Details

sample39.0ms

Algorithm

intervals

Results

15.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify1.4s

Counts

1 → 1

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	17	53
1	60	52
2	295	48
3	1832	48
done	5000	48

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 55.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ alpha beta) i)
0.1b	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
38.3b	(/ (/ (* (* 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))
47.3b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite759.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-exp-log` `add-cbrt-cube`
58×	`times-frac`
50×	`associate-/r/`
49×	`flip3-+` `flip-+`
39×	`add-sqr-sqrt`
32×	`frac-times` `*-un-lft-identity`
28×	`associate-*r/`
25×	`add-cube-cbrt`
21×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
16×	`associate-*l/`
14×	`associate-/l*` `difference-of-squares`
9×	`pow1` `associate-/l/` `add-log-exp`
7×	`div-inv`
5×	`associate-/r*`
4×	`expm1-log1p-u` `fma-def` `log1p-expm1-u` `distribute-lft-out`
3×	`associate-r` `pow-prod-down` `sum-log`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `distribute-rgt-in` `associate-+l+` `flip3--` `distribute-lft-in` `associate-l` `*-commutative` `flip--`

Counts

4 → 192

Calls

4 calls:

62.0ms	(+ (+ alpha beta) i)
127.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
308.0ms	(/ (/ (* (* 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))
239.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.4s

Counts

4 → 12

Calls

4 calls:

17.0ms	(+ (+ alpha beta) i)
115.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
963.0ms	(/ (/ (* (* 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))
267.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify708.0ms

Counts

204 → 204

Iterations

Useful iterations: done (698.0ms)

Iter	Nodes	Cost
0	349	11656
1	1252	10663
done	5001	9130

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 38.1b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta)))) (/ (fma i (+ (+ beta i) alpha) (* beta alpha)) (* (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (fma 2.0 i (+ alpha beta)))))
0.5b	(/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))))
35.4b	(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
42.3b	(/ (fma i (+ (+ beta i) alpha) (* beta alpha)) (* (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (fma 2.0 i (+ alpha beta))))

rewrite438.0ms

Algorithm

rewrite-expression-head

Rules

93×	`times-frac`
77×	`add-exp-log` `add-cbrt-cube`
74×	`*-un-lft-identity`
49×	`add-sqr-sqrt`
44×	`add-cube-cbrt`
34×	`associate-l`
32×	`cbrt-undiv` `div-exp`
22×	`prod-exp` `cbrt-unprod`
15×	`distribute-lft-out`
14×	`div-inv`
11×	`associate-/l*`
9×	`associate-r`
8×	`associate-/r*` `associate-/r/`
6×	`pow1`
5×	`associate-*l/`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `flip3-+` `associate-*r/` `clear-num` `flip-+` `associate-/l/`
2×	`flip3--` `flip--` `unswap-sqr`
1×	`frac-times` `pow-prod-down` `*-commutative`

Counts

4 → 193

Calls

4 calls:

270.0ms	(* (/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta)))) (/ (fma i (+ (+ beta i) alpha) (* beta alpha)) (* (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (fma 2.0 i (+ alpha beta)))))
73.0ms	(/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))))
61.0ms	(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
15.0ms	(/ (fma i (+ (+ beta i) alpha) (* beta alpha)) (* (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (fma 2.0 i (+ alpha beta))))

series3.9s

Counts

4 → 12

Calls

4 calls:

3.0s	(* (/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta)))) (/ (fma i (+ (+ beta i) alpha) (* beta alpha)) (* (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (fma 2.0 i (+ alpha beta)))))
306.0ms	(/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))))
143.0ms	(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
460.0ms	(/ (fma i (+ (+ beta i) alpha) (* beta alpha)) (* (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)) (fma 2.0 i (+ alpha beta))))

simplify614.0ms

Counts

205 → 205

Iterations

Useful iterations: done (602.0ms)

Iter	Nodes	Cost
0	300	9538
1	962	9210
done	5000	7662

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 35.3b

localize45.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (sqrt (fma i (+ (+ beta i) alpha) (* beta alpha))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
35.4b	(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
35.5b	(sqrt (fma i (+ (+ beta i) alpha) (* beta alpha)))
35.5b	(sqrt (fma i (+ (+ beta i) alpha) (* beta alpha)))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
39×	`times-frac`
34×	`sqrt-prod`
29×	`add-cube-cbrt`
14×	`difference-of-squares`
11×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/r*`
7×	`associate-/l*` `distribute-lft-out--`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-*r/` `clear-num` `associate-/r/` `div-inv` `associate-/l/`
1×	`flip3--` `flip3-+` `prod-exp` `flip--` `cbrt-unprod` `flip-+`

Counts

4 → 119

Calls

4 calls:

33.0ms	(/ (sqrt (fma i (+ (+ beta i) alpha) (* beta alpha))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
98.0ms	(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
3.0ms	(sqrt (fma i (+ (+ beta i) alpha) (* beta alpha)))
4.0ms	(sqrt (fma i (+ (+ beta i) alpha) (* beta alpha)))

series915.0ms

Counts

4 → 12

Calls

4 calls:

437.0ms	(/ (sqrt (fma i (+ (+ beta i) alpha) (* beta alpha))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
112.0ms	(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
155.0ms	(sqrt (fma i (+ (+ beta i) alpha) (* beta alpha)))
210.0ms	(sqrt (fma i (+ (+ beta i) alpha) (* beta alpha)))

simplify1.5s

Counts

131 → 131

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	200	3460
1	486	3218
2	2272	3071
done	5002	3066

prune840.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 35.3b

localize55.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (sqrt (fma i (+ (+ beta i) alpha) (* beta alpha))) (fma 2.0 i (+ alpha beta)))
0.6b	(/ (sqrt (fma i (+ (+ beta i) alpha) (* beta alpha))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
35.5b	(sqrt (fma i (+ (+ beta i) alpha) (* beta alpha)))
35.5b	(sqrt (fma i (+ (+ beta i) alpha) (* beta alpha)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
54×	`times-frac`
46×	`sqrt-prod`
42×	`add-cube-cbrt`
14×	`difference-of-squares`
12×	`associate-/l*`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
7×	`distribute-lft-out--`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `associate-/r/` `div-inv`
1×	`flip3--` `flip--`

Counts

4 → 135

Calls

4 calls:

9.0ms	(/ (sqrt (fma i (+ (+ beta i) alpha) (* beta alpha))) (fma 2.0 i (+ alpha beta)))
33.0ms	(/ (sqrt (fma i (+ (+ beta i) alpha) (* beta alpha))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
3.0ms	(sqrt (fma i (+ (+ beta i) alpha) (* beta alpha)))
3.0ms	(sqrt (fma i (+ (+ beta i) alpha) (* beta alpha)))

series1.4s

Counts

4 → 12

Calls

4 calls:

214.0ms	(/ (sqrt (fma i (+ (+ beta i) alpha) (* beta alpha))) (fma 2.0 i (+ alpha beta)))
473.0ms	(/ (sqrt (fma i (+ (+ beta i) alpha) (* beta alpha))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
144.0ms	(sqrt (fma i (+ (+ beta i) alpha) (* beta alpha)))
555.0ms	(sqrt (fma i (+ (+ beta i) alpha) (* beta alpha)))

simplify886.0ms

Counts

147 → 147

Iterations

Useful iterations: done (875.0ms)

Iter	Nodes	Cost
0	192	4210
1	388	3923
2	1171	3785
done	5000	3775

prune864.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 35.3b

regimes304.0ms

Accuracy

28.4% (2.6b remaining)

Error of 36.4b against oracle of 33.8b and baseline of 37.5b

bsearch131.0ms

Steps

Iters	Range		Point
9	2.981951901673282e+149	2.5738748422425065e+155	1.3624221618089403e+154

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	33	104
1	43	104
done	43	104

end0.0ms

sample1.7s

Algorithm

intervals

Results

926.0ms	8000×	body	80	valid
290.0ms	8000×	pre	80	true