Details

sample58.0ms

Algorithm

intervals

Results

12.0ms	37×	body	1280	valid
11.0ms	174×	body	80	valid
6.0ms	256×	pre	80	true
5.0ms	21×	body	640	valid
3.0ms	16×	body	320	valid
1.0ms	8×	body	160	valid

simplify614.0ms

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: 19.1b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.9b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite335.0ms

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:

76.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
255.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series144.0ms

Counts

2 → 6

Calls

2 calls:

70.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
74.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.8s

Counts

71 → 71

Iterations

Useful iterations: 3 (791.0ms)

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

prune221.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 18.5b

localize11.0ms

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))
1.9b	(- (/ 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)
38.0ms	(/ beta (+ (+ alpha beta) 2.0))
64.0ms	(/ alpha (+ (+ alpha beta) 2.0))
271.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series374.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
88.0ms	(/ beta (+ (+ alpha beta) 2.0))
63.0ms	(/ alpha (+ (+ alpha beta) 2.0))
109.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.3s

Counts

149 → 149

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	238	2750
1	542	2646
2	1480	2490
done	5000	2474

prune498.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.5b

localize71.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
0.1b	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
0.1b	(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 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 (+ (+ alpha beta) 2.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* 1.0 1.0)) (* (+ (+ alpha beta) 2.0) 2.0)))
1.8b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

245×	`*-un-lft-identity`
141×	`times-frac`
131×	`add-sqr-sqrt`
99×	`associate-*r/`
90×	`distribute-lft-out`
73×	`add-cube-cbrt`
68×	`flip3-+` `flip-+`
66×	`associate-/l/`
64×	`frac-sub`
53×	`frac-times`
48×	`frac-add`
41×	`associate-*l/`
39×	`unpow-prod-down` `cube-prod` `swap-sqr`
28×	`add-exp-log` `add-cbrt-cube`
26×	`flip3--` `flip--`
24×	`difference-of-squares`
21×	`associate-r` `associate-l`
20×	`associate-/r/`
12×	`pow1`
11×	`sqr-pow`
8×	`cbrt-undiv` `div-exp`
7×	`prod-exp` `cbrt-unprod` `div-inv`
6×	`add-log-exp`
5×	`distribute-lft-out--`
4×	`unswap-sqr`
3×	`pow-unpow` `associate-/l*`
2×	`pow-exp` `rem-cube-cbrt`
1×	`difference-cubes` `cube-div` `pow2` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `pow-plus` `diff-log` `unpow3` `div-sub` `pow-prod-down` `clear-num` `associate-/r` `pow-sqr` `-commutative` `pow-prod-up`

Counts

4 → 311

Calls

4 calls:

225.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
55.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
609.0ms	(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 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 (+ (+ alpha beta) 2.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* 1.0 1.0)) (* (+ (+ alpha beta) 2.0) 2.0)))
574.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series1.1s

Counts

4 → 12

Calls

4 calls:

105.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
114.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
705.0ms	(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 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 (+ (+ alpha beta) 2.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* 1.0 1.0)) (* (+ (+ alpha beta) 2.0) 2.0)))
163.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify1.1s

Counts

323 → 323

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	474	15145
1	1784	13341
done	5001	11990

prune2.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.5b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (* beta (+ (* 1.0 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (pow (/ alpha (+ (+ alpha beta) 2.0)) 2))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* 1.0 1.0)) (* (+ (+ alpha beta) 2.0) 2.0)))
0.6b	(exp (log (/ (- (* beta (+ (* 1.0 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (pow (/ alpha (+ (+ alpha beta) 2.0)) 2))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* 1.0 1.0)) (* (+ (+ alpha beta) 2.0) 2.0)))))
1.8b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))
11.3b	(log (/ (- (* beta (+ (* 1.0 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (pow (/ alpha (+ (+ alpha beta) 2.0)) 2))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* 1.0 1.0)) (* (+ (+ alpha beta) 2.0) 2.0))))

rewrite3.7s

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
32×	`flip3-+` `flip-+`
30×	`log-prod`
28×	`associate-*l/`
26×	`associate-*r/`
24×	`associate-/r/` `difference-of-squares`
23×	`add-exp-log`
21×	`*-un-lft-identity`
20×	`frac-times`
18×	`unpow-prod-down` `cube-prod` `associate-/l/`
17×	`times-frac`
16×	`frac-sub`
15×	`exp-sum`
13×	`add-cbrt-cube`
11×	`add-cube-cbrt`
10×	`sqr-pow`
8×	`flip3--` `flip--`
6×	`pow1` `div-exp` `prod-exp` `add-log-exp`
5×	`distribute-lft-out--`
4×	`exp-prod` `rem-log-exp`
3×	`cbrt-undiv` `cbrt-unprod` `div-inv` `associate-/l*`
2×	`log-div` `log-pow`
1×	`difference-cubes` `sub-neg` `frac-2neg` `exp-diff` `diff-log` `div-sub` `clear-num` `associate-/r*` `rem-exp-log`

Counts

4 → 148

Calls

4 calls:

1.2s	(/ (- (* beta (+ (* 1.0 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (pow (/ alpha (+ (+ alpha beta) 2.0)) 2))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* 1.0 1.0)) (* (+ (+ alpha beta) 2.0) 2.0)))
1.2s	(exp (log (/ (- (* beta (+ (* 1.0 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (pow (/ alpha (+ (+ alpha beta) 2.0)) 2))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* 1.0 1.0)) (* (+ (+ alpha beta) 2.0) 2.0)))))
670.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))
503.0ms	(log (/ (- (* beta (+ (* 1.0 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (pow (/ alpha (+ (+ alpha beta) 2.0)) 2))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* 1.0 1.0)) (* (+ (+ alpha beta) 2.0) 2.0))))

series3.1s

Counts

4 → 12

Calls

4 calls:

622.0ms	(/ (- (* beta (+ (* 1.0 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (pow (/ alpha (+ (+ alpha beta) 2.0)) 2))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* 1.0 1.0)) (* (+ (+ alpha beta) 2.0) 2.0)))
621.0ms	(exp (log (/ (- (* beta (+ (* 1.0 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (pow (/ alpha (+ (+ alpha beta) 2.0)) 2))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* 1.0 1.0)) (* (+ (+ alpha beta) 2.0) 2.0)))))
164.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))
1.7s	(log (/ (- (* beta (+ (* 1.0 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (pow (/ alpha (+ (+ alpha beta) 2.0)) 2))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* 1.0 1.0)) (* (+ (+ alpha beta) 2.0) 2.0))))

simplify735.0ms

Counts

160 → 160

Iterations

Useful iterations: done (715.0ms)

Iter	Nodes	Cost
0	350	12209
1	1056	11675
done	5001	10465

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.5b

regimes225.0ms

Accuracy

75.8% (3.1b remaining)

Error of 5.9b against oracle of 2.8b and baseline of 15.6b

bsearch66.0ms

Steps

Iters	Range		Point
5	879064267.884121	3030780229.4257846	1845090834.437638

simplify15.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	51	172
1	64	172
done	64	172

end0.0ms

sample1.8s

Algorithm

intervals

Results

779.0ms	844×	body	1280	valid
361.0ms	5878×	body	80	valid
171.0ms	697×	body	640	valid
156.0ms	8000×	pre	80	true
54.0ms	381×	body	320	valid
18.0ms	200×	body	160	valid