Details

sample30.0ms

Algorithm

intervals

Results

6.0ms	178×	body	80	valid
5.0ms	30×	body	1280	valid
4.0ms	256×	pre	80	true
3.0ms	25×	body	640	valid
2.0ms	18×	body	320	valid
0.0ms	5×	body	160	valid

simplify562.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	20	13
2	34	13
3	52	13
4	73	13
5	118	13
6	149	13
7	177	13
8	208	13
9	246	13
10	274	13
11	285	13
12	297	13
13	301	13
done	301	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.4b

localize22.0ms

Local error

Found 2 expressions with local error:

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

rewrite313.0ms

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:

78.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
233.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series181.0ms

Counts

2 → 6

Calls

2 calls:

83.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
98.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.7s

Counts

71 → 71

Iterations

Useful iterations: 3 (734.0ms)

Iter	Nodes	Cost
0	124	1134
1	320	1074
2	886	1014
3	2832	1006
done	5000	1006

prune220.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 17.5b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite934.0ms

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:

546.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
64.0ms	(/ beta (+ (+ alpha beta) 2.0))
45.0ms	(/ alpha (+ (+ alpha beta) 2.0))
275.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series356.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
54.0ms	(/ beta (+ (+ alpha beta) 2.0))
70.0ms	(/ alpha (+ (+ alpha beta) 2.0))
119.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.7s

Counts

123 → 123

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	193	1936
1	448	1814
2	1242	1730
3	4330	1698
done	5000	1686

prune462.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.9b

localize44.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
8.0b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
8.0b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
8.0b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite379.0ms

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:

256.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
35.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
38.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
40.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series758.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
201.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
215.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
225.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify1.6s

Counts

117 → 117

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	161	1985
1	334	1895
2	784	1760
3	2065	1731
done	5001	1695

prune499.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.9b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite805.0ms

Algorithm

rewrite-expression-head

Rules

234×	`*-un-lft-identity`
131×	`times-frac`
89×	`distribute-lft-out`
84×	`add-sqr-sqrt`
72×	`add-cube-cbrt`
39×	`swap-sqr`
21×	`associate-r` `associate-l`
20×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r/`
11×	`pow1`
9×	`associate-/r*`
7×	`associate-/l*`
6×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+` `div-inv` `add-log-exp` `difference-of-squares`
4×	`prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `frac-2neg` `clear-num` `flip--` `associate-/l/`
1×	`pow2` `frac-times` `sub-neg` `pow-plus` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 200

Calls

4 calls:

35.0ms	(/ alpha (+ (+ alpha beta) 2.0))
436.0ms	(/ (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
245.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
73.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

series479.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(/ alpha (+ (+ alpha beta) 2.0))
183.0ms	(/ (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
87.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
134.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

simplify1.9s

Counts

212 → 212

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	254	5292
1	734	4773
2	2659	4315
done	5002	3683

prune649.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.9b

regimes241.0ms

Accuracy

76.5% (3.1b remaining)

Error of 6.3b against oracle of 3.2b and baseline of 16.3b

bsearch117.0ms

Steps

Iters	Range		Point
8	627164805739635.8	1.0354160951297587e+18	4.2708897840755174e+17

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	31	60
1	34	60
done	34	60

end0.0ms

sample2.1s

Algorithm

intervals

Results

793.0ms	926×	body	1280	valid
451.0ms	5780×	body	80	valid
234.0ms	8000×	pre	80	true
149.0ms	718×	body	640	valid
90.0ms	377×	body	320	valid
20.0ms	199×	body	160	valid