Details

sample64.0ms

Algorithm

intervals

Results

15.0ms	182×	body	80	valid
10.0ms	25×	body	1280	valid
10.0ms	256×	pre	80	true
8.0ms	29×	body	640	valid
4.0ms	13×	body	320	valid
1.0ms	7×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	2002
18	2002
17	1985
16	1722
15	1474
14	1236
13	995
12	795
11	669
10	582
9	467
8	348
7	290
6	209
5	124
4	69
3	50
2	33
1	20
0	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.2b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.7b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite230.0ms

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` `insert-posit16` `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 → 102

Calls

2 calls:

44.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
184.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series154.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
88.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.2s

Counts

108 → 108

Iterations

Iter	Nodes
done	2016
3	2016
2	1170
1	342
0	130

prune432.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.5b

localize25.0ms

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	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
1.7b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

215×	`*-un-lft-identity`
118×	`add-sqr-sqrt`
116×	`times-frac`
93×	`add-cube-cbrt`
63×	`prod-diff`
60×	`distribute-lft-out`
21×	`fma-neg`
13×	`associate-/r` `associate-/l` `distribute-lft-out--`
12×	`associate-/r/`
10×	`add-cbrt-cube` `add-exp-log` `difference-of-squares`
7×	`div-inv`
6×	`flip3-+` `flip-+` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `associate-/l/`
3×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-exp` `flip--`
2×	`frac-sub`
1×	`sub-neg` `diff-log` `div-sub`

Counts

4 → 233

Calls

4 calls:

1.0s	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
24.0ms	(/ beta (+ (+ alpha beta) 2.0))
24.0ms	(/ alpha (+ (+ alpha beta) 2.0))
206.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series353.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
73.0ms	(/ beta (+ (+ alpha beta) 2.0))
80.0ms	(/ alpha (+ (+ alpha beta) 2.0))
93.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.3s

Counts

245 → 245

Iterations

Iter	Nodes
done	2000
2	2000
1	744
0	312

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.8b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
1.7b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
1.7b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite656.0ms

Algorithm

rewrite-expression-head

Rules

280×	`*-un-lft-identity`
141×	`add-sqr-sqrt`
137×	`times-frac`
131×	`add-cube-cbrt`
126×	`prod-diff`
87×	`distribute-lft-out`
68×	`log-prod`
65×	`exp-sum`
21×	`fma-neg`
18×	`associate-/r/`
10×	`associate-/r*`
9×	`flip3-+` `flip-+` `div-inv`
8×	`add-cbrt-cube` `add-exp-log`
7×	`log-pow`
6×	`exp-prod` `associate-/l*` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
2×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `div-exp` `distribute-lft-out--`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 269

Calls

4 calls:

38.0ms	(/ beta (+ (+ alpha beta) 2.0))
41.0ms	(/ alpha (+ (+ alpha beta) 2.0))
365.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
205.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series365.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(/ beta (+ (+ alpha beta) 2.0))
55.0ms	(/ alpha (+ (+ alpha beta) 2.0))
132.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
108.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.2s

Counts

281 → 281

Iterations

Iter	Nodes
done	2010
3	2010
2	1756
1	664
0	352

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.8b

localize54.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
1.7b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

141×	`*-un-lft-identity`
69×	`add-sqr-sqrt`
64×	`add-cube-cbrt`
63×	`prod-diff`
61×	`times-frac`
45×	`distribute-lft-out`
21×	`fma-neg`
15×	`cbrt-prod`
8×	`associate-/r/`
7×	`flip3-+` `flip-+`
6×	`cbrt-div` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`pow1/3`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 156

Calls

4 calls:

11.0ms	(cbrt (+ (+ alpha beta) 2.0))
10.0ms	(cbrt (+ (+ alpha beta) 2.0))
10.0ms	(cbrt (+ (+ alpha beta) 2.0))
133.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series447.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(cbrt (+ (+ alpha beta) 2.0))
123.0ms	(cbrt (+ (+ alpha beta) 2.0))
120.0ms	(cbrt (+ (+ alpha beta) 2.0))
89.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.1s

Counts

168 → 168

Iterations

Iter	Nodes
done	2003
3	2003
2	1186
1	472
0	206

prune939.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.8b

regimes359.0ms

Accuracy

98.5% (0.2b remaining)

Error of 3.0b against oracle of 2.8b and baseline of 15.3b

bsearch3.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	34
1	34
0	29

end0.0ms

sample2.3s

Algorithm

intervals

Results

616.0ms	5904×	body	80	valid
506.0ms	390×	body	320	valid
403.0ms	844×	body	1280	valid
339.0ms	8000×	pre	80	true
262.0ms	656×	body	640	valid
33.0ms	206×	body	160	valid