Details

sample83.0ms

Algorithm

intervals

Results

21.0ms	189×	body	80	valid
16.0ms	29×	body	1280	valid
12.0ms	256×	pre	80	true
11.0ms	24×	body	640	valid
4.0ms	11×	body	320	valid
1.0ms	3×	body	160	valid

simplify4.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
25	4885
24	4583
23	4303
22	3954
21	3572
20	3229
19	2829
18	2315
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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize37.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.5b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite207.0ms

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:

52.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
152.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series149.0ms

Counts

2 → 6

Calls

2 calls:

61.0ms	(/ (- 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	5004
2	1170
1	342
0	130

prune384.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.0b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite276.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 182

Calls

3 calls:

36.0ms	(/ alpha (+ (+ alpha beta) 2.0))
41.0ms	(/ beta (+ (+ alpha beta) 2.0))
196.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series275.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(/ alpha (+ (+ alpha beta) 2.0))
77.0ms	(/ beta (+ (+ alpha beta) 2.0))
121.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.6s

Counts

191 → 191

Iterations

Iter	Nodes
done	5001
2	1450
1	516
0	224

prune912.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.8b

localize46.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
7.2b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.2b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.2b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite259.0ms

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` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-div` `pow1/3`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 201

Calls

4 calls:

218.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
16.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
11.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
11.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series745.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
215.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
178.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
216.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify2.8s

Counts

213 → 213

Iterations

Iter	Nodes
done	5000
3	4645
2	1334
1	523
0	243

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.8b

localize49.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt beta)
0.6b	(cbrt beta)
0.6b	(cbrt beta)
1.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

126×	`*-un-lft-identity`
69×	`add-sqr-sqrt`
64×	`add-cube-cbrt`
63×	`prod-diff`
61×	`times-frac`
36×	`distribute-lft-out`
21×	`fma-neg`
9×	`cbrt-prod`
8×	`associate-/r/`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `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 → 144

Calls

4 calls:

1.0ms	(cbrt beta)
1.0ms	(cbrt beta)
1.0ms	(cbrt beta)
200.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series1.4s

Counts

4 → 12

Calls

4 calls:

625.0ms	(cbrt beta)
297.0ms	(cbrt beta)
332.0ms	(cbrt beta)
107.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.4s

Counts

156 → 156

Iterations

Iter	Nodes
done	5002
3	3507
2	1001
1	400
0	179

prune622.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.8b

regimes426.0ms

Accuracy

99% (0.1b remaining)

Error of 3.2b against oracle of 3.1b and baseline of 16.0b

bsearch3.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	31
1	31
0	27

end0.0ms

sample2.2s

Algorithm

intervals

Results

578.0ms	5827×	body	80	valid
497.0ms	873×	body	1280	valid
416.0ms	8000×	pre	80	true
313.0ms	702×	body	640	valid
118.0ms	362×	body	320	valid
42.0ms	236×	body	160	valid