Details

sample30.0ms

Algorithm

intervals

Results

12.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify761.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	17	53
1	60	52
2	265	48
3	1349	48
done	5002	48

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 49.2b

localize15.0ms

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))))
33.8b	(/ (/ (* (* 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))
42.0b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite315.0ms

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:

71.0ms	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
50.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
114.0ms	(/ (/ (* (* 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))
69.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.1s

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
102.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
760.0ms	(/ (/ (* (* 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))
169.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify501.0ms

Counts

220 → 220

Iterations

Useful iterations: done (491.0ms)

Iter	Nodes	Cost
0	366	12421
1	1231	11265
done	5001	10981

prune717.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 31.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (* 2.0 i) (+ alpha beta)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
27.8b	(/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (* 2.0 i) (+ alpha beta)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
31.1b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
31.5b	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (* 2.0 i) (+ alpha beta)))

rewrite406.0ms

Algorithm

rewrite-expression-head

Rules

104×	`times-frac`
85×	`add-sqr-sqrt`
81×	`*-un-lft-identity`
78×	`add-exp-log` `add-cbrt-cube`
41×	`add-cube-cbrt`
39×	`cbrt-undiv` `div-exp`
22×	`associate-/r/` `difference-of-squares`
17×	`prod-exp` `cbrt-unprod`
16×	`associate-/r*`
15×	`associate-/l*`
11×	`flip3-+` `sqrt-prod` `flip-+` `div-inv` `distribute-lft-out--`
9×	`distribute-lft-out`
6×	`associate-/l/`
4×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
3×	`associate-*r/`
1×	`frac-times` `flip3--` `associate-*l/` `flip--`

Counts

4 → 205

Calls

4 calls:

222.0ms	(/ (/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (* 2.0 i) (+ alpha beta)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
124.0ms	(/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (* 2.0 i) (+ alpha beta)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
35.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
15.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (* 2.0 i) (+ alpha beta)))

series3.4s

Counts

4 → 12

Calls

4 calls:

2.6s	(/ (/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (* 2.0 i) (+ alpha beta)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
589.0ms	(/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (* 2.0 i) (+ alpha beta)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
82.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
115.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (* 2.0 i) (+ alpha beta)))

simplify1.5s

Counts

217 → 217

Iterations

Useful iterations: 2 (665.0ms)

Iter	Nodes	Cost
0	351	13147
1	1020	11650
2	4917	10045
done	5000	10045

prune693.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 31.1b

localize23.0ms

Local error

Found 4 expressions with local error:

27.8b	(/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (* (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma 2.0 i (+ alpha beta))))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
31.1b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
31.4b	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
31.4b	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

130.0ms	(/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (* (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma 2.0 i (+ alpha beta))))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
36.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
1.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
1.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

series829.0ms

Counts

4 → 12

Calls

4 calls:

628.0ms	(/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (* (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma 2.0 i (+ alpha beta))))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
85.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
60.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
56.0ms	(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify1.1s

Counts

115 → 115

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	219	5030
1	697	3829
2	3137	2846
done	5000	2842

prune414.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 31.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))) (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta)))))
0.1b	(/ (* (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))) (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
31.1b	(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
31.5b	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

112×	`times-frac`
94×	`add-exp-log` `add-cbrt-cube`
90×	`*-un-lft-identity`
77×	`add-sqr-sqrt`
60×	`add-cube-cbrt`
58×	`associate-r`
43×	`cbrt-undiv` `div-exp`
25×	`prod-exp` `cbrt-unprod`
13×	`distribute-lft-out`
12×	`associate-/r*`
9×	`div-inv`
7×	`associate-l`
6×	`pow1`
5×	`associate-/l/` `associate-/l*`
4×	`expm1-log1p-u` `associate-*r/` `associate-/r/` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`frac-2neg` `clear-num` `unswap-sqr`
2×	`frac-times` `flip3-+` `associate-*l/` `sqrt-prod` `flip-+` `distribute-lft-out--`
1×	`flip3--` `pow-prod-down` `*-commutative` `flip--`

Counts

4 → 204

Calls

4 calls:

80.0ms	(* (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))) (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta)))))
118.0ms	(/ (* (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))) (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
17.0ms	(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
2.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

series3.2s

Counts

4 → 12

Calls

4 calls:

597.0ms	(* (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))) (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta)))))
2.4s	(/ (* (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))) (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
88.0ms	(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
122.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

simplify535.0ms

Counts

216 → 216

Iterations

Useful iterations: done (526.0ms)

Iter	Nodes	Cost
0	349	10550
1	1134	10002
done	5000	9542

prune626.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 31.1b

regimes156.0ms

Accuracy

0% (3.7b remaining)

Error of 37.4b against oracle of 33.7b and baseline of 37.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	53
1	27	53
done	27	53

end0.0ms

sample678.0ms

Algorithm

intervals

Results

366.0ms	8000×	body	80	valid
128.0ms	8000×	pre	80	true