Details

sample58.0ms

Algorithm

intervals

Results

10.0ms	167×	body	80	valid
9.0ms	28×	body	1280	valid
8.0ms	33×	body	640	valid
6.0ms	256×	pre	80	true
3.0ms	15×	body	320	valid
2.0ms	13×	body	160	valid

simplify6.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	244
1	20	244
2	33	244
3	50	244
4	69	244
5	124	244
6	197	244
7	267	244
8	318	244
9	431	244
10	526	244
11	607	244
12	742	244
13	931	244
14	1138	244
15	1364	244
16	1558	244
17	1763	244
18	2012	244
19	2291	244
20	2516	244
21	2698	244
22	2909	244
23	3117	244
24	3325	244
25	3502	244
26	3715	244
27	3916	244
28	4120	244
29	4301	244
30	4510	244
31	4722	244
32	4930	244
done	5001	244

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.1b

localize32.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
3.2b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite306.0ms

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:

75.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
226.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series176.0ms

Counts

2 → 6

Calls

2 calls:

81.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
95.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.3s

Counts

71 → 71

Iterations

Useful iterations: 2 (348.0ms)

Iter	Nodes	Cost
0	124	22726
1	326	20397
2	1119	19875
done	5003	19875

prune326.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 20.0b

localize18.0ms

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))
3.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite955.0ms

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:

613.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
41.0ms	(/ beta (+ (+ alpha beta) 2.0))
47.0ms	(/ alpha (+ (+ alpha beta) 2.0))
247.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series349.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
58.0ms	(/ beta (+ (+ alpha beta) 2.0))
75.0ms	(/ alpha (+ (+ alpha beta) 2.0))
138.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.8s

Counts

123 → 123

Iterations

Useful iterations: 2 (611.0ms)

Iter	Nodes	Cost
0	193	36441
1	463	31839
2	1561	31155
done	5000	31155

prune647.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.8b

localize56.0ms

Local error

Found 4 expressions with local error:

3.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
7.9b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.9b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.9b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite258.0ms

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-cbrt-cube` `add-exp-log`
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:

192.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
16.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
15.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
32.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series804.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
221.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
235.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
223.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify2.2s

Counts

117 → 117

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	161	50465
1	338	44379
2	904	43537
3	2976	42897
done	5017	42384

prune683.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.8b

localize138.0ms

Local error

Found 4 expressions with local error:

1.2b	(cbrt (/ (* (cbrt beta) (cbrt beta)) (sqrt (+ (+ alpha beta) 2.0))))
3.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
7.9b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.9b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite274.0ms

Algorithm

rewrite-expression-head

Rules

62×	`*-un-lft-identity`
56×	`cbrt-prod`
39×	`times-frac`
30×	`add-sqr-sqrt`
25×	`add-cube-cbrt`
21×	`distribute-lft-out`
6×	`associate-/r/` `add-log-exp`
5×	`sqrt-prod`
4×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`cbrt-div` `flip3-+` `pow1/3` `flip-+` `div-inv`
2×	`sqrt-div` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 98

Calls

4 calls:

24.0ms	(cbrt (/ (* (cbrt beta) (cbrt beta)) (sqrt (+ (+ alpha beta) 2.0))))
205.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
16.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
25.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series954.0ms

Counts

4 → 12

Calls

4 calls:

459.0ms	(cbrt (/ (* (cbrt beta) (cbrt beta)) (sqrt (+ (+ alpha beta) 2.0))))
101.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
194.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
199.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify1.8s

Counts

110 → 110

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	262	54480
1	552	48626
2	1488	47984
done	5000	47304

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.8b

regimes365.0ms

Accuracy

77.5% (2.9b remaining)

Error of 6.1b against oracle of 3.2b and baseline of 16.0b

bsearch58.0ms

Steps

Iters	Range		Point
7	247318.98015239072	31866126.207131654	16738773.274129016

simplify6.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	27	917
1	31	917
done	31	917

end0.0ms

sample1.7s

Algorithm

intervals

Results

622.0ms	745×	body	640	valid
321.0ms	5809×	body	80	valid
230.0ms	857×	body	1280	valid
203.0ms	8000×	pre	80	true
63.0ms	213×	body	160	valid
51.0ms	376×	body	320	valid