Details

sample34.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify80.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	17
1	114	17
2	563	17
3	4164	17
4	5002	17

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.6b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))

0.1b

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))

2.4b

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite599.0ms

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
583×	`*-un-lft-identity`
339×	`add-sqr-sqrt` `add-cube-cbrt`
122×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
28×	`flip3-+` `flip-+`
27×	`div-inv`
19×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp` `associate-/r*`
4×	`associate-/l/`
3×	`pow1` `frac-2neg` `clear-num` `add-log-exp`

Counts

3 → 450

Calls

3 calls:

169.0ms

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))

252.0ms

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))

144.0ms

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series382.0ms

Counts

3 → 9

Calls

3 calls:

146.0ms

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))

155.0ms

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))

80.0ms

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify133.0ms

Algorithm

egg-herbie

Counts

459 → 459

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1439	12925
1	5002	12452

prune951.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.9b

localize17.0ms

Local error

Found 4 expressions with local error:

2.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
2.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
13.4b	(sqrt (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
13.4b	(sqrt (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))

rewrite722.0ms

Algorithm

rewrite-expression-head

Rules

1236×	`times-frac`
888×	`*-un-lft-identity`
508×	`add-sqr-sqrt`
492×	`sqrt-prod`
488×	`add-cube-cbrt`
200×	`distribute-lft-out`
72×	`associate-/r/`
38×	`flip3-+` `flip-+`
36×	`div-inv`
8×	`add-exp-log` `rem-sqrt-square` `add-cbrt-cube` `associate-/l*`
6×	`pow1` `associate-/r*`
4×	`associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `clear-num`

Counts

4 → 590

Calls

4 calls:

142.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
140.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
190.0ms	(sqrt (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
189.0ms	(sqrt (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))

series931.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
75.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
480.0ms	(sqrt (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
299.0ms	(sqrt (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))

simplify201.0ms

Algorithm

egg-herbie

Counts

602 → 602

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1580	20724
1	5001	20206

prune1.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.9b

localize26.0ms

Local error

Found 4 expressions with local error:

2.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
2.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
8.7b	(sqrt (/ (/ (cbrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
13.4b	(sqrt (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))

rewrite816.0ms

Algorithm

rewrite-expression-head

Rules

1965×	`times-frac`
1392×	`*-un-lft-identity`
1035×	`sqrt-prod`
809×	`add-sqr-sqrt`
776×	`add-cube-cbrt`
436×	`cbrt-prod`
308×	`distribute-lft-out`
96×	`associate-/r/`
50×	`flip3-+` `flip-+`
48×	`div-inv`
12×	`rem-sqrt-square`
10×	`sqrt-div`
8×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
6×	`pow1` `associate-/r*`
4×	`associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num`

Counts

4 → 882

Calls

4 calls:

142.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
143.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
232.0ms	(sqrt (/ (/ (cbrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
193.0ms	(sqrt (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))

series1.1s

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
79.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
603.0ms	(sqrt (/ (/ (cbrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
303.0ms	(sqrt (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))

simplify330.0ms

Algorithm

egg-herbie

Counts

894 → 894

Iterations

Useful iterations: 1 (50.0ms)

Iter	Nodes	Cost
0	3664	34567
1	5002	34017

prune3.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.7b	(* (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
2.4b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.4b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite443.0ms

Algorithm

rewrite-expression-head

Rules

309×	`times-frac`
212×	`*-un-lft-identity`
187×	`sqrt-prod`
174×	`add-sqr-sqrt`
164×	`add-cube-cbrt`
27×	`associate-/l*`
24×	`distribute-lft-out`
18×	`sqrt-div`
16×	`flip3-+` `associate-/r/` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
8×	`div-inv`
7×	`associate-l`
6×	`associate-r` `associate-/r*`
4×	`frac-times` `sqrt-pow1` `pow1/2` `add-log-exp` `unswap-sqr`
3×	`cbrt-undiv` `div-exp` `pow-prod-down`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`frac-2neg` `sqrt-unprod` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `associate-/l/`

Counts

4 → 283

Calls

4 calls:

142.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
159.0ms	(* (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
60.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
63.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series346.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
62.0ms	(* (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
53.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
54.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify138.0ms

Algorithm

egg-herbie

Counts

295 → 295

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	1017	6640
1	4202	6295
2	5001	6281

prune821.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.9b

regimes102.0ms

Accuracy

80.5% (0.5b remaining)

Error of 1.7b against oracle of 1.2b and baseline of 3.8b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	54
1	27	54

end0.0ms

sample845.0ms

Algorithm

intervals

Results

558.0ms	8000×	body	80	valid
133.0ms	8000×	pre	80	true