Details

sample42.0ms

Algorithm

intervals

Results

6.0ms	175×	body	80	valid
5.0ms	34×	body	1280	valid
4.0ms	32×	body	640	valid
4.0ms	256×	pre	80	true
1.0ms	13×	body	320	valid
0.0ms	2×	body	160	valid

simplify57.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.3b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.2b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite204.0ms

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:

47.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
155.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series119.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
69.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify35.0ms

Counts: 71 → 71

prune152.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 18.4b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite291.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 89

Calls

3 calls:

35.0ms	(/ alpha (+ (+ alpha beta) 2.0))
47.0ms	(/ beta (+ (+ alpha beta) 2.0))
206.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series187.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(/ alpha (+ (+ alpha beta) 2.0))
53.0ms	(/ beta (+ (+ alpha beta) 2.0))
85.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify157.0ms

Counts: 98 → 98

prune236.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.2b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
1.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite629.0ms

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-exp-log` `add-cbrt-cube`
7×	`log-pow`
6×	`exp-prod` `associate-/l*` `add-log-exp`
5×	`pow1` `log-prod`
4×	`associate-/r/` `difference-of-squares`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `div-exp` `exp-sum` `clear-num` `flip-+` `div-inv` `distribute-lft-out--`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 110

Calls

4 calls:

35.0ms	(/ alpha (+ (+ alpha beta) 2.0))
35.0ms	(/ beta (+ (+ alpha beta) 2.0))
371.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
183.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series269.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ alpha (+ (+ alpha beta) 2.0))
53.0ms	(/ beta (+ (+ alpha beta) 2.0))
83.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
84.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify37.0ms

Counts: 122 → 122

prune311.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.9b

localize22.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
6.6b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.6b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.6b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite237.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
63×	`cbrt-prod`
46×	`times-frac`
36×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
27×	`distribute-lft-out`
6×	`associate-/r/` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`cbrt-div` `flip3-+` `pow1/3` `flip-+` `div-inv`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 105

Calls

4 calls:

174.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
18.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
23.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
18.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series540.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
153.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
153.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
152.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify120.0ms

Counts: 117 → 117

prune415.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.9b

regimes83.0ms

Accuracy

77% (3.0b remaining)

Error of 6.2b against oracle of 3.2b and baseline of 16.3b

bsearch77.0ms

Steps

Iters	Range		Point
10	3496066392446.565	3.3456001817085606e+23	14320040807966044.0

simplify1.0ms

end0.0ms

sample1.3s

Algorithm

intervals

Results

488.0ms	5763×	body	80	valid
230.0ms	749×	body	640	valid
163.0ms	856×	body	1280	valid
150.0ms	8000×	pre	80	true
40.0ms	413×	body	320	valid
14.0ms	219×	body	160	valid