Details

sample45.0ms

Algorithm

intervals

Results

10.0ms	44×	body	1280	valid
9.0ms	182×	body	80	valid
5.0ms	256×	pre	80	true
3.0ms	15×	body	640	valid
2.0ms	11×	body	320	valid
0.0ms	4×	body	160	valid

simplify855.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.2b

localize29.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
0.7b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite329.0ms

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

Counts

2 → 65

Calls

2 calls:

77.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
249.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series137.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
75.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.7s

Counts: 71 → 71

prune237.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.8b

localize23.0ms

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	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.7b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite2.0s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 137

Calls

4 calls:

1.6s	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
43.0ms	(/ beta (+ (+ alpha beta) 2.0))
72.0ms	(/ alpha (+ (+ alpha beta) 2.0))
285.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series303.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
63.0ms	(/ beta (+ (+ alpha beta) 2.0))
54.0ms	(/ alpha (+ (+ alpha beta) 2.0))
107.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify882.0ms

Counts: 149 → 149

prune489.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.3b

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite361.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
15×	`cbrt-prod`
12×	`add-sqr-sqrt`
9×	`distribute-lft-out`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3-+` `pow1/3` `flip-+`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `times-frac` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

31.0ms	(cbrt (+ (+ alpha beta) 2.0))
22.0ms	(cbrt (+ (+ alpha beta) 2.0))
16.0ms	(cbrt (+ (+ alpha beta) 2.0))
289.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series490.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(cbrt (+ (+ alpha beta) 2.0))
124.0ms	(cbrt (+ (+ alpha beta) 2.0))
127.0ms	(cbrt (+ (+ alpha beta) 2.0))
100.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.3s

Counts: 72 → 72

prune442.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.3b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.4b	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
0.7b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
11.3b	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

89×	`*-un-lft-identity`
72×	`add-sqr-sqrt`
64×	`times-frac`
50×	`log-prod`
37×	`add-cube-cbrt`
25×	`exp-sum`
19×	`distribute-lft-out--`
14×	`difference-of-squares`
12×	`distribute-lft-out`
9×	`add-exp-log`
6×	`pow1` `add-cbrt-cube` `add-log-exp`
5×	`associate-/r*`
4×	`exp-prod`
3×	`div-inv` `associate-/l*`
2×	`log-div` `div-exp` `rem-log-exp` `associate-/r/` `log-pow`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `exp-diff` `diff-log` `clear-num` `flip--` `flip-+` `rem-exp-log`

Counts

4 → 126

Calls

4 calls:

48.0ms	(/ alpha (+ (+ alpha beta) 2.0))
500.0ms	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
252.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
494.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

series482.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(/ alpha (+ (+ alpha beta) 2.0))
114.0ms	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
112.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
190.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

simplify725.0ms

Counts: 138 → 138

prune533.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.3b

regimes138.0ms

Accuracy

72.6% (3.7b remaining)

Error of 6.9b against oracle of 3.1b and baseline of 16.7b

bsearch118.0ms

Steps

Iters	Range		Point
10	925325.9807075356	3.4641089617611155e+20	5062494549189153.0

simplify1.1s

end0.0ms

sample1.8s

Algorithm

intervals

Results

775.0ms	5818×	body	80	valid
254.0ms	8000×	pre	80	true
217.0ms	731×	body	640	valid
206.0ms	869×	body	1280	valid
52.0ms	378×	body	320	valid
18.0ms	204×	body	160	valid