Details

sample25.0ms

Algorithm

intervals

Results

4.0ms	184×	body	80	valid
3.0ms	256×	pre	80	true
3.0ms	25×	body	1280	valid
2.0ms	22×	body	640	valid
1.0ms	15×	body	320	valid
0.0ms	10×	body	160	valid

simplify70.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	6
1	34	6
2	52	6
3	73	6
4	123	6
5	172	6
6	224	6
7	261	6
8	323	6
9	411	6
10	532	6
11	612	6
12	654	6
13	697	6
14	922	6
15	980	6
16	1007	6
17	1027	6
18	1035	6
19	1035	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.4b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
25×	`times-frac`
19×	`distribute-lft-out`
14×	`add-cube-cbrt`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`pow1` `flip3-+` `div-sub` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `flip3--` `frac-2neg` `div-exp` `clear-num` `sum-log` `flip--` `div-inv`

Counts

2 → 65

Calls

2 calls:

45.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
154.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series106.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
59.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify35.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	320	535
1	1022	510
2	5001	502

prune150.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.1b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
2.4b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite211.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
16×	`times-frac`
12×	`add-cube-cbrt` `distribute-lft-out`
5×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `associate-/r/` `difference-of-squares`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `flip--` `flip-+` `div-inv` `distribute-lft-out--`

Counts

2 → 52

Calls

2 calls:

35.0ms	(/ alpha (+ (+ alpha beta) 2.0))
175.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series117.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(/ alpha (+ (+ alpha beta) 2.0))
74.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify117.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	248	359
1	805	344
2	3674	337
3	5002	337

prune144.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 2.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
2.4b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
2.4b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite908.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
32×	`add-sqr-sqrt`
18×	`times-frac`
17×	`add-cube-cbrt`
12×	`exp-prod` `distribute-lft-out`
9×	`add-log-exp`
7×	`log-pow`
6×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
5×	`pow1` `log-prod` `associate-/r*`
4×	`exp-sum`
3×	`sub-neg` `associate-/l*` `distribute-lft-out--`
2×	`exp-diff` `diff-log` `associate-/r/` `rem-exp-log`
1×	`cbrt-undiv` `log-div` `flip3--` `frac-2neg` `flip3-+` `div-exp` `rem-log-exp` `clear-num` `flip--` `flip-+` `div-inv`

Counts

4 → 91

Calls

4 calls:

35.0ms	(/ alpha (+ (+ alpha beta) 2.0))
330.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
172.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
367.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series267.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ alpha (+ (+ alpha beta) 2.0))
65.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
74.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
78.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify139.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	325	652
1	1066	606
2	4506	591
3	5002	591

prune239.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 2.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (+ alpha beta) 2.0))
0.3b	(/ (/ alpha (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0)))
0.4b	(/ alpha (sqrt (+ (+ alpha beta) 2.0)))
10.0b	(- (/ (/ alpha (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0))) 1.0)

rewrite674.0ms

Algorithm

rewrite-expression-head

Rules

536×	`*-un-lft-identity`
490×	`times-frac`
320×	`sqrt-prod`
244×	`add-sqr-sqrt`
219×	`add-cube-cbrt`
189×	`distribute-lft-out`
33×	`associate-/l*`
24×	`sqrt-div`
22×	`associate-/r/`
16×	`associate-/r*`
12×	`flip3-+` `flip-+`
11×	`add-exp-log` `add-cbrt-cube` `div-inv`
7×	`difference-of-squares`
6×	`add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
2×	`frac-2neg` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `flip--` `associate-/l/` `distribute-lft-out--`

Counts

4 → 381

Calls

4 calls:

30.0ms	(sqrt (+ (+ alpha beta) 2.0))
97.0ms	(/ (/ alpha (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0)))
35.0ms	(/ alpha (sqrt (+ (+ alpha beta) 2.0)))
482.0ms	(- (/ (/ alpha (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0))) 1.0)

series226.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(sqrt (+ (+ alpha beta) 2.0))
48.0ms	(/ (/ alpha (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0)))
71.0ms	(/ alpha (sqrt (+ (+ alpha beta) 2.0)))
75.0ms	(- (/ (/ alpha (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0))) 1.0)

simplify254.0ms

Algorithm

egg-herbie

Counts

393 → 393

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	838	5641
1	3003	4917
2	5002	4810

prune524.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 2.9b

regimes54.0ms

Accuracy

75.4% (3.1b remaining)

Error of 6.4b against oracle of 3.2b and baseline of 15.9b

bsearch19.0ms

Steps

Iters	Range		Point
3	101403271.01852646	122647865.33979332	121320078.19471414

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	38
1	46	38

end0.0ms

sample630.0ms

Algorithm

intervals

Results

142.0ms	5804×	body	80	valid
101.0ms	896×	body	1280	valid
95.0ms	8000×	pre	80	true
65.0ms	696×	body	640	valid
25.0ms	376×	body	320	valid
10.0ms	228×	body	160	valid