Details

sample25.0ms

Algorithm

intervals

Results

5.0ms	188×	body	80	valid
4.0ms	256×	pre	80	true
3.0ms	26×	body	1280	valid
3.0ms	28×	body	640	valid
1.0ms	12×	body	320	valid
0.0ms	2×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	13
1	20	13
2	33	13
3	51	13
4	70	13
5	121	13
6	166	13
7	208	13
8	243	13
9	306	13
10	413	13
11	475	13
12	522	13
13	575	13
14	730	13
15	889	13
16	928	13
17	971	13
18	1003	13
19	1011	13
done	1011	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.3b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
0.9b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

104×	`*-un-lft-identity`
50×	`times-frac`
47×	`add-sqr-sqrt`
34×	`distribute-lft-out`
31×	`fma-def`
25×	`add-cube-cbrt`
11×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `associate-/r/` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow1` `expm1-log1p-u` `div-sub` `log1p-expm1-u` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `flip3--` `frac-2neg` `div-exp` `clear-num` `sum-log` `flip--`

Counts

2 → 100

Calls

2 calls:

24.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
96.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series109.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
63.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify2.1s

Counts

106 → 106

Iterations

Useful iterations: 3 (412.0ms)

Iter	Nodes	Cost
0	128	1178
1	336	1110
2	1021	1056
3	4786	1048
done	5000	1048

prune217.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 15.6b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.9b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite470.0ms

Algorithm

rewrite-expression-head

Rules

512×	`*-un-lft-identity`
328×	`add-sqr-sqrt`
263×	`times-frac`
252×	`prod-diff`
213×	`add-cube-cbrt`
150×	`distribute-lft-out`
65×	`associate--r+`
46×	`difference-of-squares`
42×	`fma-neg`
32×	`associate-/r/`
25×	`distribute-lft-out--`
16×	`flip3-+` `flip-+` `div-inv`
11×	`add-log-exp`
10×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`pow1` `expm1-log1p-u` `diff-log` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub`
1×	`associate--r-`

Counts

4 → 413

Calls

4 calls:

17.0ms	(/ beta (+ (+ alpha beta) 2.0))
292.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
17.0ms	(/ alpha (+ (+ alpha beta) 2.0))
115.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series237.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ beta (+ (+ alpha beta) 2.0))
60.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
48.0ms	(/ alpha (+ (+ alpha beta) 2.0))
80.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.2s

Counts

425 → 425

Iterations

Useful iterations: 2 (308.0ms)

Iter	Nodes	Cost
0	402	16706
1	991	13361
2	3076	11298
done	5001	11298

prune754.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.9b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
0.9b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite564.0ms

Algorithm

rewrite-expression-head

Rules

346×	`*-un-lft-identity`
189×	`prod-diff`
185×	`add-sqr-sqrt`
170×	`add-cube-cbrt`
168×	`times-frac`
130×	`exp-sum`
102×	`distribute-lft-out`
68×	`log-prod`
22×	`associate-/r/`
21×	`fma-neg`
12×	`exp-prod`
11×	`flip3-+` `flip-+` `div-inv`
9×	`add-log-exp`
7×	`log-pow`
6×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
5×	`pow1` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `associate-/l*` `distribute-lft-out--`
2×	`exp-diff` `diff-log` `rem-exp-log`
1×	`cbrt-undiv` `log-div` `flip3--` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `flip--`

Counts

4 → 309

Calls

4 calls:

193.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
17.0ms	(/ alpha (+ (+ alpha beta) 2.0))
215.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
114.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series278.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
48.0ms	(/ alpha (+ (+ alpha beta) 2.0))
76.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
80.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify684.0ms

Counts

321 → 321

Iterations

Useful iterations: done (668.0ms)

Iter	Nodes	Cost
0	320	8581
1	599	6326
2	1698	5281
done	5000	5245

prune491.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.9b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.9b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite258.0ms

Algorithm

rewrite-expression-head

Rules

254×	`*-un-lft-identity`
130×	`add-sqr-sqrt`
126×	`prod-diff`
122×	`times-frac`
120×	`add-cube-cbrt`
78×	`distribute-lft-out`
42×	`fma-neg`
16×	`associate-/r/`
10×	`cbrt-prod` `flip3-+` `flip-+`
8×	`div-inv` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `log1p-expm1-u` `difference-of-squares`
2×	`sub-neg` `flip3--` `pow1/3` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 236

Calls

4 calls:

8.0ms	(cbrt (+ (+ alpha beta) 2.0))
9.0ms	(cbrt (+ (+ alpha beta) 2.0))
113.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
114.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series361.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(cbrt (+ (+ alpha beta) 2.0))
100.0ms	(cbrt (+ (+ alpha beta) 2.0))
80.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
80.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify546.0ms

Counts

248 → 248

Iterations

Useful iterations: done (531.0ms)

Iter	Nodes	Cost
0	204	5724
1	466	4422
2	1316	3728
done	5001	3636

prune567.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.8b

regimes119.0ms

Accuracy

74.4% (3.4b remaining)

Error of 6.4b against oracle of 3.0b and baseline of 16.3b

bsearch57.0ms

Steps

Iters	Range		Point
8	1.4366889122671085e+27	3.2593449619462425e+30	4.836259073578557e+29

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	72
1	39	72
done	39	72

end0.0ms

sample620.0ms

Algorithm

intervals

Results

148.0ms	5765×	body	80	valid
104.0ms	855×	body	1280	valid
102.0ms	8000×	pre	80	true
69.0ms	733×	body	640	valid
31.0ms	436×	body	320	valid
13.0ms	211×	body	160	valid