Details

sample56.0ms

Algorithm

intervals

Results

24.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify971.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	17	53
1	60	52
2	295	48
3	1807	48
done	5001	48

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 40.7b

localize26.0ms

Local error

Found 4 expressions with local error:

4.7b	(/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (/ (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))))
31.7b	(/ (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))))
36.8b	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))
36.8b	(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

1058×	`times-frac`
426×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
85×	`div-inv`
63×	`associate-/r*`
52×	`add-cbrt-cube` `add-exp-log`
30×	`cbrt-undiv` `div-exp`
14×	`associate-/l*`
10×	`associate-/r/`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l/`
2×	`associate-*r/`
1×	`flip3-+` `flip-+`

Counts

4 → 517

Calls

4 calls:

80.0ms	(/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (/ (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))))
8.0ms	(/ (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))))
9.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))
33.0ms	(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))

series2.0s

Counts

4 → 12

Calls

4 calls:

1.2s	(/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (/ (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))))
390.0ms	(/ (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))))
189.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))
156.0ms	(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))

simplify1.5s

Counts

529 → 529

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	913	40134
1	3274	39500
done	5000	38245

prune4.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 37.7b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (+ alpha beta) i) (fma 2.0 i (+ alpha beta)))
4.8b	(/ (/ i 1) (/ (/ (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))) (/ (+ (+ alpha beta) i) (fma 2.0 i (+ alpha beta)))))
31.7b	(/ (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))))
36.8b	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

rewrite3.8s

Algorithm

rewrite-expression-head

Rules

57110×	`times-frac`
30086×	`*-un-lft-identity`
20826×	`add-sqr-sqrt` `add-cube-cbrt`
5556×	`distribute-lft-out`
2544×	`div-inv`
860×	`associate-/r*`
282×	`associate-/r/`
107×	`add-exp-log`
85×	`div-exp`
78×	`add-cbrt-cube`
56×	`cbrt-undiv`
24×	`associate-/l*`
7×	`1-exp`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l/`
1×	`flip3-+` `flip-+`

Counts

4 → 11976

Calls

4 calls:

86.0ms	(/ (+ (+ alpha beta) i) (fma 2.0 i (+ alpha beta)))
476.0ms	(/ (/ i 1) (/ (/ (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))) (/ (+ (+ alpha beta) i) (fma 2.0 i (+ alpha beta)))))
23.0ms	(/ (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))))
8.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

series1.9s

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (+ (+ alpha beta) i) (fma 2.0 i (+ alpha beta)))
1.2s	(/ (/ i 1) (/ (/ (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))) (/ (+ (+ alpha beta) i) (fma 2.0 i (+ alpha beta)))))
384.0ms	(/ (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))))
216.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

simplify8.2s

Counts

11988 → 11988

Iterations

Useful iterations: 0 (1.8s)

Iter	Nodes	Cost
0	15252	1235767
done	15252	1235767

prune1.4m

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 32.1b

localize40.0ms

Local error

Found 4 expressions with local error:

36.7b	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
36.7b	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
40.0b	(sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))
40.0b	(sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-exp-log` `log1p-expm1-u` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

1.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
1.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
1.0ms	(sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))
1.0ms	(sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))

series717.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
64.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
291.0ms	(sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))
299.0ms	(sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))

simplify980.0ms

Counts

72 → 72

Iterations

Useful iterations: 3 (442.0ms)

Iter	Nodes	Cost
0	88	1332
1	205	1178
2	643	1104
3	3715	1088
done	5000	1088

prune444.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 32.1b

localize30.0ms

Local error

Found 4 expressions with local error:

36.9b	(/ (sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0))) (fma beta alpha (* i (+ (+ alpha beta) i))))
37.8b	(/ (/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (/ (sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0))) (fma beta alpha (* i (+ (+ alpha beta) i))))) (/ (sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0))) (/ 1 (fma 2.0 i (+ alpha beta)))))
40.0b	(sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))
40.0b	(sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))

rewrite2.2s

Algorithm

rewrite-expression-head

Rules

63399×	`times-frac`
22487×	`add-sqr-sqrt`
22485×	`*-un-lft-identity` `add-cube-cbrt`
11550×	`sqrt-prod`
3642×	`div-inv`
245×	`associate-/r/`
186×	`add-exp-log`
165×	`associate-/l*`
143×	`div-exp`
114×	`add-cbrt-cube`
86×	`associate-/r*`
82×	`cbrt-undiv`
10×	`prod-exp`
7×	`rec-exp` `1-exp`
6×	`pow1` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`
1×	`associate-/l/`

Counts

4 → 13580

Calls

4 calls:

5.0ms	(/ (sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0))) (fma beta alpha (* i (+ (+ alpha beta) i))))
543.0ms	(/ (/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (/ (sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0))) (fma beta alpha (* i (+ (+ alpha beta) i))))) (/ (sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0))) (/ 1 (fma 2.0 i (+ alpha beta)))))
1.0ms	(sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))
1.0ms	(sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))

series2.7s

Counts

4 → 12

Calls

4 calls:

1.3s	(/ (sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0))) (fma beta alpha (* i (+ (+ alpha beta) i))))
815.0ms	(/ (/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (/ (sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0))) (fma beta alpha (* i (+ (+ alpha beta) i))))) (/ (sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0))) (/ 1 (fma 2.0 i (+ alpha beta)))))
279.0ms	(sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))
285.0ms	(sqrt (fma (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)) (- 1.0)))

simplify5.6s

Counts

13592 → 13592

Iterations

Useful iterations: 0 (1.5s)

Iter	Nodes	Cost
0	14983	1873634
done	14983	1873634

prune1.2m

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 32.1b

regimes168.0ms

Accuracy

55.2% (4.0b remaining)

Error of 34.7b against oracle of 30.6b and baseline of 39.7b

bsearch44.0ms

Steps

Iters	Range		Point
5	1.7755832848648711e+143	4.187935348951431e+143	4.111529511681401e+143

simplify12.0ms

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	38	119
1	48	111
2	51	109
done	51	109

end0.0ms

sample1.0s

Algorithm

intervals

Results

570.0ms	8000×	body	80	valid
190.0ms	8000×	pre	80	true