Details

sample30.0ms

Algorithm

intervals

Results

15.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify113.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (111.0ms)

Iter	Nodes	Cost
0	4949	35
1	4949	35

prune190.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 3.1b

Counts

2 → 2

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

rewrite118.0ms

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)
24.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
38.0ms	(/ (/ (/ (+ (+ (+ 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))
15.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
20.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
28.0ms	(/ (/ (/ (+ (+ (+ 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))
12.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify185.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4973	23485
1	4973	23485

prune1.5s

Filtered

288 candidates to 477 candidates (-65.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	469	8	477
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	471	8	479

Merged error: 0.8b

Counts

479 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ alpha beta) (* beta alpha))
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 3.0)))
2.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

954×	`times-frac`
828×	`*-un-lft-identity`
383×	`add-sqr-sqrt` `add-cube-cbrt`
253×	`distribute-lft-out`
82×	`associate-/l*`
62×	`associate-/r/`
33×	`flip3-+` `flip-+`
31×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/r*`
10×	`cbrt-undiv` `div-exp`
9×	`add-log-exp`
4×	`pow1` `associate-/l/`
3×	`frac-2neg` `clear-num` `sum-log`
1×	`+-commutative` `associate-+l+`

Counts

4 → 524

Calls

4 calls:

6.0ms	(+ (+ alpha beta) (* beta alpha))
21.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
40.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ beta 3.0)))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ (+ alpha beta) (* beta alpha))
25.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
22.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ beta 3.0)))
12.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify165.0ms

Algorithm

egg-herbie

Counts

536 → 536

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5040	24742

prune1.3s

Filtered

286 candidates to 536 candidates (-87.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	530	6	536
Fresh	6	1	7
Picked	0	1	1
Done	0	0	0
Total	536	8	544

Merged error: 0.8b

Counts

544 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ alpha (+ beta (* 1.0 2.0))))
0.0b	(/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta 3.0)))
0.1b	(* (/ 1 (+ alpha (+ beta (* 1.0 2.0)))) (/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta 3.0))))
2.9b	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

845×	`*-un-lft-identity`
539×	`times-frac`
374×	`distribute-lft-out`
226×	`add-sqr-sqrt`
196×	`add-cube-cbrt`
136×	`associate-r`
54×	`add-exp-log`
34×	`add-cbrt-cube` `associate-/l*`
32×	`associate-/r/`
24×	`div-exp`
18×	`associate-l`
17×	`flip3-+` `flip-+`
16×	`div-inv`
14×	`cbrt-undiv`
13×	`associate-/r*`
12×	`prod-exp`
9×	`unswap-sqr`
7×	`pow1`
6×	`cbrt-unprod`
4×	`rec-exp` `1-exp` `add-log-exp`
3×	`frac-2neg` `clear-num` `associate-/l/`
1×	`frac-times` `pow-flip` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `inv-pow`

Counts

4 → 453

Calls

4 calls:

6.0ms	(/ 1 (+ alpha (+ beta (* 1.0 2.0))))
23.0ms	(/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta 3.0)))
76.0ms	(* (/ 1 (+ alpha (+ beta (* 1.0 2.0)))) (/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta 3.0))))
14.0ms	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

series62.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1 (+ alpha (+ beta (* 1.0 2.0))))
23.0ms	(/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta 3.0)))
22.0ms	(* (/ 1 (+ alpha (+ beta (* 1.0 2.0)))) (/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta 3.0))))
12.0ms	(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

simplify122.0ms

Algorithm

egg-herbie

Counts

465 → 465

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5223	14094

prune733.0ms

Filtered

201 candidates to 465 candidates (-131.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	465	0	465
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	465	8	473

Merged error: 0.8b

Counts

473 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))
0.1b	(/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))
2.8b	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
2.8b	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

140×	`*-un-lft-identity`
64×	`times-frac`
60×	`sqrt-prod`
54×	`distribute-lft-out`
46×	`add-sqr-sqrt`
44×	`add-cube-cbrt`
16×	`associate-/l*`
8×	`add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube`
6×	`pow1` `flip3-+` `flip-+`
4×	`associate-/r/` `associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 154

Calls

4 calls:

16.0ms	(/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))
14.0ms	(/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))
7.0ms	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
7.0ms	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))

series108.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))
43.0ms	(/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))
9.0ms	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
9.0ms	(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))

simplify52.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5093	3988

prune312.0ms

Filtered

98 candidates to 166 candidates (-69.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	166	8	174

Merged error: 0.8b

Counts

174 → 8

regimes129.0ms

Accuracy

55% (1.1b remaining)

Error of 2.2b against oracle of 1.2b and baseline of 3.5b

bsearch21.0ms

Steps

Iters	Range		Point
9	6.300476410860683e+173	2.597255871059942e+180	7.012982988649128e+174

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	60
1	53	60

end0.0ms

sample829.0ms

Algorithm

intervals

Results

479.0ms	8000×	body	80	valid
125.0ms	8000×	pre	80	true

Details

sample30.0ms

simplify113.0ms

prune190.0ms

localize12.0ms

rewrite118.0ms

series63.0ms

simplify185.0ms

prune1.5s

localize13.0ms

rewrite126.0ms

series63.0ms

simplify165.0ms

prune1.3s

localize15.0ms

rewrite155.0ms

series62.0ms

simplify122.0ms

prune733.0ms

localize15.0ms

rewrite50.0ms

series108.0ms

simplify52.0ms

prune312.0ms

regimes129.0ms

bsearch21.0ms

simplify2.0ms

end0.0ms

sample829.0ms

Profiling