Details

sample32.0ms

Algorithm

intervals

Results

6.0ms	177×	body	80	valid
5.0ms	31×	body	1280	valid
4.0ms	256×	pre	80	true
4.0ms	27×	body	640	valid
1.0ms	12×	body	320	valid
1.0ms	9×	body	160	valid

simplify3.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	20	13
2	34	13
3	53	13
4	74	13
5	163	13
6	302	13
7	625	13
8	1439	13
9	4374	13
done	5000	13

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.4b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.8b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite342.0ms

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:

88.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
252.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series146.0ms

Counts

2 → 6

Calls

2 calls:

80.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
66.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify851.0ms

Counts

71 → 71

Iterations

Useful iterations: 2 (238.0ms)

Iter	Nodes	Cost
0	124	1134
1	326	1074
2	1354	1014
done	5001	1014

prune234.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 17.7b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
2.8b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite1.0s

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:

647.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
53.0ms	(/ alpha (+ (+ alpha beta) 2.0))
47.0ms	(/ beta (+ (+ alpha beta) 2.0))
292.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series387.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
92.0ms	(/ alpha (+ (+ alpha beta) 2.0))
58.0ms	(/ beta (+ (+ alpha beta) 2.0))
122.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.1s

Counts

123 → 123

Iterations

Useful iterations: 2 (407.0ms)

Iter	Nodes	Cost
0	193	1936
1	462	1814
2	1916	1730
done	5000	1730

prune433.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.4b

localize18.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (/ 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)))

rewrite363.0ms

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:

257.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
34.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
36.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
26.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series791.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
176.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
233.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
252.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify735.0ms

Counts

117 → 117

Iterations

Useful iterations: done (728.0ms)

Iter	Nodes	Cost
0	161	1985
1	338	1895
2	1038	1760
done	5001	1731

prune565.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.4b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
0.1b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
0.1b	(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (+ alpha beta) 2.0) (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))))
2.7b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

376×	`*-un-lft-identity`
211×	`times-frac`
178×	`associate-*r/`
172×	`add-sqr-sqrt`
144×	`distribute-lft-out`
102×	`add-cube-cbrt`
85×	`flip3-+` `flip-+`
78×	`swap-sqr`
72×	`frac-times`
66×	`frac-add` `associate-/l/`
64×	`frac-sub`
42×	`associate-r` `associate-l` `associate-*l/` `associate-/r/`
33×	`add-exp-log` `add-cbrt-cube`
26×	`flip3--` `flip--`
24×	`difference-of-squares`
18×	`pow1` `unpow-prod-down` `cube-prod`
10×	`cbrt-undiv` `div-exp` `sqr-pow`
9×	`prod-exp` `cbrt-unprod` `div-inv`
8×	`unswap-sqr`
6×	`add-log-exp`
5×	`distribute-lft-out--`
3×	`associate-/l*`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`difference-cubes` `sub-neg` `frac-2neg` `diff-log` `div-sub` `clear-num` `associate-/r*`

Counts

4 → 374

Calls

4 calls:

230.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
190.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
366.0ms	(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (+ alpha beta) 2.0) (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))))
623.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series1.3s

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
88.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
955.0ms	(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (+ alpha beta) 2.0) (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))))
189.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify944.0ms

Counts

386 → 386

Iterations

Useful iterations: done (920.0ms)

Iter	Nodes	Cost
0	468	18162
1	1920	16726
done	5001	15332

prune2.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.4b

regimes119.0ms

Accuracy

76.9% (3.1b remaining)

Error of 5.9b against oracle of 2.8b and baseline of 16.2b

bsearch63.0ms

Steps

Iters	Range		Point
9	0.5849616174094538	51624944.521682866	49032803.70070513

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	69
1	36	69
done	36	69

end0.0ms

sample1.5s

Algorithm

intervals

Results

308.0ms	5789×	body	80	valid
250.0ms	8000×	pre	80	true
250.0ms	883×	body	1280	valid
228.0ms	750×	body	640	valid
65.0ms	207×	body	160	valid
52.0ms	371×	body	320	valid