Details

sample23.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify77.0ms

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

Filtered

1 candidates to 0 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: 4.1b

Counts

2 → 1

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))
3.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite121.0ms

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)))
42.0ms	(/ (/ (/ (+ (+ (+ 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)))

series365.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
134.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
146.0ms	(/ (/ (/ (+ (+ (+ 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))
72.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify140.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1492	13034
1	5002	12552

prune968.0ms

Filtered

477 candidates to 281 candidates (58.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	471	6	477
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	472	6	478

Merged error: 1.7b

Counts

478 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.2b	(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
3.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

444×	`times-frac`
384×	`sqrt-prod`
336×	`*-un-lft-identity`
236×	`add-sqr-sqrt` `add-cube-cbrt`
50×	`distribute-lft-out` `associate-/l*`
36×	`associate-/r/`
20×	`flip3-+` `flip-+`
18×	`associate-/r*` `div-inv`
12×	`add-exp-log` `add-cbrt-cube`
6×	`sqrt-div` `associate-/l/`
4×	`pow1` `cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `add-log-exp`
2×	`sqrt-undiv`

Counts

4 → 408

Calls

4 calls:

25.0ms	(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
21.0ms	(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series533.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
189.0ms	(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
76.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
78.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify139.0ms

Algorithm

egg-herbie

Counts

420 → 420

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	598	10288
1	2167	9666
2	5002	9512

prune1.2s

Filtered

420 candidates to 244 candidates (58.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	420	0	420
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	420	6	426

Merged error: 1.7b

Counts

426 → 6

localize14.0ms

Local error

Found 4 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) (* 2.0 1.0)) 1.0) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
0.4b	(/ (/ 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)))))
3.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite996.0ms

Algorithm

rewrite-expression-head

Rules

14603×	`times-frac`
8256×	`*-un-lft-identity`
5324×	`add-sqr-sqrt` `add-cube-cbrt`
1466×	`distribute-lft-out`
516×	`associate-/r/`
512×	`div-inv`
311×	`associate-/r*`
252×	`flip3-+` `flip-+`
114×	`add-exp-log`
96×	`div-exp`
52×	`add-cbrt-cube`
39×	`associate-/l*`
34×	`cbrt-undiv`
20×	`1-exp`
8×	`rec-exp`
6×	`associate-/l/`
4×	`pow1` `frac-2neg` `clear-num` `add-log-exp`

Counts

4 → 3941

Calls

4 calls:

20.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
45.0ms	(/ (+ (+ (+ 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))))
127.0ms	(/ (/ 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)))

series578.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
219.0ms	(/ (+ (+ (+ 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))))
150.0ms	(/ (/ 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)))))
72.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.4s

Algorithm

egg-herbie

Counts

3953 → 3953

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5001	152207

prune6.6s

Filtered

3953 candidates to 1493 candidates (37.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	3951	2	3953
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	3953	6	3959

Merged error: 1.7b

Counts

3959 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 (/ (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) 1)) (/ (sqrt (+ (+ (+ 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)))))
0.1b	(/ (sqrt (+ (+ (+ 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))))
0.6b	(/ 1 (/ (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) 1))
3.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite8.3s

Algorithm

rewrite-expression-head

Rules

179149×	`times-frac`
91603×	`*-un-lft-identity`
63711×	`add-sqr-sqrt` `add-cube-cbrt`
35068×	`sqrt-prod`
13946×	`distribute-lft-out`
5112×	`associate-/r/`
4093×	`div-inv`
2303×	`flip3-+` `flip-+`
513×	`associate-/r*`
194×	`add-exp-log`
167×	`div-exp`
94×	`associate-/l*`
74×	`add-cbrt-cube`
52×	`cbrt-undiv`
30×	`1-exp`
15×	`rec-exp`
5×	`pow1` `associate-/l/`
4×	`frac-2neg` `clear-num` `add-log-exp`
2×	`sqrt-div`
1×	`pow-flip` `inv-pow`

Counts

4 → 35237

Calls

4 calls:

816.0ms	(/ (/ 1 (/ (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) 1)) (/ (sqrt (+ (+ (+ 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)))))
44.0ms	(/ (sqrt (+ (+ (+ 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))))
13.0ms	(/ 1 (/ (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) 1))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series667.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(/ (/ 1 (/ (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) 1)) (/ (sqrt (+ (+ (+ 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)))))
374.0ms	(/ (sqrt (+ (+ (+ 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))))
63.0ms	(/ 1 (/ (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) 1))
77.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify19.3s

Algorithm

egg-herbie

Counts

35249 → 35249

Iterations

Useful iterations: 0 (479.0ms)

Iter	Nodes	Cost
0	26037	2085545

prune1.5m

Filtered

35249 candidates to 14180 candidates (40.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	35247	2	35249
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	35247	8	35255

Merged error: 1.7b

Counts

35255 → 8

regimes81.0ms

Accuracy

50.4% (1.3b remaining)

Error of 2.4b against oracle of 1.0b and baseline of 3.7b

bsearch115.0ms

Steps

Iters	Range		Point
9	3.2413021921128853e+209	4.9138192989047715e+214	6.012482012918054e+212

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	52
1	52	52

end0.0ms

sample542.0ms

Algorithm

intervals

Results

296.0ms	8000×	body	80	valid
103.0ms	8000×	pre	80	true