Details

sample31.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify987.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	17	53
1	60	52
2	295	48
3	1651	48
done	5002	48

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 54.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* i (+ (+ alpha beta) i))
0.1b	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
34.3b	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
46.6b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite551.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-exp-log` `add-cbrt-cube`
58×	`times-frac`
50×	`associate-/r/`
49×	`flip3-+` `flip-+`
42×	`add-sqr-sqrt`
32×	`frac-times`
31×	`*-un-lft-identity`
30×	`associate-*r/`
26×	`add-cube-cbrt`
22×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
16×	`associate-*l/`
14×	`associate-/l*` `difference-of-squares`
11×	`pow1`
9×	`associate-/l/`
8×	`associate-r`
7×	`div-inv`
5×	`associate-/r*`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-out`
2×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `*-commutative`
1×	`flip3--` `flip--` `unswap-sqr`

Counts

4 → 197

Calls

4 calls:

70.0ms	(* i (+ (+ alpha beta) i))
102.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
230.0ms	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
136.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.2s

Counts

4 → 12

Calls

4 calls:

24.0ms	(* i (+ (+ alpha beta) i))
111.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
849.0ms	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
187.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify533.0ms

Counts

209 → 209

Iterations

Useful iterations: done (523.0ms)

Iter	Nodes	Cost
0	353	11780
1	1190	10755
done	5000	9194

prune718.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 34.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
5.0b	(/ (* i (+ (+ alpha beta) i)) (/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
34.3b	(/ (/ (* i (+ (+ alpha beta) i)) (/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
39.2b	(/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
61×	`add-exp-log` `add-cbrt-cube`
57×	`add-sqr-sqrt`
42×	`add-cube-cbrt` `*-un-lft-identity`
29×	`cbrt-undiv` `div-exp`
15×	`div-inv`
14×	`associate-/r` `associate-/l`
13×	`difference-of-squares`
12×	`prod-exp` `cbrt-unprod`
11×	`pow1`
8×	`associate-/r/`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `swap-sqr` `associate-r` `associate-l` `clear-num` `associate-/l/`
2×	`associate-*r/` `fma-udef`
1×	`pow2` `distribute-rgt-in` `flip3--` `distribute-lft-in` `flip3-+` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `flip-+` `unswap-sqr`

Counts

4 → 187

Calls

4 calls:

7.0ms	(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
42.0ms	(/ (* i (+ (+ alpha beta) i)) (/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
128.0ms	(/ (/ (* i (+ (+ alpha beta) i)) (/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
10.0ms	(/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.3s

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
194.0ms	(/ (* i (+ (+ alpha beta) i)) (/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
855.0ms	(/ (/ (* i (+ (+ alpha beta) i)) (/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
146.0ms	(/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify1.6s

Counts

199 → 199

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	330	10445
1	909	9614
2	3975	8391
done	5001	7837

prune721.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 31.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ i (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))))) (/ (/ (+ (+ alpha beta) i) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))))
6.1b	(/ i (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
32.0b	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
32.0b	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite540.0ms

Algorithm

rewrite-expression-head

Rules

1905×	`times-frac`
1544×	`*-un-lft-identity`
1135×	`add-sqr-sqrt`
696×	`associate-r`
654×	`add-cube-cbrt`
396×	`distribute-lft-out`
392×	`sqrt-prod`
230×	`difference-of-squares`
115×	`distribute-lft-out--`
93×	`add-exp-log` `add-cbrt-cube`
44×	`cbrt-undiv` `div-exp`
39×	`div-inv`
26×	`prod-exp` `cbrt-unprod`
18×	`associate-/r/`
12×	`associate-l`
8×	`pow1`
5×	`frac-times` `associate-*l/` `unswap-sqr`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`associate-r/` `associate-/l`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`flip3--` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `flip--`

Counts

4 → 819

Calls

4 calls:

421.0ms	(* (/ i (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))))) (/ (/ (+ (+ alpha beta) i) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))))
18.0ms	(/ i (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
2.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
2.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

series3.0s

Counts

4 → 12

Calls

4 calls:

2.3s	(* (/ i (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))))) (/ (/ (+ (+ alpha beta) i) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))))
556.0ms	(/ i (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
65.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
69.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify1.4s

Counts

831 → 831

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	833	54880
1	2765	51762
done	5001	49603

prune1.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 31.1b

localize31.0ms

Local error

Found 4 expressions with local error:

6.1b	(/ i (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
32.0b	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
32.0b	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
32.0b	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
7×	`pow1`
5×	`associate-/r/`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `times-frac` `pow1/2` `associate-/l*`
2×	`frac-times` `flip3-+` `associate-*l/` `prod-exp` `cbrt-unprod` `flip-+`
1×	`frac-2neg` `associate-r/` `clear-num` `associate-/r` `div-inv`

Counts

4 → 75

Calls

4 calls:

18.0ms	(/ i (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
1.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
1.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
2.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

series751.0ms

Counts

4 → 12

Calls

4 calls:

563.0ms	(/ i (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
64.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
59.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
65.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify851.0ms

Counts

87 → 87

Iterations

Useful iterations: done (848.0ms)

Iter	Nodes	Cost
0	136	2025
1	349	1872
2	1260	1617
done	5000	1590

prune402.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 31.1b

regimes153.0ms

Accuracy

35.9% (2.4b remaining)

Error of 36.8b against oracle of 34.4b and baseline of 38.1b

bsearch66.0ms

Steps

Iters	Range		Point
7	1.7703642706139512e+221	1.2100692140006563e+223	1.7918517454980545e+221

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	148
1	50	148
done	50	148

end0.0ms

sample705.0ms

Algorithm

intervals

Results

343.0ms	8000×	body	80	valid
116.0ms	8000×	pre	80	true