0ms	(- (/ alpha (+ (+ alpha 2.0) beta)) 1.0)
408.0ms	(log (- (/ 1 (/ (+ alpha (+ 2.0 beta)) beta)) (- (/ alpha (+ (+ alpha 2.0) beta)) 1.0)))

series471.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(/ 1 (/ (+ alpha (+ 2.0 beta)) beta))
124.0ms	(exp (log (- (/ 1 (/ (+ alpha (+ 2.0 beta)) beta)) (- (/ alpha (+ (+ alpha 2.0) beta)) 1.0))))
94.0ms	(- (/ alpha (+ (+ alpha 2.0) beta)) 1.0)
165.0ms	(log (- (/ 1 (/ (+ alpha (+ 2.0 beta)) beta)) (- (/ alpha (+ (+ alpha 2.0) beta)) 1.0)))

simplify1.5s

Counts

180 → 180

Iterations

Iter	Nodes
done	5000
2	3026
1	758
0	317

prune743.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.1b

regimes170.0ms

Accuracy

62.5% (5.4b remaining)

Error of 6.2b against oracle of 0.8b and baseline of 15.3b

bsearch117.0ms

Steps

Iters	Range		Point
9	7.141495025384564e+25	1.1524881963593713e+31	1.6348256570929846e+27

simplify7.0ms

Iterations

Iter	Nodes
done	41
1	41
0	34

end0.0ms

sample1.8s

Algorithm

intervals

Results

646.0ms	810×	body	1280	valid
459.0ms	5915×	body	80	valid
201.0ms	8000×	pre	80	true
136.0ms	715×	body	640	valid
52.0ms	364×	body	320	valid
18.0ms	196×	body	160	valid