Details

sample25.0ms

Algorithm

intervals

Results

4.0ms	176×	body	80	valid
3.0ms	31×	body	1280	valid
3.0ms	256×	pre	80	true
2.0ms	21×	body	640	valid
1.0ms	18×	body	320	valid
0.0ms	10×	body	160	valid

simplify73.0ms

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: 18.7b

localize8.0ms

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)

rewrite203.0ms

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))
155.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series99.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
58.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify43.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (30.0ms)

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

prune153.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 17.8b

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

rewrite652.0ms

Algorithm

rewrite-expression-head

Rules

71×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
32×	`times-frac`
24×	`add-cube-cbrt` `distribute-lft-out`
11×	`add-log-exp`
10×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`pow1` `diff-log` `associate-/r/` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `frac-sub` `flip-+` `div-inv` `associate--r+`
1×	`associate--r-`

Counts

4 → 111

Calls

4 calls:

399.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
36.0ms	(/ beta (+ (+ alpha beta) 2.0))
36.0ms	(/ alpha (+ (+ alpha beta) 2.0))
177.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series221.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
42.0ms	(/ beta (+ (+ alpha beta) 2.0))
46.0ms	(/ alpha (+ (+ alpha beta) 2.0))
72.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify48.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	450	903
1	1596	871
2	5002	859

prune288.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.8b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite225.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
15×	`cbrt-prod`
12×	`add-sqr-sqrt`
9×	`distribute-lft-out`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3-+` `pow1/3` `flip-+`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `times-frac` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

16.0ms	(cbrt (+ (+ alpha beta) 2.0))
16.0ms	(cbrt (+ (+ alpha beta) 2.0))
16.0ms	(cbrt (+ (+ alpha beta) 2.0))
175.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series352.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(cbrt (+ (+ alpha beta) 2.0))
93.0ms	(cbrt (+ (+ alpha beta) 2.0))
93.0ms	(cbrt (+ (+ alpha beta) 2.0))
72.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify70.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (62.0ms)

Iter	Nodes	Cost
0	278	567
1	708	537
2	2658	521
3	5001	512

prune278.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.8b	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
2.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
11.5b	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite817.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 95

Calls

4 calls:

35.0ms	(/ alpha (+ (+ alpha beta) 2.0))
301.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
173.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
303.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ alpha (+ (+ alpha beta) 2.0))
60.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
74.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
116.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify49.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	462	1120
1	1490	1058
2	5001	1031

prune272.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.8b

regimes246.0ms

Accuracy

99.3% (0.1b remaining)

Error of 3.2b against oracle of 3.1b and baseline of 15.9b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	29
1	40	29

end0.0ms

sample615.0ms

Algorithm

intervals

Results

138.0ms	5875×	body	80	valid
95.0ms	856×	body	1280	valid
93.0ms	8000×	pre	80	true
62.0ms	692×	body	640	valid
31.0ms	390×	body	320	valid
8.0ms	187×	body	160	valid