Details

sample24.0ms

Algorithm

intervals

Results

5.0ms	183×	body	80	valid
4.0ms	37×	body	640	valid
3.0ms	256×	pre	80	true
2.0ms	18×	body	1280	valid
1.0ms	12×	body	320	valid
0.0ms	6×	body	160	valid

simplify71.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.3b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.8b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite105.0ms

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:

22.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
81.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series104.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
60.0ms	(+ (/ (- 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

prune149.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.4b

localize9.0ms

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))
1.8b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite347.0ms

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:

213.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
18.0ms	(/ beta (+ (+ alpha beta) 2.0))
17.0ms	(/ alpha (+ (+ alpha beta) 2.0))
96.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series230.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
45.0ms	(/ beta (+ (+ alpha beta) 2.0))
49.0ms	(/ alpha (+ (+ alpha beta) 2.0))
76.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify47.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (36.0ms)

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

prune286.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
1.8b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
1.8b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite326.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

17.0ms	(/ beta (+ (+ alpha beta) 2.0))
17.0ms	(/ alpha (+ (+ alpha beta) 2.0))
196.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
93.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series245.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ beta (+ (+ alpha beta) 2.0))
49.0ms	(/ alpha (+ (+ alpha beta) 2.0))
76.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
75.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify37.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	368	741
1	1178	696
2	5001	683

prune309.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ alpha beta) 2.0))
0.1b	(* beta (/ 1 (+ (+ alpha beta) 2.0)))
1.8b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
1.8b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite354.0ms

Algorithm

rewrite-expression-head

Rules

66×	`*-un-lft-identity`
43×	`add-sqr-sqrt`
34×	`times-frac`
26×	`add-cube-cbrt`
21×	`associate-r` `distribute-lft-out`
17×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`pow1`
7×	`log-pow`
6×	`exp-prod` `add-log-exp`
5×	`log-prod` `associate-/r*`
4×	`div-exp` `prod-exp` `associate-/r/` `difference-of-squares`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `sub-neg` `rec-exp` `flip3-+` `1-exp` `exp-sum` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out--`
1×	`log-div` `flip3--` `pow-flip` `frac-2neg` `exp-diff` `diff-log` `associate-r/` `rem-log-exp` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `flip--` `inv-pow`

Counts

4 → 121

Calls

4 calls:

18.0ms	(/ 1 (+ (+ alpha beta) 2.0))
42.0ms	(* beta (/ 1 (+ (+ alpha beta) 2.0)))
198.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
92.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series240.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ 1 (+ (+ alpha beta) 2.0))
46.0ms	(* beta (/ 1 (+ (+ alpha beta) 2.0)))
76.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
77.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify49.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	427	777
1	1670	686
2	5001	630

prune270.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.7b

regimes108.0ms

Accuracy

77.8% (2.8b remaining)

Error of 6.0b against oracle of 3.2b and baseline of 15.9b

bsearch53.0ms

Steps

Iters	Range		Point
8	523281070680199.5	9.528795435980767e+18	27638105531957988.0

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	27
1	43	27

end0.0ms

sample622.0ms

Algorithm

intervals

Results

147.0ms	5813×	body	80	valid
116.0ms	851×	body	1280	valid
101.0ms	8000×	pre	80	true
78.0ms	746×	body	640	valid
28.0ms	379×	body	320	valid
10.0ms	211×	body	160	valid