Details

sample24.0ms

Algorithm

intervals

Results

5.0ms	187×	body	80	valid
4.0ms	35×	body	1280	valid
3.0ms	256×	pre	80	true
1.0ms	15×	body	640	valid
1.0ms	16×	body	320	valid
0.0ms	3×	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: 16.3b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.6b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite117.0ms

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:

24.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
90.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series110.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
63.0ms	(+ (/ (- 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

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.7b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
1.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite377.0ms

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:

19.0ms	(/ beta (+ (+ alpha beta) 2.0))
19.0ms	(/ alpha (+ (+ alpha beta) 2.0))
233.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
103.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series239.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ beta (+ (+ alpha beta) 2.0))
51.0ms	(/ alpha (+ (+ alpha beta) 2.0))
63.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
78.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify46.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (35.0ms)

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

prune286.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.8b	(cbrt (+ (+ alpha beta) 2.0))
0.8b	(cbrt (+ (+ alpha beta) 2.0))
0.8b	(cbrt (+ (+ alpha beta) 2.0))
1.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite131.0ms

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:

9.0ms	(cbrt (+ (+ alpha beta) 2.0))
9.0ms	(cbrt (+ (+ alpha beta) 2.0))
9.0ms	(cbrt (+ (+ alpha beta) 2.0))
102.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series395.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(cbrt (+ (+ alpha beta) 2.0))
103.0ms	(cbrt (+ (+ alpha beta) 2.0))
104.0ms	(cbrt (+ (+ alpha beta) 2.0))
79.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify70.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (63.0ms)

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

prune275.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.7b	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
1.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
11.9b	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite699.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
14×	`log-prod`
11×	`add-log-exp`
10×	`distribute-lft-out--`
8×	`log-div` `difference-of-squares`
7×	`add-cube-cbrt` `flip3--` `exp-sum` `flip--`
6×	`pow1` `frac-sub`
5×	`add-exp-log`
4×	`exp-prod` `times-frac` `exp-diff` `diff-log` `add-cbrt-cube`
3×	`sub-neg`
2×	`log-pow` `associate--r+`
1×	`rem-log-exp` `rem-exp-log` `associate--r-`

Counts

4 → 80

Calls

4 calls:

233.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
180.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
100.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
182.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series334.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
65.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
79.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
126.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify112.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 3 (99.0ms)

Iter	Nodes	Cost
0	356	1237
1	1012	1165
2	4957	1120
3	5001	1116

prune236.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.2b

regimes132.0ms

Accuracy

77.9% (2.8b remaining)

Error of 5.9b against oracle of 3.1b and baseline of 15.8b

bsearch73.0ms

Steps

Iters	Range		Point
11	1.8524788714334402e-09	2.900155845354824e+24	16045536794042094.0

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	38
1	47	38

end0.0ms

sample598.0ms

Algorithm

intervals

Results

142.0ms	5846×	body	80	valid
111.0ms	856×	body	1280	valid
92.0ms	8000×	pre	80	true
72.0ms	735×	body	640	valid
27.0ms	382×	body	320	valid
9.0ms	181×	body	160	valid