Details

sample51.0ms

Algorithm

intervals

Results

14.0ms	205×	body	80	valid
6.0ms	256×	pre	80	true
5.0ms	21×	body	1280	valid
2.0ms	13×	body	640	valid
2.0ms	12×	body	320	valid
0.0ms	5×	body	160	valid

simplify655.0ms

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: 12.1b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.1b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite355.0ms

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:

70.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
281.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series147.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
89.0ms	(+ (/ (- 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

prune375.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.5b

localize14.0ms

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))
2.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite1.4s

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:

817.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
67.0ms	(/ beta (+ (+ alpha beta) 2.0))
43.0ms	(/ alpha (+ (+ alpha beta) 2.0))
361.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series367.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
87.0ms	(/ beta (+ (+ alpha beta) 2.0))
87.0ms	(/ alpha (+ (+ alpha beta) 2.0))
90.0ms	(- (/ 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

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
2.1b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
2.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

346×	`*-un-lft-identity`
189×	`prod-diff`
185×	`add-sqr-sqrt`
170×	`add-cube-cbrt`
168×	`times-frac`
130×	`exp-sum`
102×	`distribute-lft-out`
68×	`log-prod`
22×	`associate-/r/`
21×	`fma-neg`
12×	`exp-prod`
11×	`flip3-+` `flip-+` `div-inv`
9×	`add-log-exp`
7×	`log-pow`
6×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
5×	`pow1` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `associate-/l*` `distribute-lft-out--`
2×	`exp-diff` `diff-log` `rem-exp-log`
1×	`cbrt-undiv` `log-div` `flip3--` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `flip--`

Counts

4 → 309

Calls

4 calls:

511.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
42.0ms	(/ alpha (+ (+ alpha beta) 2.0))
543.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
282.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series316.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
45.0ms	(/ alpha (+ (+ alpha beta) 2.0))
78.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
108.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.8s

Counts

321 → 321

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	320	8581
1	586	6326
2	1321	5488
3	4105	4730
done	5000	4730

prune712.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.1b	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
2.1b	(- (cbrt (pow (/ alpha (+ (+ alpha beta) 2.0)) 3)) 1.0)
24.7b	(cbrt (pow (/ alpha (+ (+ alpha beta) 2.0)) 3))

rewrite904.0ms

Algorithm

rewrite-expression-head

Rules

385×	`*-un-lft-identity`
246×	`cbrt-prod`
198×	`add-sqr-sqrt`
197×	`times-frac`
183×	`add-cube-cbrt`
153×	`prod-diff`
128×	`unpow-prod-down` `cube-prod`
120×	`distribute-lft-out`
51×	`fma-neg`
26×	`associate-/r/`
13×	`flip3-+` `flip-+` `div-inv`
9×	`add-exp-log` `add-cbrt-cube`
7×	`difference-of-squares` `sqr-pow`
6×	`cube-mult` `unpow3` `add-log-exp`
5×	`pow1` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `associate-/l*`
2×	`cbrt-undiv` `cube-div` `div-exp` `pow-exp` `rem-cube-cbrt`
1×	`pow-to-exp` `sub-neg` `cbrt-div` `flip3--` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `clear-num` `flip--` `rem-cbrt-cube` `distribute-lft-out--`

Counts

4 → 389

Calls

4 calls:

57.0ms	(/ alpha (+ (+ alpha beta) 2.0))
52.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
696.0ms	(- (cbrt (pow (/ alpha (+ (+ alpha beta) 2.0)) 3)) 1.0)
45.0ms	(cbrt (pow (/ alpha (+ (+ alpha beta) 2.0)) 3))

series384.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ alpha (+ (+ alpha beta) 2.0))
87.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
112.0ms	(- (cbrt (pow (/ alpha (+ (+ alpha beta) 2.0)) 3)) 1.0)
100.0ms	(cbrt (pow (/ alpha (+ (+ alpha beta) 2.0)) 3))

simplify1.9s

Counts

401 → 401

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	316	9841
1	785	6414
2	2131	5311
done	5000	5190

prune808.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.1b

regimes198.0ms

Accuracy

98.4% (0.2b remaining)

Error of 3.1b against oracle of 2.9b and baseline of 15.7b

bsearch2.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	52
1	31	52
done	31	52

end0.0ms

sample913.0ms

Algorithm

intervals

Results

202.0ms	5855×	body	80	valid
153.0ms	901×	body	1280	valid
135.0ms	8000×	pre	80	true
90.0ms	685×	body	640	valid
37.0ms	375×	body	320	valid
12.0ms	184×	body	160	valid