Details

sample89.0ms

Algorithm

intervals

Results

22.0ms	19×	body	640	valid
20.0ms	194×	body	80	valid
13.0ms	25×	body	1280	valid
11.0ms	256×	pre	80	true
3.0ms	10×	body	320	valid
2.0ms	8×	body	160	valid

simplify414.0ms

Counts

1 → 1

Iterations

Iter	Nodes
15	445
14	445
13	442
12	437
11	416
10	364
9	276
8	211
7	186
6	152
5	112
4	69
3	50
2	33
1	20
0	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.6b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite253.0ms

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:

62.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
186.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series150.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
95.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.3s

Counts

108 → 108

Iterations

Iter	Nodes
3	3331
2	1010
1	340
0	130

prune777.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.0b

localize42.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
2.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite301.0ms

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:

49.0ms	(/ alpha (+ (+ alpha beta) 2.0))
46.0ms	(/ beta (+ (+ alpha beta) 2.0))
199.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series269.0ms

Counts

3 → 9

Calls

3 calls:

82.0ms	(/ alpha (+ (+ alpha beta) 2.0))
65.0ms	(/ beta (+ (+ alpha beta) 2.0))
122.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.7s

Counts

191 → 191

Iterations

Iter	Nodes
3	3803
2	1193
1	490
0	224

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.5b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
2.6b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
2.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite685.0ms

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:

48.0ms	(/ alpha (+ (+ alpha beta) 2.0))
45.0ms	(/ beta (+ (+ alpha beta) 2.0))
358.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
222.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series366.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ alpha (+ (+ alpha beta) 2.0))
85.0ms	(/ beta (+ (+ alpha beta) 2.0))
119.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
102.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.1s

Counts

281 → 281

Iterations

Iter	Nodes
3	4163
2	1421
1	640
0	352

prune1.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.5b

localize46.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
2.6b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
2.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite627.0ms

Algorithm

rewrite-expression-head

Rules

232×	`*-un-lft-identity`
126×	`prod-diff`
123×	`add-sqr-sqrt`
113×	`add-cube-cbrt`
107×	`times-frac`
69×	`distribute-lft-out`
68×	`log-prod`
65×	`exp-sum`
21×	`fma-neg`
14×	`associate-/r/`
10×	`cbrt-prod`
9×	`flip3-+` `flip-+`
7×	`log-pow` `div-inv`
6×	`exp-prod` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
2×	`sub-neg` `pow1/3` `distribute-lft-out--`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 225

Calls

4 calls:

10.0ms	(cbrt (+ (+ alpha beta) 2.0))
14.0ms	(cbrt (+ (+ alpha beta) 2.0))
360.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
238.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series513.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(cbrt (+ (+ alpha beta) 2.0))
131.0ms	(cbrt (+ (+ alpha beta) 2.0))
123.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
84.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.9s

Counts

237 → 237

Iterations

Iter	Nodes
3	3656
2	1312
1	607
0	334

prune2.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.5b

regimes214.0ms

Accuracy

76.4% (3.1b remaining)

Error of 6.1b against oracle of 3.0b and baseline of 16.1b

bsearch108.0ms

Steps

Iters	Range		Point
10	62780.91749966379	1.4916330892545423e+18	12052311324865314.0

simplify4.0ms

Iterations

Iter	Nodes
2	29
1	29
0	26

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.1s	5804×	body	80	valid
431.0ms	8000×	pre	80	true
410.0ms	837×	body	1280	valid
310.0ms	763×	body	640	valid
117.0ms	386×	body	320	valid
38.0ms	210×	body	160	valid

Iter	Nodes
15	445
14	445
13	442
12	437
11	416
10	364
9	276
8	211
7	186
6	152
5	112
4	69
3	50
2	33
1	20
0	10

Iter	Nodes
15	445
14	445
13	442
12	437
11	416
10	364
9	276
8	211
7	186
6	152
5	112
4	69
3	50
2	33
1	20
0	10

Iter	Nodes
15	445
14	445
13	442
12	437
11	416
10	364
9	276
8	211
7	186
6	152
5	112
4	69
3	50
2	33
1	20
0	10