Details

sample44.0ms

Algorithm

intervals

Results

12.0ms	183×	body	80	valid
5.0ms	27×	body	1280	valid
4.0ms	256×	pre	80	true
3.0ms	23×	body	640	valid
1.0ms	12×	body	160	valid
1.0ms	11×	body	320	valid

simplify2.1s

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha 2.0) beta))
2.2b	(+ (/ (- beta alpha) (+ (+ alpha 2.0) beta)) 1.0)

rewrite182.0ms

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:

38.0ms	(/ (- beta alpha) (+ (+ alpha 2.0) beta))
142.0ms	(+ (/ (- beta alpha) (+ (+ alpha 2.0) beta)) 1.0)

series172.0ms

Counts

2 → 6

Calls

2 calls:

85.0ms	(/ (- beta alpha) (+ (+ alpha 2.0) beta))
86.0ms	(+ (/ (- beta alpha) (+ (+ alpha 2.0) beta)) 1.0)

simplify631.0ms

Counts

71 → 71

Iterations

Iter	Nodes
done	5002
2	1315
1	326
0	123

prune309.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 16.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ beta (+ (+ alpha 2.0) beta)) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0))
0.0b	(/ beta (+ (+ alpha 2.0) beta))
0.0b	(/ alpha (+ beta (+ alpha 2.0)))
2.2b	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

rewrite788.0ms

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:

535.0ms	(- (/ beta (+ (+ alpha 2.0) beta)) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0))
35.0ms	(/ beta (+ (+ alpha 2.0) beta))
27.0ms	(/ alpha (+ beta (+ alpha 2.0)))
187.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

series325.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(- (/ beta (+ (+ alpha 2.0) beta)) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0))
55.0ms	(/ beta (+ (+ alpha 2.0) beta))
58.0ms	(/ alpha (+ beta (+ alpha 2.0)))
118.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

simplify1.1s

Counts

123 → 123

Iterations

Iter	Nodes
done	5002
2	2206
1	501
0	205

prune667.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.7b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha 2.0) beta))
0.0b	(/ alpha (+ beta (+ alpha 2.0)))
2.2b	(log (exp (- (/ alpha (+ beta (+ alpha 2.0))) 1.0)))
2.2b	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

rewrite643.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity`
36×	`add-sqr-sqrt`
32×	`times-frac`
26×	`add-cube-cbrt`
24×	`distribute-lft-out`
10×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log`
7×	`log-pow`
6×	`exp-prod` `associate-/l*` `add-log-exp`
5×	`pow1` `log-prod`
4×	`associate-/r/` `difference-of-squares`
2×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `div-exp` `exp-sum` `flip-+` `div-inv` `distribute-lft-out--`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 110

Calls

4 calls:

32.0ms	(/ beta (+ (+ alpha 2.0) beta))
40.0ms	(/ alpha (+ beta (+ alpha 2.0)))
397.0ms	(log (exp (- (/ alpha (+ beta (+ alpha 2.0))) 1.0)))
167.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

series384.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(/ beta (+ (+ alpha 2.0) beta))
75.0ms	(/ alpha (+ beta (+ alpha 2.0)))
109.0ms	(log (exp (- (/ alpha (+ beta (+ alpha 2.0))) 1.0)))
130.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

simplify746.0ms

Counts

122 → 122

Iterations

Iter	Nodes
done	5000
2	1781
1	436
0	194

prune613.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.7b

localize79.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ 2.0 (+ alpha beta)))
0.7b	(cbrt (+ 2.0 (+ alpha beta)))
2.2b	(log (exp (- (/ alpha (+ beta (+ alpha 2.0))) 1.0)))
2.2b	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

rewrite544.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
10×	`cbrt-prod`
8×	`add-cube-cbrt`
7×	`log-pow`
6×	`exp-prod` `distribute-lft-out` `add-log-exp`
5×	`pow1` `log-prod`
4×	`cbrt-div` `add-cbrt-cube` `add-exp-log` `difference-of-squares`
2×	`sub-neg` `flip3-+` `times-frac` `pow1/3` `exp-sum` `flip-+` `distribute-lft-out--`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 66

Calls

4 calls:

11.0ms	(cbrt (+ 2.0 (+ alpha beta)))
10.0ms	(cbrt (+ 2.0 (+ alpha beta)))
358.0ms	(log (exp (- (/ alpha (+ beta (+ alpha 2.0))) 1.0)))
160.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

series456.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(cbrt (+ 2.0 (+ alpha beta)))
109.0ms	(cbrt (+ 2.0 (+ alpha beta)))
128.0ms	(log (exp (- (/ alpha (+ beta (+ alpha 2.0))) 1.0)))
99.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

simplify690.0ms

Counts

78 → 78

Iterations

Iter	Nodes
done	5000
2	1061
1	344
0	152

prune617.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.7b

regimes258.0ms

Accuracy

76.4% (3.0b remaining)

Error of 6.3b against oracle of 3.4b and baseline of 15.9b

bsearch95.0ms

Steps

Iters	Range		Point
9	390.6412587448322	77665801.66036974	76510312.31317446

simplify9.0ms

Iterations

Iter	Nodes
done	45
2	45
1	44
0	40

end0.0ms

sample1.9s

Algorithm

intervals

Results

785.0ms	5808×	body	80	valid
300.0ms	849×	body	1280	valid
235.0ms	8000×	pre	80	true
139.0ms	733×	body	640	valid
56.0ms	379×	body	320	valid
46.0ms	231×	body	160	valid