Details

sample41.0ms

Algorithm

intervals

Results

8.0ms	179×	body	80	valid
6.0ms	29×	body	1280	valid
5.0ms	27×	body	640	valid
5.0ms	256×	pre	80	true
1.0ms	11×	body	320	valid
1.0ms	10×	body	160	valid

simplify3.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
32	4930
31	4722
30	4510
29	4301
28	4120
27	3916
26	3715
25	3502
24	3325
23	3117
22	2909
21	2698
20	2516
19	2291
18	2012
17	1763
16	1558
15	1364
14	1138
13	931
12	742
11	607
10	526
9	431
8	318
7	267
6	197
5	124
4	69
3	50
2	33
1	20
0	10

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.0b

localize24.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.5b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite247.0ms

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-cbrt-cube` `add-exp-log` `add-log-exp`
2×	`pow1` `flip3-+` `div-sub` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3--` `div-exp` `associate-+l-` `div-inv` `flip--`

Counts

2 → 65

Calls

2 calls:

59.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
185.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series151.0ms

Counts

2 → 6

Calls

2 calls:

61.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
90.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.4s

Counts

71 → 71

Iterations

Iter	Nodes
done	5003
2	1119
1	326
0	124

prune371.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 17.2b

localize41.0ms

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))
2.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite828.0ms

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

Counts

4 → 111

Calls

4 calls:

494.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
60.0ms	(/ alpha (+ (+ alpha beta) 2.0))
39.0ms	(/ beta (+ (+ alpha beta) 2.0))
229.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series347.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
60.0ms	(/ alpha (+ (+ alpha beta) 2.0))
50.0ms	(/ beta (+ (+ alpha beta) 2.0))
132.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.5s

Counts

123 → 123

Iterations

Iter	Nodes
done	5002
2	1572
1	463
0	193

prune636.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.1b

localize109.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha))))
0.1b	(* (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha))))
0.1b	(* (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha))))
2.5b	(- (* (/ alpha (+ 2.0 (+ beta alpha))) (* (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha))))) (* (* 1.0 1.0) 1.0))

rewrite693.0ms

Algorithm

rewrite-expression-head

Rules

544×	`*-un-lft-identity`
300×	`times-frac`
216×	`distribute-lft-out`
184×	`add-sqr-sqrt`
148×	`add-cube-cbrt`
117×	`swap-sqr`
63×	`associate-r` `associate-l`
40×	`add-cbrt-cube` `add-exp-log`
25×	`pow1`
24×	`associate-/r/`
12×	`cbrt-undiv` `flip3-+` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr`
6×	`add-log-exp`
3×	`pow2` `frac-times` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`difference-cubes` `sub-neg` `flip3--` `diff-log` `cube-unmult` `pow3` `flip--`

Counts

4 → 340

Calls

4 calls:

155.0ms	(* (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha))))
152.0ms	(* (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha))))
181.0ms	(* (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha))))
178.0ms	(- (* (/ alpha (+ 2.0 (+ beta alpha))) (* (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha))))) (* (* 1.0 1.0) 1.0))

series408.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha))))
80.0ms	(* (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha))))
81.0ms	(* (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha))))
156.0ms	(- (* (/ alpha (+ 2.0 (+ beta alpha))) (* (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha))))) (* (* 1.0 1.0) 1.0))

simplify2.1s

Counts

352 → 352

Iterations

Iter	Nodes
done	5000
2	2255
1	631
0	189

prune2.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.0b

localize220.0ms

Local error

Found 4 expressions with local error:

8.3b	(cbrt (/ alpha (+ 2.0 (+ beta alpha))))
8.3b	(cbrt (/ alpha (+ 2.0 (+ beta alpha))))
8.3b	(cbrt (/ alpha (+ 2.0 (+ beta alpha))))
8.3b	(cbrt (/ alpha (+ 2.0 (+ beta alpha))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

100×	`*-un-lft-identity`
84×	`cbrt-prod`
60×	`times-frac`
40×	`add-sqr-sqrt` `add-cube-cbrt`
36×	`distribute-lft-out`
8×	`associate-/r/`
4×	`pow1` `cbrt-div` `flip3-+` `add-cbrt-cube` `pow1/3` `add-exp-log` `flip-+` `div-inv` `add-log-exp`

Counts

4 → 120

Calls

4 calls:

13.0ms	(cbrt (/ alpha (+ 2.0 (+ beta alpha))))
13.0ms	(cbrt (/ alpha (+ 2.0 (+ beta alpha))))
13.0ms	(cbrt (/ alpha (+ 2.0 (+ beta alpha))))
13.0ms	(cbrt (/ alpha (+ 2.0 (+ beta alpha))))

series856.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(cbrt (/ alpha (+ 2.0 (+ beta alpha))))
201.0ms	(cbrt (/ alpha (+ 2.0 (+ beta alpha))))
223.0ms	(cbrt (/ alpha (+ 2.0 (+ beta alpha))))
252.0ms	(cbrt (/ alpha (+ 2.0 (+ beta alpha))))

simplify1.8s

Counts

132 → 132

Iterations

Iter	Nodes
done	5001
3	1861
2	592
1	231
0	112

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 4.0b

regimes182.0ms

Accuracy

77.6% (2.9b remaining)

Error of 5.9b against oracle of 3.0b and baseline of 15.9b

bsearch74.0ms

Steps

Iters	Range		Point
10	3.3757913299230946	47603267695671.21	17302899711342.29

simplify10.0ms

Iterations

Iter	Nodes
done	33
1	33
0	27

end0.0ms

sample1.4s

Algorithm

intervals

Results

416.0ms	5834×	body	80	valid
254.0ms	8000×	pre	80	true
249.0ms	830×	body	1280	valid
190.0ms	729×	body	640	valid
58.0ms	396×	body	320	valid
21.0ms	211×	body	160	valid