Details

sample50.0ms

Algorithm

intervals

Results

12.0ms	189×	body	80	valid
9.0ms	29×	body	1280	valid
7.0ms	256×	pre	80	true
6.0ms	24×	body	640	valid
2.0ms	10×	body	320	valid
0.0ms	4×	body	160	valid

simplify602.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	20	13
2	34	13
3	52	13
4	73	13
5	118	13
6	161	13
7	199	13
8	230	13
9	268	13
10	296	13
11	307	13
12	319	13
13	323	13
done	323	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.2b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite304.0ms

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

Counts

2 → 100

Calls

2 calls:

67.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
229.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series178.0ms

Counts

2 → 6

Calls

2 calls:

88.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
90.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify2.3s

Counts

106 → 106

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	128	1178
1	335	1110
2	950	1056
3	3094	1048
done	5001	1043

prune348.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 15.4b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
1.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite466.0ms

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-exp-log` `add-cbrt-cube`
6×	`flip3-+` `flip-+` `div-inv` `associate-/l*`
5×	`add-log-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

3 → 179

Calls

3 calls:

56.0ms	(/ beta (+ (+ alpha beta) 2.0))
42.0ms	(/ alpha (+ (+ alpha beta) 2.0))
350.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series237.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(/ beta (+ (+ alpha beta) 2.0))
63.0ms	(/ alpha (+ (+ alpha beta) 2.0))
104.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.7s

Counts

188 → 188

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	221	3563
1	492	2856
2	1161	2541
3	3586	2159
done	5000	2159

prune461.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (+ alpha beta) 2.0) beta)
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.7b	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
1.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite491.0ms

Algorithm

rewrite-expression-head

Rules

299×	`*-un-lft-identity`
208×	`times-frac`
142×	`add-sqr-sqrt`
137×	`add-cube-cbrt`
96×	`distribute-lft-out`
63×	`prod-diff`
27×	`associate-/r*`
21×	`fma-neg`
19×	`add-exp-log`
13×	`add-cbrt-cube`
11×	`associate-/r/` `div-inv` `associate-/l*`
9×	`div-exp`
6×	`flip3-+` `flip-+` `add-log-exp`
5×	`pow1` `cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`frac-2neg` `clear-num`
2×	`rec-exp` `1-exp` `associate-/l/` `difference-of-squares`
1×	`sub-neg` `flip3--` `pow-flip` `diff-log` `flip--` `distribute-lft-out--` `inv-pow`

Counts

4 → 281

Calls

4 calls:

96.0ms	(/ (+ (+ alpha beta) 2.0) beta)
37.0ms	(/ alpha (+ (+ alpha beta) 2.0))
42.0ms	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
290.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series298.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (+ (+ alpha beta) 2.0) beta)
89.0ms	(/ alpha (+ (+ alpha beta) 2.0))
83.0ms	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
100.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify3.3s

Counts

293 → 293

Iterations

Useful iterations: 3 (2.0s)

Iter	Nodes	Cost
0	325	5357
1	726	4313
2	1644	3820
3	4890	3532
done	5000	3532

prune521.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.2b

localize32.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
9.4b	(cbrt (/ (+ (+ alpha beta) 2.0) beta))
9.4b	(cbrt (/ (+ (+ alpha beta) 2.0) beta))
9.4b	(cbrt (/ (+ (+ alpha beta) 2.0) beta))

rewrite490.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 191

Calls

4 calls:

371.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
31.0ms	(cbrt (/ (+ (+ alpha beta) 2.0) beta))
32.0ms	(cbrt (/ (+ (+ alpha beta) 2.0) beta))
45.0ms	(cbrt (/ (+ (+ alpha beta) 2.0) beta))

series818.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
249.0ms	(cbrt (/ (+ (+ alpha beta) 2.0) beta))
203.0ms	(cbrt (/ (+ (+ alpha beta) 2.0) beta))
278.0ms	(cbrt (/ (+ (+ alpha beta) 2.0) beta))

simplify2.7s

Counts

203 → 203

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	252	4390
1	528	3687
2	1235	3353
3	3712	2920
done	5000	2914

prune690.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.2b

regimes146.0ms

Accuracy

72.4% (3.8b remaining)

Error of 6.9b against oracle of 3.1b and baseline of 16.9b

bsearch58.0ms

Steps

Iters	Range		Point
5	3.726174372304574e+36	1.2219886942032108e+37	9.24917919805738e+36

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	34	73
1	38	73
done	38	73

end0.0ms

sample1.8s

Algorithm

intervals

Results

407.0ms	210×	body	160	valid
394.0ms	5789×	body	80	valid
273.0ms	864×	body	1280	valid
258.0ms	8000×	pre	80	true
187.0ms	731×	body	640	valid
60.0ms	406×	body	320	valid