Details

sample208.0ms

Algorithm

intervals

Results

44.0ms	256×	pre	80	true
34.0ms	202×	body	80	valid
23.0ms	14×	body	320	valid
6.0ms	22×	body	1280	valid
3.0ms	13×	body	640	valid
1.0ms	5×	body	160	valid

simplify16.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
30	4882
29	4699
28	4512
27	4259
26	4080
25	3901
24	3724
23	3479
22	3302
21	3117
20	2921
19	2681
18	2442
17	2220
16	1938
15	1583
14	1283
13	942
12	774
11	653
10	576
9	459
8	330
7	269
6	198
5	124
4	69
3	50
2	33
1	20
0	10

prune52.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.6b

localize282.0ms

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)

rewrite582.0ms

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:

142.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
374.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series376.0ms

Counts

2 → 6

Calls

2 calls:

91.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
276.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify4.6s

Counts

71 → 71

Iterations

Iter	Nodes
done	5004
2	1118
1	326
0	124

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.1b

localize62.0ms

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

rewrite4.1s

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:

3.0s	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
77.0ms	(/ alpha (+ (+ alpha beta) 2.0))
88.0ms	(/ beta (+ (+ alpha beta) 2.0))
797.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series729.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
93.0ms	(/ alpha (+ (+ alpha beta) 2.0))
198.0ms	(/ beta (+ (+ alpha beta) 2.0))
306.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify5.6s

Counts

149 → 149

Iterations

Iter	Nodes
done	5003
2	1873
1	562
0	238

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.9b

localize204.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 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)))) (* 2.0 (* (+ (+ alpha beta) 2.0) (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))))
1.2b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite2.9s

Algorithm

rewrite-expression-head

Rules

245×	`*-un-lft-identity`
141×	`times-frac`
137×	`associate-*r/`
131×	`add-sqr-sqrt`
90×	`distribute-lft-out`
83×	`flip3-+` `flip-+`
73×	`add-cube-cbrt`
71×	`frac-times`
66×	`frac-add` `associate-/l/`
64×	`frac-sub`
41×	`associate-*l/`
39×	`unpow-prod-down` `cube-prod` `swap-sqr`
38×	`associate-/r/`
28×	`add-exp-log` `add-cbrt-cube`
26×	`flip3--` `flip--`
24×	`difference-of-squares`
21×	`associate-r` `associate-l`
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 → 329

Calls

4 calls:

482.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
88.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
1.2s	(/ (- (* 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)))) (* 2.0 (* (+ (+ alpha beta) 2.0) (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))))
1.1s	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series2.2s

Counts

4 → 12

Calls

4 calls:

117.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
168.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
1.7s	(/ (- (* 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)))) (* 2.0 (* (+ (+ alpha beta) 2.0) (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))))
257.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify5.5s

Counts

341 → 341

Iterations

Iter	Nodes
done	5004
1	2341
0	550

prune4.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.9b

localize183.0ms

Local error

Found 4 expressions with local error:

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 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (log (exp (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (/ alpha (+ (+ alpha beta) 2.0))))) (pow 1.0 3)))) (* 2.0 (* (+ (+ alpha beta) 2.0) (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))))
1.0b	(log (exp (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (/ alpha (+ (+ alpha beta) 2.0)))))
1.2b	(- (log (exp (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (/ alpha (+ (+ alpha beta) 2.0))))) (pow 1.0 3))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

191×	`*-un-lft-identity`
137×	`associate-*r/`
103×	`times-frac`
81×	`flip3-+` `flip-+`
75×	`add-sqr-sqrt`
72×	`distribute-lft-out`
71×	`frac-times`
66×	`frac-add` `associate-/l/`
64×	`frac-sub`
56×	`add-cube-cbrt`
41×	`associate-*l/`
39×	`swap-sqr`
34×	`associate-/r/`
26×	`flip3--` `flip--`
25×	`add-exp-log` `add-cbrt-cube`
21×	`associate-r` `associate-l`
13×	`pow1`
7×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
6×	`log-prod` `add-log-exp`
5×	`div-inv`
4×	`log-pow` `difference-of-squares` `unswap-sqr`
3×	`associate--l+` `associate-/l*`
2×	`distribute-lft-out--`
1×	`pow2` `sub-neg` `unpow-prod-down` `exp-prod` `exp-to-pow` `frac-2neg` `pow-plus` `diff-log` `div-sub` `cube-prod` `rem-log-exp` `pow-prod-down` `clear-num` `associate-/r` `pow-sqr` `-commutative` `pow-prod-up` `sqr-pow`

Counts

4 → 260

Calls

4 calls:

308.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
858.0ms	(/ (- (* 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) (- (log (exp (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (/ alpha (+ (+ alpha beta) 2.0))))) (pow 1.0 3)))) (* 2.0 (* (+ (+ alpha beta) 2.0) (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))))
9.0ms	(log (exp (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (/ alpha (+ (+ alpha beta) 2.0)))))
36.0ms	(- (log (exp (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (/ alpha (+ (+ alpha beta) 2.0))))) (pow 1.0 3))

series1.3s

Counts

4 → 12

Calls

4 calls:

122.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
852.0ms	(/ (- (* 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) (- (log (exp (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (/ alpha (+ (+ alpha beta) 2.0))))) (pow 1.0 3)))) (* 2.0 (* (+ (+ alpha beta) 2.0) (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))))
153.0ms	(log (exp (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (/ alpha (+ (+ alpha beta) 2.0)))))
203.0ms	(- (log (exp (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (/ alpha (+ (+ alpha beta) 2.0))))) (pow 1.0 3))

simplify5.1s

Counts

272 → 272

Iterations

Iter	Nodes
done	5004
1	2031
0	506

prune4.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.9b

regimes299.0ms

Accuracy

56.9% (5.5b remaining)

Error of 8.5b against oracle of 3.0b and baseline of 15.8b

bsearch568.0ms

Steps

Iters	Range		Point
7	3.9227933197023594e+166	7.439987087167839e+167	1.1437212734780832e+167
5	7.445604319051971e+112	1.5393751381298674e+113	1.5264500717710571e+113
8	4.6091985256205887e+33	6.133200959176609e+37	7.863989155318433e+36

simplify49.0ms

Iterations

Iter	Nodes
done	65
3	65
2	62
1	59
0	45

end0.0ms

sample2.2s

Algorithm

intervals

Results

575.0ms	874×	body	1280	valid
530.0ms	5842×	body	80	valid
318.0ms	8000×	pre	80	true
262.0ms	719×	body	640	valid
135.0ms	381×	body	320	valid
29.0ms	184×	body	160	valid