Details

sample56.0ms

Algorithm

intervals

Results

11.0ms	192×	body	80	valid
10.0ms	32×	body	1280	valid
6.0ms	256×	pre	80	true
4.0ms	16×	body	640	valid
2.0ms	13×	body	320	valid
0.0ms	3×	body	160	valid

simplify4.4s

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize14.0ms

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)

rewrite237.0ms

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:

60.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
172.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series161.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
88.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.2s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	1160
1	340
0	128

prune477.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.5b

localize30.0ms

Local error

Found 3 expressions with local error:

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

rewrite339.0ms

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` `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 → 179

Calls

3 calls:

43.0ms	(/ beta (+ (+ alpha beta) 2.0))
51.0ms	(/ alpha (+ (+ alpha beta) 2.0))
238.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series259.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(/ beta (+ (+ alpha beta) 2.0))
62.0ms	(/ alpha (+ (+ alpha beta) 2.0))
129.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.5s

Counts

188 → 188

Iterations

Iter	Nodes
done	5013
2	1501
1	513
0	221

prune871.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.2b

localize62.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (+ (+ alpha beta) 2.0))) (/ beta (sqrt (+ (+ alpha beta) 2.0))))
0.4b	(/ beta (sqrt (+ (+ alpha beta) 2.0)))
0.6b	(/ 1 (sqrt (+ (+ alpha beta) 2.0)))
1.0b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite564.0ms

Algorithm

rewrite-expression-head

Rules

263×	`*-un-lft-identity`
179×	`times-frac`
176×	`add-sqr-sqrt`
125×	`add-cube-cbrt`
81×	`sqrt-prod`
78×	`distribute-lft-out`
63×	`prod-diff`
32×	`add-exp-log`
30×	`associate-r` `associate-l`
21×	`fma-neg`
20×	`add-cbrt-cube`
16×	`associate-/r*` `associate-/r/`
15×	`unswap-sqr`
11×	`div-exp`
8×	`pow1` `flip3-+` `sqrt-div` `prod-exp` `flip-+` `div-inv`
6×	`cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u`
3×	`rec-exp` `1-exp` `pow-flip`
2×	`clear-num` `frac-2neg` `difference-of-squares`
1×	`frac-times` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip--` `distribute-lft-out--` `inv-pow`

Counts

4 → 310

Calls

4 calls:

212.0ms	(* (/ 1 (sqrt (+ (+ alpha beta) 2.0))) (/ beta (sqrt (+ (+ alpha beta) 2.0))))
38.0ms	(/ beta (sqrt (+ (+ alpha beta) 2.0)))
40.0ms	(/ 1 (sqrt (+ (+ alpha beta) 2.0)))
255.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series460.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (/ 1 (sqrt (+ (+ alpha beta) 2.0))) (/ beta (sqrt (+ (+ alpha beta) 2.0))))
122.0ms	(/ beta (sqrt (+ (+ alpha beta) 2.0)))
112.0ms	(/ 1 (sqrt (+ (+ alpha beta) 2.0)))
140.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.2s

Counts

322 → 322

Iterations

Iter	Nodes
done	5006
2	2730
1	984
0	374

prune1.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.2b

localize55.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (+ (+ alpha beta) 2.0))) (/ beta (sqrt (+ (+ alpha beta) 2.0))))
0.4b	(/ beta (sqrt (+ (+ alpha beta) 2.0)))
0.6b	(/ 1 (sqrt (+ (+ alpha beta) 2.0)))
1.0b	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

rewrite398.0ms

Algorithm

rewrite-expression-head

Rules

144×	`*-un-lft-identity`
118×	`times-frac`
114×	`add-sqr-sqrt`
81×	`sqrt-prod`
68×	`add-cube-cbrt`
42×	`distribute-lft-out`
32×	`add-exp-log`
30×	`associate-r` `associate-l`
20×	`add-cbrt-cube`
16×	`associate-/r*`
15×	`unswap-sqr`
11×	`div-exp`
8×	`pow1` `sqrt-div` `prod-exp` `associate-/r/`
6×	`cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `flip3-+` `cbrt-unprod` `flip-+` `log1p-expm1-u` `div-inv`
3×	`rec-exp` `1-exp` `pow-flip`
2×	`clear-num` `frac-2neg`
1×	`frac-times` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip--` `inv-pow` `difference-of-squares`

Counts

4 → 226

Calls

4 calls:

220.0ms	(* (/ 1 (sqrt (+ (+ alpha beta) 2.0))) (/ beta (sqrt (+ (+ alpha beta) 2.0))))
51.0ms	(/ beta (sqrt (+ (+ alpha beta) 2.0)))
53.0ms	(/ 1 (sqrt (+ (+ alpha beta) 2.0)))
60.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

series439.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (/ 1 (sqrt (+ (+ alpha beta) 2.0))) (/ beta (sqrt (+ (+ alpha beta) 2.0))))
85.0ms	(/ beta (sqrt (+ (+ alpha beta) 2.0)))
117.0ms	(/ 1 (sqrt (+ (+ alpha beta) 2.0)))
145.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

simplify2.4s

Counts

238 → 238

Iterations

Iter	Nodes
done	5000
2	2424
1	822
0	296

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.2b

regimes212.0ms

Accuracy

75.1% (3.1b remaining)

Error of 6.1b against oracle of 3.0b and baseline of 15.6b

bsearch92.0ms

Steps

Iters	Range		Point
8	1541639454070.677	19367525498197844.0	10272132967178968.0

simplify12.0ms

Iterations

Iter	Nodes
done	41
1	41
0	33

end0.0ms

sample1.4s

Algorithm

intervals

Results

373.0ms	5862×	body	80	valid
223.0ms	8000×	pre	80	true
206.0ms	694×	body	640	valid
198.0ms	841×	body	1280	valid
60.0ms	410×	body	320	valid
17.0ms	193×	body	160	valid