Details

sample87.0ms

Algorithm

intervals

Results

44.0ms	256×	body	80	valid
8.0ms	256×	pre	80	true

simplify741.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
3	1753
2	282
1	58
0	17

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.3b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ (+ alpha beta) i) (+ (+ (* 2.0 i) beta) alpha)) i)
4.0b	(/ (/ (+ (* (+ (+ alpha beta) i) i) (* beta alpha)) (+ (+ (* 2.0 i) beta) alpha)) (/ (- (* (+ (+ (* 2.0 i) beta) alpha) (+ (+ (* 2.0 i) beta) alpha)) 1.0) (* (/ (+ (+ alpha beta) i) (+ (+ (* 2.0 i) beta) alpha)) i)))
31.7b	(/ (- (* (+ (+ (* 2.0 i) beta) alpha) (+ (+ (* 2.0 i) beta) alpha)) 1.0) (* (/ (+ (+ alpha beta) i) (+ (+ (* 2.0 i) beta) alpha)) i))
36.1b	(/ (+ (* (+ (+ alpha beta) i) i) (* beta alpha)) (+ (+ (* 2.0 i) beta) alpha))

rewrite875.0ms

Algorithm

rewrite-expression-head

Rules

395×	`times-frac`
242×	`*-un-lft-identity`
170×	`add-sqr-sqrt`
144×	`add-cube-cbrt`
52×	`add-cbrt-cube` `add-exp-log`
51×	`distribute-lft-out`
45×	`associate-/r/`
33×	`div-inv`
26×	`cbrt-undiv` `div-exp` `associate-l`
25×	`associate-/l*`
21×	`associate-*l/` `difference-of-squares`
14×	`associate-/r*`
13×	`flip3-+` `flip-+`
8×	`prod-exp` `cbrt-unprod`
6×	`pow1`
5×	`associate-/l/`
4×	`add-log-exp`
3×	`clear-num` `frac-2neg` `associate-r`
2×	`unswap-sqr`
1×	`flip3--` `div-sub` `pow-prod-down` `*-commutative` `flip--`

Counts

4 → 326

Calls

4 calls:

151.0ms	(* (/ (+ (+ alpha beta) i) (+ (+ (* 2.0 i) beta) alpha)) i)
355.0ms	(/ (/ (+ (* (+ (+ alpha beta) i) i) (* beta alpha)) (+ (+ (* 2.0 i) beta) alpha)) (/ (- (* (+ (+ (* 2.0 i) beta) alpha) (+ (+ (* 2.0 i) beta) alpha)) 1.0) (* (/ (+ (+ alpha beta) i) (+ (+ (* 2.0 i) beta) alpha)) i)))
229.0ms	(/ (- (* (+ (+ (* 2.0 i) beta) alpha) (+ (+ (* 2.0 i) beta) alpha)) 1.0) (* (/ (+ (+ alpha beta) i) (+ (+ (* 2.0 i) beta) alpha)) i))
119.0ms	(/ (+ (* (+ (+ alpha beta) i) i) (* beta alpha)) (+ (+ (* 2.0 i) beta) alpha))

series1.1s

Counts

4 → 12

Calls

4 calls:

118.0ms	(* (/ (+ (+ alpha beta) i) (+ (+ (* 2.0 i) beta) alpha)) i)
421.0ms	(/ (/ (+ (* (+ (+ alpha beta) i) i) (* beta alpha)) (+ (+ (* 2.0 i) beta) alpha)) (/ (- (* (+ (+ (* 2.0 i) beta) alpha) (+ (+ (* 2.0 i) beta) alpha)) 1.0) (* (/ (+ (+ alpha beta) i) (+ (+ (* 2.0 i) beta) alpha)) i)))
395.0ms	(/ (- (* (+ (+ (* 2.0 i) beta) alpha) (+ (+ (* 2.0 i) beta) alpha)) 1.0) (* (/ (+ (+ alpha beta) i) (+ (+ (* 2.0 i) beta) alpha)) i))
132.0ms	(/ (+ (* (+ (+ alpha beta) i) i) (* beta alpha)) (+ (+ (* 2.0 i) beta) alpha))

simplify594.0ms

Counts

338 → 338

Iterations

Iter	Nodes
done	5001
1	1740
0	536

prune2.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 35.3b

localize87.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (sqrt (/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ alpha (+ beta (* i 2.0))))) (/ (+ (* i 2.0) (+ beta (+ alpha (sqrt 1.0)))) (/ (+ beta (+ alpha i)) (+ alpha (+ beta (* i 2.0)))))) (/ (sqrt (/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ alpha (+ beta (* i 2.0))))) (/ (+ alpha (- (+ beta (* i 2.0)) (sqrt 1.0))) i)))
0.7b	(/ (sqrt (/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ alpha (+ beta (* i 2.0))))) (/ (+ (* i 2.0) (+ beta (+ alpha (sqrt 1.0)))) (/ (+ beta (+ alpha i)) (+ alpha (+ beta (* i 2.0))))))
36.1b	(/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ alpha (+ beta (* i 2.0))))
36.1b	(/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ alpha (+ beta (* i 2.0))))

rewrite11.5s

Algorithm

rewrite-expression-head

Rules

12647×	`times-frac`
9655×	`*-un-lft-identity`
4735×	`add-sqr-sqrt`
4338×	`add-cube-cbrt`
3430×	`sqrt-prod`
2885×	`distribute-lft-out`
1748×	`associate-l`
680×	`associate-/r/`
404×	`associate-r`
384×	`div-inv`
319×	`flip3-+` `flip-+`
91×	`associate-/r*`
71×	`add-cbrt-cube` `add-exp-log`
70×	`unswap-sqr`
63×	`distribute-lft-out--`
38×	`cbrt-undiv` `div-exp`
27×	`associate-/l*`
12×	`prod-exp` `cbrt-unprod`
6×	`pow1`
5×	`associate-/l/`
4×	`add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`frac-times` `sqrt-div` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 4193

Calls

4 calls:

9.9s	(* (/ (sqrt (/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ alpha (+ beta (* i 2.0))))) (/ (+ (* i 2.0) (+ beta (+ alpha (sqrt 1.0)))) (/ (+ beta (+ alpha i)) (+ alpha (+ beta (* i 2.0)))))) (/ (sqrt (/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ alpha (+ beta (* i 2.0))))) (/ (+ alpha (- (+ beta (* i 2.0)) (sqrt 1.0))) i)))
290.0ms	(/ (sqrt (/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ alpha (+ beta (* i 2.0))))) (/ (+ (* i 2.0) (+ beta (+ alpha (sqrt 1.0)))) (/ (+ beta (+ alpha i)) (+ alpha (+ beta (* i 2.0))))))
83.0ms	(/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ alpha (+ beta (* i 2.0))))
105.0ms	(/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ alpha (+ beta (* i 2.0))))

series4.5s

Counts

4 → 12

Calls

4 calls:

3.5s	(* (/ (sqrt (/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ alpha (+ beta (* i 2.0))))) (/ (+ (* i 2.0) (+ beta (+ alpha (sqrt 1.0)))) (/ (+ beta (+ alpha i)) (+ alpha (+ beta (* i 2.0)))))) (/ (sqrt (/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ alpha (+ beta (* i 2.0))))) (/ (+ alpha (- (+ beta (* i 2.0)) (sqrt 1.0))) i)))
781.0ms	(/ (sqrt (/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ alpha (+ beta (* i 2.0))))) (/ (+ (* i 2.0) (+ beta (+ alpha (sqrt 1.0)))) (/ (+ beta (+ alpha i)) (+ alpha (+ beta (* i 2.0))))))
120.0ms	(/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ alpha (+ beta (* i 2.0))))
136.0ms	(/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ alpha (+ beta (* i 2.0))))

simplify2.1s

Counts

4205 → 4205

Iterations

Iter	Nodes
done	5001
0	3113

prune32.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 35.3b

localize146.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (sqrt (+ (* i (+ beta (+ alpha i))) (* alpha beta))) (sqrt (- (+ (+ alpha beta) (* i 2.0)) (sqrt 1.0))))
0.7b	(/ (sqrt (/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ (+ alpha beta) (* i 2.0)))) (/ (+ (+ (* i 2.0) beta) (+ alpha (sqrt 1.0))) (/ (+ beta (+ alpha i)) (+ (+ alpha beta) (* i 2.0)))))
36.0b	(sqrt (+ (* i (+ beta (+ alpha i))) (* alpha beta)))
36.1b	(/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ (+ alpha beta) (* i 2.0)))

rewrite921.0ms

Algorithm

rewrite-expression-head

Rules

6462×	`times-frac`
5642×	`*-un-lft-identity`
2237×	`add-sqr-sqrt`
2208×	`add-cube-cbrt`
2052×	`distribute-lft-out`
1747×	`sqrt-prod`
436×	`associate-/r/`
228×	`div-inv`
210×	`flip3-+` `flip-+`
122×	`associate-/r*`
27×	`associate-/l*`
17×	`add-cbrt-cube` `add-exp-log`
14×	`difference-of-squares`
8×	`cbrt-undiv` `div-exp`
7×	`sqrt-div` `distribute-lft-out--`
5×	`pow1` `associate-/l/`
4×	`add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`rem-sqrt-square` `sqrt-undiv` `sqrt-pow1` `flip3--` `pow1/2` `flip--`

Counts

4 → 2258

Calls

4 calls:

173.0ms	(/ (sqrt (+ (* i (+ beta (+ alpha i))) (* alpha beta))) (sqrt (- (+ (+ alpha beta) (* i 2.0)) (sqrt 1.0))))
286.0ms	(/ (sqrt (/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ (+ alpha beta) (* i 2.0)))) (/ (+ (+ (* i 2.0) beta) (+ alpha (sqrt 1.0))) (/ (+ beta (+ alpha i)) (+ (+ alpha beta) (* i 2.0)))))
26.0ms	(sqrt (+ (* i (+ beta (+ alpha i))) (* alpha beta)))
80.0ms	(/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ (+ alpha beta) (* i 2.0)))

series2.0s

Counts

4 → 12

Calls

4 calls:

858.0ms	(/ (sqrt (+ (* i (+ beta (+ alpha i))) (* alpha beta))) (sqrt (- (+ (+ alpha beta) (* i 2.0)) (sqrt 1.0))))
857.0ms	(/ (sqrt (/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ (+ alpha beta) (* i 2.0)))) (/ (+ (+ (* i 2.0) beta) (+ alpha (sqrt 1.0))) (/ (+ beta (+ alpha i)) (+ (+ alpha beta) (* i 2.0)))))
163.0ms	(sqrt (+ (* i (+ beta (+ alpha i))) (* alpha beta)))
113.0ms	(/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ (+ alpha beta) (* i 2.0)))

simplify1.3s

Counts

2270 → 2270

Iterations

Iter	Nodes
done	5000
0	2056

prune18.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 35.3b

localize83.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (sqrt (+ (* i (+ beta (+ alpha i))) (* alpha beta))) (/ (+ (* i 2.0) (+ beta (+ alpha (sqrt 1.0)))) (/ (+ beta (+ alpha i)) (+ alpha (+ beta (* i 2.0))))))
6.6b	(/ (sqrt (+ (* i (+ beta (+ alpha i))) (* alpha beta))) (* (/ (+ alpha (- (+ beta (* i 2.0)) (sqrt 1.0))) i) (+ alpha (+ beta (* i 2.0)))))
36.0b	(sqrt (+ (* i (+ beta (+ alpha i))) (* alpha beta)))
36.0b	(sqrt (+ (* i (+ beta (+ alpha i))) (* alpha beta)))

rewrite559.0ms

Algorithm

rewrite-expression-head

Rules

1470×	`times-frac`
1207×	`*-un-lft-identity`
579×	`add-sqr-sqrt`
577×	`add-cube-cbrt`
357×	`distribute-lft-out`
264×	`sqrt-prod`
84×	`associate-/r*`
55×	`associate-/r/`
30×	`div-inv`
27×	`flip3-+` `flip-+`
22×	`add-cbrt-cube` `add-exp-log`
12×	`associate-/l*`
10×	`cbrt-undiv` `div-exp`
8×	`sqrt-div`
6×	`pow1`
4×	`add-log-exp` `associate-/l/`
2×	`frac-times` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `associate-*r/` `cbrt-unprod`
1×	`associate-*l/`

Counts

4 → 672

Calls

4 calls:

294.0ms	(/ (sqrt (+ (* i (+ beta (+ alpha i))) (* alpha beta))) (/ (+ (* i 2.0) (+ beta (+ alpha (sqrt 1.0)))) (/ (+ beta (+ alpha i)) (+ alpha (+ beta (* i 2.0))))))
122.0ms	(/ (sqrt (+ (* i (+ beta (+ alpha i))) (* alpha beta))) (* (/ (+ alpha (- (+ beta (* i 2.0)) (sqrt 1.0))) i) (+ alpha (+ beta (* i 2.0)))))
43.0ms	(sqrt (+ (* i (+ beta (+ alpha i))) (* alpha beta)))
31.0ms	(sqrt (+ (* i (+ beta (+ alpha i))) (* alpha beta)))

series2.1s

Counts

4 → 12

Calls

4 calls:

909.0ms	(/ (sqrt (+ (* i (+ beta (+ alpha i))) (* alpha beta))) (/ (+ (* i 2.0) (+ beta (+ alpha (sqrt 1.0)))) (/ (+ beta (+ alpha i)) (+ alpha (+ beta (* i 2.0))))))
841.0ms	(/ (sqrt (+ (* i (+ beta (+ alpha i))) (* alpha beta))) (* (/ (+ alpha (- (+ beta (* i 2.0)) (sqrt 1.0))) i) (+ alpha (+ beta (* i 2.0)))))
173.0ms	(sqrt (+ (* i (+ beta (+ alpha i))) (* alpha beta)))
223.0ms	(sqrt (+ (* i (+ beta (+ alpha i))) (* alpha beta)))

simplify1.6s

Counts

684 → 684

Iterations

Iter	Nodes
done	5000
1	2413
0	822

prune4.7s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 35.3b

regimes344.0ms

Accuracy

17% (3.3b remaining)

Error of 38.1b against oracle of 34.7b and baseline of 38.7b

bsearch135.0ms

Steps

Iters	Range		Point
9	2.997562247900697e+97	3.916531947114467e+103	4.817585748747987e+97

simplify29.0ms

Iterations

Iter	Nodes
done	84
3	84
2	81
1	78
0	56

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.4s	8000×	body	80	valid
325.0ms	8000×	pre	80	true