Details

sample38.0ms

Algorithm

intervals

Results

7.0ms	181×	body	80	valid
5.0ms	34×	body	640	valid
5.0ms	24×	body	1280	valid
4.0ms	256×	pre	80	true
2.0ms	14×	body	320	valid
0.0ms	3×	body	160	valid

simplify2.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
9	4691
8	1531
7	665
6	318
5	164
4	74
3	53
2	34
1	20
0	10

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.9b

localize27.0ms

Local error

Found 2 expressions with local error:

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

rewrite305.0ms

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-cbrt-cube` `add-exp-log` `associate-/r/` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`expm1-log1p-u` `pow1` `div-sub` `log1p-expm1-u` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3--` `div-exp` `associate-+l-` `flip--`

Counts

2 → 100

Calls

2 calls:

73.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
224.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series148.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
97.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.4s

Counts

106 → 106

Iterations

Iter	Nodes
done	5002
2	1431
1	340
0	128

prune572.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 17.0b

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

rewrite1.1s

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-cbrt-cube` `add-exp-log`
6×	`associate-/l*`
4×	`expm1-log1p-u` `pow1` `diff-log` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `frac-sub`
1×	`associate--r-`

Counts

4 → 413

Calls

4 calls:

708.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
56.0ms	(/ beta (+ (+ alpha beta) 2.0))
48.0ms	(/ alpha (+ (+ alpha beta) 2.0))
262.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series329.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
58.0ms	(/ beta (+ (+ alpha beta) 2.0))
74.0ms	(/ alpha (+ (+ alpha beta) 2.0))
125.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.4s

Counts

425 → 425

Iterations

Iter	Nodes
done	5000
2	3883
1	992
0	402

prune2.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(fma beta (/ 1 (+ (+ alpha beta) 2.0)) (- (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
1.0b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite403.0ms

Algorithm

rewrite-expression-head

Rules

183×	`*-un-lft-identity`
91×	`times-frac`
86×	`add-sqr-sqrt`
81×	`add-cube-cbrt`
63×	`prod-diff`
60×	`distribute-lft-out`
21×	`fma-neg`
12×	`associate-/r/`
10×	`associate-/r*` `add-exp-log`
8×	`add-cbrt-cube`
6×	`flip3-+` `flip-+` `div-inv` `associate-/l*` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`div-exp`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `difference-of-squares`
1×	`rec-exp` `sub-neg` `flip3--` `diff-log` `1-exp` `fma-udef` `pow-flip` `flip--` `distribute-lft-out--` `inv-pow`

Counts

4 → 193

Calls

4 calls:

38.0ms	(/ 1 (+ (+ alpha beta) 2.0))
28.0ms	(/ alpha (+ (+ alpha beta) 2.0))
0.0ms	(fma beta (/ 1 (+ (+ alpha beta) 2.0)) (- (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
318.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series328.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ 1 (+ (+ alpha beta) 2.0))
55.0ms	(/ alpha (+ (+ alpha beta) 2.0))
99.0ms	(fma beta (/ 1 (+ (+ alpha beta) 2.0)) (- (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
115.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.9s

Counts

205 → 205

Iterations

Iter	Nodes
done	5000
2	2335
1	548
0	240

prune878.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.6b

localize88.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
5.7b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
5.7b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
5.7b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite439.0ms

Algorithm

rewrite-expression-head

Rules

195×	`*-un-lft-identity`
106×	`times-frac`
93×	`add-sqr-sqrt`
88×	`add-cube-cbrt`
63×	`cbrt-prod` `prod-diff` `distribute-lft-out`
21×	`fma-neg`
14×	`associate-/r/`
7×	`flip3-+` `flip-+` `div-inv`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`cbrt-div` `pow1/3`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 197

Calls

4 calls:

339.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
28.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
26.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
28.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series748.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
218.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
219.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
211.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify1.3s

Counts

209 → 209

Iterations

Iter	Nodes
done	5001
2	1591
1	522
0	241

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.6b

regimes263.0ms

Accuracy

75.7% (3.1b remaining)

Error of 6.3b against oracle of 3.2b and baseline of 15.8b

bsearch63.0ms

Steps

Iters	Range		Point
9	32200978691.942776	2.815342563409213e+16	337398417361397.56

simplify11.0ms

Iterations

Iter	Nodes
done	33
1	33
0	29

end0.0ms

sample1.6s

Algorithm

intervals

Results

606.0ms	726×	body	640	valid
340.0ms	5820×	body	80	valid
209.0ms	854×	body	1280	valid
125.0ms	8000×	pre	80	true
52.0ms	202×	body	160	valid
50.0ms	398×	body	320	valid