Details

sample24.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify78.0ms

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: 4.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
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))
4.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
586×	`*-un-lft-identity`
340×	`add-sqr-sqrt` `add-cube-cbrt`
123×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
29×	`flip3-+` `flip-+`
27×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
13×	`add-log-exp`
10×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`sum-log`
4×	`pow1` `associate-/l/`
3×	`frac-2neg` `clear-num`
1×	`+-commutative` `associate-+l+`

Counts

4 → 465

Calls

4 calls:

8.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
19.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
41.0ms	(/ (/ (/ (+ (+ (+ 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))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series425.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
139.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
162.0ms	(/ (/ (/ (+ (+ (+ 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))
111.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify139.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1492	13034
1	5002	12552

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3)
0.1b	(/ (/ (cbrt (pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
4.1b	(cbrt (pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3))
4.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

1659×	`times-frac`
1185×	`*-un-lft-identity`
689×	`add-sqr-sqrt` `add-cube-cbrt`
672×	`cbrt-prod`
306×	`unpow-prod-down` `cube-prod`
248×	`distribute-lft-out`
145×	`associate-/l*`
82×	`associate-/r/`
42×	`flip3-+` `flip-+`
41×	`div-inv`
17×	`cube-mult` `unpow3` `sqr-pow`
14×	`add-exp-log`
13×	`add-cbrt-cube`
7×	`associate-/r*`
5×	`pow1` `cbrt-undiv` `div-exp`
4×	`add-log-exp`
3×	`pow-unpow` `associate-/l/`
2×	`cube-div` `frac-2neg` `pow-exp` `clear-num` `rem-cube-cbrt`
1×	`pow-to-exp` `cbrt-div` `pow-pow` `pow1/3` `rem-cbrt-cube`

Counts

4 → 869

Calls

4 calls:

14.0ms	(pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3)
57.0ms	(/ (/ (cbrt (pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
14.0ms	(cbrt (pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series490.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3)
142.0ms	(/ (/ (cbrt (pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
74.0ms	(cbrt (pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3))
76.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify266.0ms

Algorithm

egg-herbie

Counts

881 → 881

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1984	26584
1	5001	26211

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.1b	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
4.5b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
4.5b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
109×	`sqrt-prod`
94×	`*-un-lft-identity`
74×	`add-sqr-sqrt`
64×	`add-cube-cbrt`
48×	`associate-/l*`
26×	`sqrt-div`
18×	`add-exp-log` `add-cbrt-cube`
16×	`flip3-+` `flip-+`
15×	`distribute-lft-out`
12×	`associate-/r/`
10×	`pow1`
8×	`frac-times`
7×	`associate-l`
6×	`cbrt-undiv` `div-exp` `associate-r`
4×	`sqrt-pow1` `pow1/2` `associate-r/` `associate-l/` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod` `div-inv`
2×	`rem-sqrt-square`
1×	`frac-2neg` `sqrt-unprod` `clear-num` `associate-/r` `-commutative` `associate-/l/`

Counts

4 → 195

Calls

4 calls:

16.0ms	(* (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
35.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
7.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series305.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
147.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
44.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
51.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify106.0ms

Algorithm

egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	832	4198
1	3682	3888
2	5001	3837

prune634.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
0.0b	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
0.6b	(/ (/ (cbrt 1) 1) (* (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))))
4.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

325×	`times-frac`
286×	`*-un-lft-identity`
159×	`add-sqr-sqrt`
150×	`add-cube-cbrt`
77×	`associate-l`
68×	`distribute-lft-out`
66×	`add-exp-log`
48×	`add-cbrt-cube`
36×	`div-exp`
30×	`associate-/l*`
27×	`associate-/r/`
25×	`cbrt-undiv`
22×	`associate-/r*`
18×	`cbrt-prod`
16×	`flip3-+` `flip-+`
15×	`div-inv`
12×	`prod-exp`
9×	`cbrt-unprod`
6×	`pow1`
5×	`associate-/l/`
4×	`frac-times` `1-exp` `associate-*r/` `add-log-exp`
3×	`frac-2neg` `associate-r` `clear-num` `unswap-sqr`
2×	`associate-*l/`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `*-commutative`

Counts

4 → 332

Calls

4 calls:

39.0ms	(* (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
21.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
32.0ms	(/ (/ (cbrt 1) 1) (* (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series574.0ms

Counts

4 → 12

Calls

4 calls:

223.0ms	(* (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
120.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
154.0ms	(/ (/ (cbrt 1) 1) (* (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))))
77.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify96.0ms

Algorithm

egg-herbie

Counts

344 → 344

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1560	7320
1	5002	6718

prune834.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.2b

regimes69.0ms

Accuracy

64.6% (1.4b remaining)

Error of 1.5b against oracle of 0.1b and baseline of 4.1b

bsearch79.0ms

Steps

Iters	Range		Point
9	3.899060091422951e+156	6.680668213688069e+161	6.2833328260900076e+156

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	30
1	42	30

end0.0ms

sample531.0ms

Algorithm

intervals

Results

297.0ms	8000×	body	80	valid
95.0ms	8000×	pre	80	true