Details

sample52.0ms

Algorithm

intervals

Results

21.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 2 (36.0ms)

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

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 54.5b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
0.1b	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
37.2b	(/ (/ (* (* 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))
46.5b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 208

Calls

4 calls:

212.0ms	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
190.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
397.0ms	(/ (/ (* (* 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))
233.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.9s

Counts

4 → 12

Calls

4 calls:

88.0ms	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
171.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
1.3s	(/ (/ (* (* 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))
282.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify985.0ms

Counts

220 → 220

Iterations

Useful iterations: done (971.0ms)

Iter	Nodes	Cost
0	366	12421
1	1232	11265
done	5000	9611

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 37.1b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
3.8b	(/ (* i (+ (+ alpha beta) i)) (/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
37.2b	(/ (/ (* 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))
41.6b	(/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite323.0ms

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:

8.0ms	(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
68.0ms	(/ (* i (+ (+ alpha beta) i)) (/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
228.0ms	(/ (/ (* 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))
12.0ms	(/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.8s

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
277.0ms	(/ (* i (+ (+ alpha beta) i)) (/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
1.2s	(/ (/ (* 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))
211.0ms	(/ (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify2.7s

Counts

199 → 199

Iterations

Useful iterations: done (2.6s)

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

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 34.6b

localize28.0ms

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))))
3.1b	(/ i (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
35.3b	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
35.3b	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite862.0ms

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:

701.0ms	(* (/ 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))))
40.0ms	(/ i (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
3.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
3.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

series4.4s

Counts

4 → 12

Calls

4 calls:

3.0s	(* (/ 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))))
1.2s	(/ i (* (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))) (/ (fma 2.0 i (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
103.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
82.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify2.1s

Counts

831 → 831

Iterations

Useful iterations: done (2.1s)

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

prune2.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 34.6b

localize61.0ms

Local error

Found 4 expressions with local error:

35.3b	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
35.3b	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
35.3b	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
35.3b	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

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

series379.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
115.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
90.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
88.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify10.4s

Counts

72 → 72

Iterations

Useful iterations: 5 (1.6s)

Iter	Nodes	Cost
0	41	1060
1	88	928
2	196	872
3	476	856
4	1070	844
5	1955	656
6	2547	656
7	3088	656
8	4538	656
done	5000	656

prune619.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 34.6b

regimes171.0ms

Accuracy

36% (2.4b remaining)

Error of 36.9b against oracle of 34.5b and baseline of 38.2b

bsearch78.0ms

Steps

Iters	Range		Point
6	1.713823017139382e+208	1.2819070550181894e+209	1.7370313896506854e+208

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	138
1	32	138
done	32	138

end0.0ms

sample2.0s

Algorithm

intervals

Results

959.0ms	8000×	body	80	valid
622.0ms	8000×	pre	80	true