Details

sample24.0ms

Algorithm

intervals

Results

5.0ms	188×	body	80	valid
3.0ms	256×	pre	80	true
3.0ms	26×	body	1280	valid
3.0ms	28×	body	640	valid
1.0ms	12×	body	320	valid
0.0ms	2×	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.3b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
0.9b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite115.0ms

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:

25.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
87.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series107.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
58.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify37.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (29.0ms)

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

prune148.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.6b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.9b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite369.0ms

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))
227.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
20.0ms	(/ alpha (+ (+ alpha beta) 2.0))
98.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series239.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ beta (+ (+ alpha beta) 2.0))
64.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
45.0ms	(/ alpha (+ (+ alpha beta) 2.0))
78.0ms	(- (/ 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

prune288.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.8b

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))
0.9b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
0.9b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite519.0ms

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:

188.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
18.0ms	(/ alpha (+ (+ alpha beta) 2.0))
211.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
99.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series270.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
44.0ms	(/ alpha (+ (+ alpha beta) 2.0))
77.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
76.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify141.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	325	652
1	1064	606
2	4504	591
3	5001	591

prune263.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.8b

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))
0.9b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite126.0ms

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))
8.0ms	(cbrt (+ (+ alpha beta) 2.0))
9.0ms	(cbrt (+ (+ alpha beta) 2.0))
99.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series372.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(cbrt (+ (+ alpha beta) 2.0))
98.0ms	(cbrt (+ (+ alpha beta) 2.0))
98.0ms	(cbrt (+ (+ alpha beta) 2.0))
77.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify69.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (61.0ms)

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

prune256.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.8b

regimes116.0ms

Accuracy

98% (0.3b remaining)

Error of 3.2b against oracle of 3.0b and baseline of 16.3b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	28
1	35	28

end0.0ms

sample589.0ms

Algorithm

intervals

Results

140.0ms	5765×	body	80	valid
106.0ms	855×	body	1280	valid
91.0ms	8000×	pre	80	true
68.0ms	733×	body	640	valid
30.0ms	436×	body	320	valid
13.0ms	211×	body	160	valid