Details

sample190.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 43.768318%

Space saved by search: 43.768318%

Guaranteed chance to sample good point: 98.831177%

Results

15.0ms	256×	body	80	valid
4.0ms	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

prune3.0ms

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: 2.6b

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

rewrite113.0ms

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)
18.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
37.0ms	(/ (/ (/ (+ (+ (+ 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))
13.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
21.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
23.0ms	(/ (/ (/ (+ (+ (+ 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)))

simplify141.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1492	13034
1	5002	12552

prune1.4s

Filtered

281 candidates to 477 candidates (-69.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	467	10	477
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	468	10	478

Merged error: 0.9b

Counts

478 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite399.0ms

Algorithm

rewrite-expression-head

Rules

1471×	`times-frac`
1040×	`*-un-lft-identity`
673×	`add-sqr-sqrt`
627×	`sqrt-prod`
590×	`add-cube-cbrt`
258×	`associate-r`
225×	`distribute-lft-out`
88×	`associate-/r/`
71×	`associate-/l*`
63×	`associate-l`
46×	`flip3-+` `flip-+`
44×	`div-inv`
20×	`unswap-sqr`
15×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*`
6×	`pow1`
5×	`associate-/l/`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`frac-2neg` `sqrt-div` `clear-num`
2×	`prod-exp` `cbrt-unprod`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 761

Calls

4 calls:

251.0ms	(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 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)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
39.0ms	(/ (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))
13.0ms	(/ (+ (+ (+ 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)))

series71.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 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)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
22.0ms	(/ (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))
12.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
13.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify249.0ms

Algorithm

egg-herbie

Counts

773 → 773

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	1953	24980
1	5001	24018

prune5.0s

Filtered

494 candidates to 773 candidates (-56.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	773	0	773
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	773	10	783

Merged error: 0.9b

Counts

783 → 10

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))))
0.3b	(/ 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)))))
2.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite315.0ms

Algorithm

rewrite-expression-head

Rules

3939×	`times-frac`
2530×	`*-un-lft-identity`
1518×	`add-sqr-sqrt` `add-cube-cbrt`
506×	`distribute-lft-out`
311×	`associate-/r*`
186×	`associate-/r/`
96×	`div-inv`
92×	`flip3-+` `flip-+`
54×	`add-exp-log`
36×	`div-exp`
34×	`add-cbrt-cube`
29×	`associate-/l*`
20×	`cbrt-undiv`
5×	`pow1` `associate-/l/`
4×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `add-log-exp`
1×	`pow-flip` `inv-pow`

Counts

4 → 1462

Calls

4 calls:

20.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
43.0ms	(/ (+ (+ (+ 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))))
66.0ms	(/ 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)))

series101.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
42.0ms	(/ (+ (+ (+ 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))))
23.0ms	(/ 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)))))
12.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify485.0ms

Algorithm

egg-herbie

Counts

1474 → 1474

Iterations

Useful iterations: 1 (72.0ms)

Iter	Nodes	Cost
0	3694	48037
1	5001	46600

prune6.9s

Filtered

759 candidates to 1474 candidates (-94.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	1473	1	1474
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	1474	10	1484

Merged error: 0.9b

Counts

1484 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (+ (+ alpha beta) (* 2.0 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))) (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
2.7b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.7b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.7b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite332.0ms

Algorithm

rewrite-expression-head

Rules

603×	`times-frac`
424×	`*-un-lft-identity`
375×	`add-sqr-sqrt`
279×	`cbrt-prod`
244×	`add-cube-cbrt`
194×	`associate-l`
114×	`associate-r`
90×	`distribute-lft-out`
40×	`add-exp-log`
28×	`add-cbrt-cube` `unswap-sqr`
25×	`associate-/r/`
20×	`cbrt-div`
18×	`cbrt-undiv` `div-exp`
15×	`flip3-+` `flip-+`
13×	`div-inv`
9×	`prod-exp` `cbrt-unprod`
6×	`pow1`
4×	`add-log-exp`
3×	`pow1/3`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 408

Calls

4 calls:

278.0ms	(* (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (+ (+ alpha beta) (* 2.0 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))) (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
6.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
6.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series75.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (+ (+ alpha beta) (* 2.0 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))) (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
15.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
21.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
15.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify140.0ms

Algorithm

egg-herbie

Counts

420 → 420

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1780	13550
1	5001	13120

prune2.6s

Filtered

315 candidates to 420 candidates (-33.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	420	0	420
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	420	10	430

Merged error: 0.9b

Counts

430 → 10

regimes147.0ms

Accuracy

54.2% (1.3b remaining)

Error of 2.5b against oracle of 1.2b and baseline of 4.0b

bsearch25.0ms

Steps

Iters	Range		Point
8	2.71869189743255e+186	2.442944090390655e+189	2.844213818584587e+186

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	48
1	43	48

end0.0ms

sample1.0s

Algorithm

intervals

sampling

Space saved by range analysis: 43.768318%

Space saved by search: 43.768318%

Guaranteed chance to sample good point: 98.831177%

Results

494.0ms	8000×	body	80	valid
134.0ms	8000×	pre	80	true

Details

sample190.0ms

simplify79.0ms

prune3.0ms

localize12.0ms

rewrite113.0ms

series64.0ms

simplify141.0ms

prune1.4s

localize15.0ms

rewrite399.0ms

series71.0ms

simplify249.0ms

prune5.0s

localize14.0ms

rewrite315.0ms

series101.0ms

simplify485.0ms

prune6.9s

localize17.0ms

rewrite332.0ms

series75.0ms

simplify140.0ms

prune2.6s

regimes147.0ms

bsearch25.0ms

simplify2.0ms

end0.0ms

sample1.0s

Profiling