Details

sample37.0ms

Algorithm

intervals

Results

21.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify79.0ms

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: 3.1b

localize12.0ms

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))

2.9b

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

rewrite593.0ms

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:

167.0ms

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

250.0ms

(/ (/ (/ (+ (+ (+ 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))

141.0ms

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

series364.0ms

Counts

3 → 9

Calls

3 calls:

137.0ms

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

149.0ms

(/ (/ (/ (+ (+ (+ 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))

79.0ms

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

simplify136.0ms

Algorithm

egg-herbie

Counts

459 → 459

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1439	12925
1	5002	12452

prune931.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(* (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
2.9b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.9b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite751.0ms

Algorithm

rewrite-expression-head

Rules

257×	`times-frac`
216×	`*-un-lft-identity`
169×	`add-sqr-sqrt`
120×	`add-cube-cbrt`
114×	`associate-r`
91×	`sqrt-prod`
48×	`distribute-lft-out`
27×	`add-exp-log` `associate-l` `add-cbrt-cube`
14×	`associate-/r/`
12×	`unswap-sqr`
10×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+`
8×	`pow1`
7×	`div-inv` `associate-/l*`
6×	`sqrt-div` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`associate-/r*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 256

Calls

4 calls:

108.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
506.0ms	(* (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
60.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
61.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series437.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
145.0ms	(* (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
61.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
50.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify75.0ms

Algorithm

egg-herbie

Counts

268 → 268

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1168	5889
1	5001	5395

prune592.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.3b	(* (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
2.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
2.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

1494×	`times-frac`
1264×	`sqrt-prod`
987×	`*-un-lft-identity`
975×	`add-sqr-sqrt`
617×	`add-cube-cbrt`
238×	`swap-sqr`
161×	`distribute-lft-out`
132×	`associate-r` `associate-l`
84×	`associate-/r/`
49×	`unswap-sqr`
44×	`flip3-+` `flip-+`
42×	`div-inv`
29×	`associate-/l*`
22×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r*`
11×	`pow1` `sqrt-div`
7×	`cbrt-undiv` `div-exp`
5×	`sqrt-undiv` `associate-/l/`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `pow-prod-down` `associate-l/` `rem-square-sqrt` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 816

Calls

4 calls:

139.0ms	(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
604.0ms	(* (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
139.0ms	(/ (+ (+ (+ 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)))

series473.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
140.0ms	(* (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
75.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
73.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify285.0ms

Algorithm

egg-herbie

Counts

828 → 828

Iterations

Useful iterations: 1 (41.0ms)

Iter	Nodes	Cost
0	2204	31755
1	5001	30220

prune1.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))))
2.9b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.9b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.9b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite446.0ms

Algorithm

rewrite-expression-head

Rules

94×	`sqrt-prod`
52×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
35×	`sqrt-pow1`
30×	`pow1` `sqrt-div`
19×	`add-cube-cbrt` `pow1/2`
18×	`swap-sqr`
10×	`associate-r` `associate-l`
9×	`flip3-+` `pow-prod-up` `flip-+` `distribute-lft-out` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `add-log-exp`
3×	`rem-sqrt-square`
2×	`associate-r/` `associate-l/`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 136

Calls

4 calls:

261.0ms	(* (sqrt (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))))
60.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
60.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
59.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series194.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sqrt (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))))
51.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
46.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
51.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify56.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	244	1328
1	1017	1223
2	5001	1197

prune340.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.2b

regimes67.0ms

Accuracy

0% (2.6b remaining)

Error of 3.9b against oracle of 1.3b and baseline of 3.9b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	34
1	24	34

end0.0ms

sample849.0ms

Algorithm

intervals

Results

559.0ms	8000×	body	80	valid
146.0ms	8000×	pre	80	true