Details

sample34.0ms

Algorithm

intervals

Results

6.0ms	180×	body	80	valid
5.0ms	28×	body	1280	valid
5.0ms	256×	pre	80	true
3.0ms	25×	body	640	valid
2.0ms	14×	body	320	valid
1.0ms	9×	body	160	valid

simplify715.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.9b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.2b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite386.0ms

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:

56.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
321.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series155.0ms

Counts

2 → 6

Calls

2 calls:

81.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
74.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify2.4s

Counts

106 → 106

Iterations

Useful iterations: done (2.4s)

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

prune374.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 17.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
2.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

512×	`*-un-lft-identity`
328×	`add-sqr-sqrt`
263×	`times-frac`
252×	`prod-diff`
213×	`add-cube-cbrt`
150×	`distribute-lft-out`
65×	`associate--r+`
46×	`difference-of-squares`
42×	`fma-neg`
32×	`associate-/r/`
25×	`distribute-lft-out--`
16×	`flip3-+` `flip-+` `div-inv`
11×	`add-log-exp`
10×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`pow1` `expm1-log1p-u` `diff-log` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub`
1×	`associate--r-`

Counts

4 → 413

Calls

4 calls:

790.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
57.0ms	(/ beta (+ (+ alpha beta) 2.0))
63.0ms	(/ alpha (+ (+ alpha beta) 2.0))
367.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series285.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
51.0ms	(/ beta (+ (+ alpha beta) 2.0))
56.0ms	(/ alpha (+ (+ alpha beta) 2.0))
92.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.0s

Counts

425 → 425

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	402	16706
1	942	13361
2	2393	11385
done	5000	9914

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (/ (cbrt beta) (cbrt (+ (+ alpha beta) 2.0))) 3)
0.6b	(cbrt beta)
0.7b	(cbrt (+ (+ alpha beta) 2.0))
2.2b	(- (/ alpha (+ 2.0 (+ alpha beta))) 1.0)

rewrite470.0ms

Algorithm

rewrite-expression-head

Rules

249×	`*-un-lft-identity`
157×	`times-frac`
127×	`add-sqr-sqrt`
122×	`add-cube-cbrt`
116×	`cbrt-prod`
75×	`distribute-lft-out`
63×	`prod-diff`
54×	`unpow-prod-down` `cube-prod`
21×	`fma-neg`
12×	`associate-/r/`
7×	`add-exp-log` `flip3-+` `flip-+`
6×	`cbrt-div` `div-inv` `add-log-exp`
5×	`pow1` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow`
2×	`pow1/3` `pow-exp` `rem-cube-cbrt` `difference-of-squares`
1×	`cbrt-undiv` `cube-div` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `unpow3` `div-exp` `flip--` `distribute-lft-out--` `sqr-pow`

Counts

4 → 261

Calls

4 calls:

81.0ms	(pow (/ (cbrt beta) (cbrt (+ (+ alpha beta) 2.0))) 3)
1.0ms	(cbrt beta)
17.0ms	(cbrt (+ (+ alpha beta) 2.0))
338.0ms	(- (/ alpha (+ 2.0 (+ alpha beta))) 1.0)

series895.0ms

Counts

4 → 12

Calls

4 calls:

306.0ms	(pow (/ (cbrt beta) (cbrt (+ (+ alpha beta) 2.0))) 3)
302.0ms	(cbrt beta)
159.0ms	(cbrt (+ (+ alpha beta) 2.0))
127.0ms	(- (/ alpha (+ 2.0 (+ alpha beta))) 1.0)

simplify2.0s

Counts

273 → 273

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	394	6013
1	1140	4872
2	3100	3978
done	5002	3749

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (/ (cbrt beta) (pow (+ (+ alpha beta) 2.0) 1/3)) 3)
0.6b	(cbrt beta)
2.2b	(- (/ alpha (+ 2.0 (+ alpha beta))) 1.0)
3.0b	(pow (+ (+ alpha beta) 2.0) 1/3)

rewrite480.0ms

Algorithm

rewrite-expression-head

Rules

254×	`*-un-lft-identity`
169×	`times-frac`
132×	`add-sqr-sqrt`
127×	`add-cube-cbrt`
123×	`unpow-prod-down`
75×	`distribute-lft-out`
63×	`prod-diff`
58×	`cube-prod`
57×	`cbrt-prod`
21×	`fma-neg`
14×	`sqr-pow`
11×	`add-exp-log`
8×	`associate-/r/`
6×	`pow1` `pow-unpow` `pow-exp` `add-cbrt-cube` `div-inv` `add-log-exp`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u`
3×	`pow-to-exp` `div-exp` `rem-cube-cbrt`
2×	`cbrt-undiv` `pow-pow` `unpow1/3` `difference-of-squares`
1×	`cube-div` `cube-mult` `sub-neg` `flip3--` `pow1/3` `diff-log` `unpow3` `flip--` `distribute-lft-out--`

Counts

4 → 277

Calls

4 calls:

121.0ms	(pow (/ (cbrt beta) (pow (+ (+ alpha beta) 2.0) 1/3)) 3)
1.0ms	(cbrt beta)
272.0ms	(- (/ alpha (+ 2.0 (+ alpha beta))) 1.0)
53.0ms	(pow (+ (+ alpha beta) 2.0) 1/3)

series935.0ms

Counts

4 → 12

Calls

4 calls:

324.0ms	(pow (/ (cbrt beta) (pow (+ (+ alpha beta) 2.0) 1/3)) 3)
329.0ms	(cbrt beta)
118.0ms	(- (/ alpha (+ 2.0 (+ alpha beta))) 1.0)
163.0ms	(pow (+ (+ alpha beta) 2.0) 1/3)

simplify2.4s

Counts

289 → 289

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	419	6555
1	1165	5135
2	3272	4049
done	5001	3917

prune799.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.0b

regimes124.0ms

Accuracy

77.1% (2.9b remaining)

Error of 5.9b against oracle of 2.9b and baseline of 15.8b

bsearch76.0ms

Steps

Iters	Range		Point
7	9579072.400219804	506205769.9975147	307451316.1096792

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	38	59
1	41	55
done	41	55

end0.0ms

sample1.5s

Algorithm

intervals

Results

353.0ms	860×	body	1280	valid
339.0ms	5834×	body	80	valid
236.0ms	8000×	pre	80	true
171.0ms	697×	body	640	valid
98.0ms	385×	body	320	valid
24.0ms	224×	body	160	valid