Details

sample28.0ms

Algorithm

intervals

Results

6.0ms	256×	pre	80	true
4.0ms	178×	body	80	valid
4.0ms	34×	body	1280	valid
2.0ms	19×	body	640	valid
1.0ms	15×	body	320	valid
1.0ms	10×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	13
1	20	13
2	33	13
3	51	13
4	70	13
5	119	13
6	144	13
7	173	13
8	208	13
9	259	13
10	298	13
11	331	13
12	378	13
13	415	13
14	463	13
15	525	13
16	551	13
17	578	13
18	610	13
19	618	13
done	618	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.6b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite121.0ms

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:

27.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
91.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series107.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
59.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.5s

Counts

71 → 71

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	124	1134
1	319	1074
2	867	1014
3	3700	1006
done	5000	1005

prune148.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 17.3b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
2.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite381.0ms

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

Counts

4 → 111

Calls

4 calls:

19.0ms	(/ alpha (+ (+ alpha beta) 2.0))
235.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
18.0ms	(/ beta (+ (+ alpha beta) 2.0))
104.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series227.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ alpha (+ (+ alpha beta) 2.0))
61.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
48.0ms	(/ beta (+ (+ alpha beta) 2.0))
74.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify502.0ms

Counts

123 → 123

Iterations

Useful iterations: done (498.0ms)

Iter	Nodes	Cost
0	193	1936
1	448	1814
2	1350	1730
done	5000	1700

prune284.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.7b

localize21.0ms

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))
2.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite131.0ms

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:

9.0ms	(cbrt (+ (+ alpha beta) 2.0))
9.0ms	(cbrt (+ (+ alpha beta) 2.0))
9.0ms	(cbrt (+ (+ alpha beta) 2.0))
102.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series377.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(cbrt (+ (+ alpha beta) 2.0))
100.0ms	(cbrt (+ (+ alpha beta) 2.0))
100.0ms	(cbrt (+ (+ alpha beta) 2.0))
76.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify808.0ms

Counts

72 → 72

Iterations

Useful iterations: 3 (279.0ms)

Iter	Nodes	Cost
0	120	1076
1	282	1043
2	674	977
3	2050	888
done	5000	888

prune313.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.6b	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
2.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
10.6b	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite511.0ms

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

Counts

4 → 95

Calls

4 calls:

20.0ms	(/ beta (+ (+ alpha beta) 2.0))
181.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
100.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
208.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series319.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ beta (+ (+ alpha beta) 2.0))
65.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
80.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
128.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify488.0ms

Counts

107 → 107

Iterations

Useful iterations: done (485.0ms)

Iter	Nodes	Cost
0	211	2358
1	467	2197
2	1315	2032
done	5001	1980

prune264.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.7b

regimes125.0ms

Accuracy

78.1% (2.8b remaining)

Error of 6.0b against oracle of 3.3b and baseline of 15.9b

bsearch39.0ms

Steps

Iters	Range		Point
5	391248603.19673574	1027443772.3458656	1015227874.2528594

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	99
1	41	99
done	41	99

end0.0ms

sample614.0ms

Algorithm

intervals

Results

149.0ms	5870×	body	80	valid
104.0ms	828×	body	1280	valid
102.0ms	8000×	pre	80	true
69.0ms	692×	body	640	valid
30.0ms	409×	body	320	valid
10.0ms	201×	body	160	valid