Details

sample51.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify1.5s

Counts

1 → 1

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	17	485
1	60	460
2	295	435
3	1807	435
done	5001	435

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.5b

localize72.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
0.1b	(* (fma beta alpha (* i (+ (+ alpha beta) i))) (* i (+ (+ alpha beta) i)))
38.0b	(/ (/ (* (fma beta alpha (* i (+ (+ alpha beta) i))) (* i (+ (+ alpha beta) i))) (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))) (- (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) 1.0))
45.3b	(/ (* (fma beta alpha (* i (+ (+ alpha beta) i))) (* i (+ (+ alpha beta) i))) (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))))

rewrite316.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-cbrt-cube` `add-exp-log`
28×	`add-sqr-sqrt`
26×	`times-frac`
22×	`prod-exp` `cbrt-unprod`
20×	`*-un-lft-identity` `add-cube-cbrt`
19×	`cbrt-undiv` `div-exp`
16×	`pow1`
8×	`associate-*r/`
7×	`div-inv`
6×	`associate-l` `associate-/l*` `difference-of-squares`
5×	`distribute-rgt-in` `associate-/r*` `distribute-lft-in`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`swap-sqr` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3-+` `associate-/r/` `*-commutative` `flip-+` `fma-udef`
1×	`pow2` `pow-plus` `flip3--` `pow-sqr` `pow-prod-up` `flip--` `unswap-sqr`

Counts

4 → 142

Calls

4 calls:

11.0ms	(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
72.0ms	(* (fma beta alpha (* i (+ (+ alpha beta) i))) (* i (+ (+ alpha beta) i)))
112.0ms	(/ (/ (* (fma beta alpha (* i (+ (+ alpha beta) i))) (* i (+ (+ alpha beta) i))) (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))) (- (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) 1.0))
113.0ms	(/ (* (fma beta alpha (* i (+ (+ alpha beta) i))) (* i (+ (+ alpha beta) i))) (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))))

series1.1s

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
215.0ms	(* (fma beta alpha (* i (+ (+ alpha beta) i))) (* i (+ (+ alpha beta) i)))
476.0ms	(/ (/ (* (fma beta alpha (* i (+ (+ alpha beta) i))) (* i (+ (+ alpha beta) i))) (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))) (- (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) 1.0))
359.0ms	(/ (* (fma beta alpha (* i (+ (+ alpha beta) i))) (* i (+ (+ alpha beta) i))) (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))))

simplify1.4s

Counts

154 → 154

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	252	71616
1	762	65163
done	5000	63177

prune968.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 36.3b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
0.1b	(* (/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))))
34.5b	(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
35.6b	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

rewrite350.0ms

Algorithm

rewrite-expression-head

Rules

266×	`times-frac`
193×	`*-un-lft-identity`
174×	`add-sqr-sqrt`
125×	`add-cube-cbrt`
70×	`add-cbrt-cube` `add-exp-log`
58×	`associate-l`
48×	`associate-r`
33×	`cbrt-undiv` `div-exp`
27×	`distribute-lft-out`
20×	`div-inv`
17×	`associate-/l*`
16×	`prod-exp` `cbrt-unprod`
14×	`difference-of-squares`
10×	`associate-/r*`
7×	`sqrt-prod` `distribute-lft-out--`
6×	`pow1` `associate-/r/` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `flip3-+` `associate-*r/` `flip-+` `associate-/l/`
1×	`frac-times` `flip3--` `pow-prod-down` `associate-l/` `-commutative` `flip--`

Counts

4 → 292

Calls

4 calls:

33.0ms	(/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
235.0ms	(* (/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))))
47.0ms	(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
4.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

series1.6s

Counts

4 → 12

Calls

4 calls:

409.0ms	(/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
912.0ms	(* (/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))))
126.0ms	(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
176.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

simplify2.7s

Counts

304 → 304

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	422	189476
1	1418	181430
done	5001	179264

prune2.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 36.3b

localize87.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))) (/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))))
34.5b	(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
35.6b	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))
35.6b	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

rewrite264.0ms

Algorithm

rewrite-expression-head

Rules

179×	`times-frac`
139×	`add-sqr-sqrt`
125×	`*-un-lft-identity`
85×	`add-cube-cbrt`
71×	`sqrt-prod`
61×	`associate-l`
48×	`associate-r`
27×	`add-cbrt-cube` `add-exp-log`
15×	`div-inv`
14×	`difference-of-squares`
13×	`distribute-lft-out`
9×	`cbrt-undiv` `associate-/r*` `div-exp`
8×	`unswap-sqr`
7×	`associate-/l*` `distribute-lft-out--`
6×	`pow1` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-*r/`
2×	`flip3-+` `sqrt-div` `flip-+` `associate-/l/`
1×	`frac-times` `flip3--` `pow-prod-down` `associate-l/` `-commutative` `flip--`

Counts

4 → 222

Calls

4 calls:

204.0ms	(* (sqrt (/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))) (/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))))
38.0ms	(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
4.0ms	(/ (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)))

series2.0s

Counts

4 → 12

Calls

4 calls:

1.5s	(* (sqrt (/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))) (/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))))
165.0ms	(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
186.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))
156.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

simplify2.7s

Counts

234 → 234

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	399	135277
1	1097	131207
done	5000	130563

prune2.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 36.3b

localize98.0ms

Local error

Found 4 expressions with local error:

34.5b	(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
34.5b	(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
35.6b	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))
35.6b	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac` `add-cube-cbrt`
18×	`add-cbrt-cube` `add-exp-log`
12×	`associate-/r*`
8×	`associate-/l*`
6×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `associate-*r/` `log1p-expm1-u` `div-inv` `add-log-exp` `associate-/l/`
2×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+`

Counts

4 → 108

Calls

4 calls:

34.0ms	(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
44.0ms	(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
4.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))
4.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

series589.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
124.0ms	(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
169.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))
165.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

simplify1.6s

Counts

120 → 120

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	109	40842
1	272	39452
2	1440	39132
done	5002	38812

prune1.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 36.3b

regimes289.0ms

Accuracy

29.4% (2.6b remaining)

Error of 36.8b against oracle of 34.2b and baseline of 37.8b

bsearch55.0ms

Steps

Iters	Range		Point
6	7.023507660211354e+153	3.1516654515805976e+154	1.3375206427593509e+154

simplify10.0ms

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	24	767
1	30	767
done	30	767

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.3s	8000×	body	80	valid
246.0ms	8000×	pre	80	true