Details

sample45.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
6.0ms	256×	pre	80	true

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: 2 (50.0ms)

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

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 55.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(* i (+ (+ alpha beta) i))
0.0b	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
36.9b	(/ (/ (* (* 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))
46.9b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite909.0ms

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:

86.0ms	(* i (+ (+ alpha beta) i))
157.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
430.0ms	(/ (/ (* (* 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))
226.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.8s

Counts

4 → 12

Calls

4 calls:

37.0ms	(* i (+ (+ alpha beta) i))
181.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
1.4s	(/ (/ (* (* 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))
258.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify850.0ms

Counts

209 → 209

Iterations

Useful iterations: done (841.0ms)

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

prune1.6s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 36.8b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (* (+ (+ alpha beta) i) i) (fma 2.0 i (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))))
35.5b	(/ (* (+ (+ alpha beta) i) i) (fma 2.0 i (+ alpha beta)))
36.5b	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))
36.9b	(/ (* (/ (* (+ (+ alpha beta) i) i) (fma 2.0 i (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))

rewrite503.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-exp-log` `add-cbrt-cube`
32×	`add-sqr-sqrt`
29×	`times-frac`
25×	`add-cube-cbrt` `*-un-lft-identity`
24×	`cbrt-undiv` `div-exp`
17×	`prod-exp` `cbrt-unprod`
13×	`associate-r`
10×	`associate-/r*`
7×	`associate-l`
6×	`pow1`
5×	`div-inv` `associate-/l/` `associate-/l*`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`frac-times` `associate-*r/` `associate-/r/` `difference-of-squares` `unswap-sqr`
1×	`flip3--` `flip3-+` `pow-prod-down` `*-commutative` `flip--` `flip-+`

Counts

4 → 142

Calls

4 calls:

168.0ms	(* (/ (* (+ (+ alpha beta) i) i) (fma 2.0 i (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))))
81.0ms	(/ (* (+ (+ alpha beta) i) i) (fma 2.0 i (+ alpha beta)))
10.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))
234.0ms	(/ (* (/ (* (+ (+ alpha beta) i) i) (fma 2.0 i (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

376.0ms	(* (/ (* (+ (+ alpha beta) i) i) (fma 2.0 i (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))))
168.0ms	(/ (* (+ (+ alpha beta) i) i) (fma 2.0 i (+ alpha beta)))
166.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))
580.0ms	(/ (* (/ (* (+ (+ alpha beta) i) i) (fma 2.0 i (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))

simplify1.9s

Counts

154 → 154

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	232	6311
1	661	6108
2	3207	4589
done	5001	4549

prune704.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 35.1b

localize52.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (* (/ (* (+ (+ alpha beta) i) 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	(/ (* (/ (* (+ (+ alpha beta) i) 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))))
35.5b	(/ (* (+ (+ alpha beta) i) i) (fma 2.0 i (+ alpha beta)))
36.5b	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

rewrite626.0ms

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×	`difference-of-squares`
18×	`associate-/r/`
17×	`prod-exp` `cbrt-unprod`
16×	`associate-/r*`
15×	`associate-/l*`
11×	`sqrt-prod` `div-inv` `distribute-lft-out--`
9×	`flip3-+` `flip-+` `distribute-lft-out`
6×	`associate-/l/`
4×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
3×	`associate-*l/`
1×	`frac-times` `flip3--` `associate-*r/` `flip--`

Counts

4 → 201

Calls

4 calls:

367.0ms	(/ (/ (* (/ (* (+ (+ alpha beta) i) 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)))
184.0ms	(/ (* (/ (* (+ (+ alpha beta) i) 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))))
52.0ms	(/ (* (+ (+ alpha beta) i) i) (fma 2.0 i (+ alpha beta)))
5.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

series2.1s

Counts

4 → 12

Calls

4 calls:

733.0ms	(/ (/ (* (/ (* (+ (+ alpha beta) i) 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)))
1.1s	(/ (* (/ (* (+ (+ alpha beta) i) 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))))
144.0ms	(/ (* (+ (+ alpha beta) i) i) (fma 2.0 i (+ alpha beta)))
177.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

simplify2.0s

Counts

213 → 213

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	339	12343
1	936	11570
2	4040	9956
done	5000	9952

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 35.1b

localize50.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (* (+ (+ alpha beta) i) i) (fma 2.0 i (+ alpha beta))) (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))))
0.3b	(/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
35.5b	(/ (* (+ (+ alpha beta) i) i) (fma 2.0 i (+ alpha beta)))
36.5b	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

rewrite228.0ms

Algorithm

rewrite-expression-head

Rules

196×	`times-frac`
151×	`add-sqr-sqrt`
139×	`*-un-lft-identity`
95×	`add-cube-cbrt`
28×	`difference-of-squares`
25×	`add-exp-log` `add-cbrt-cube`
24×	`associate-/l*`
16×	`associate-/r*` `div-inv`
14×	`sqrt-prod` `distribute-lft-out--`
11×	`cbrt-undiv` `div-exp`
8×	`distribute-lft-out`
4×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `associate-/r/` `log1p-expm1-u` `associate-/l/` `add-log-exp`
2×	`flip3-+` `associate-*l/` `prod-exp` `cbrt-unprod` `flip-+`
1×	`flip3--` `flip--`

Counts

4 → 230

Calls

4 calls:

86.0ms	(/ (/ (* (+ (+ alpha beta) i) i) (fma 2.0 i (+ alpha beta))) (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))))
38.0ms	(/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
70.0ms	(/ (* (+ (+ alpha beta) i) i) (fma 2.0 i (+ alpha beta)))
11.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

series1.3s

Counts

4 → 12

Calls

4 calls:

494.0ms	(/ (/ (* (+ (+ alpha beta) i) i) (fma 2.0 i (+ alpha beta))) (+ (sqrt 1.0) (fma 2.0 i (+ alpha beta))))
507.0ms	(/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
123.0ms	(/ (* (+ (+ alpha beta) i) i) (fma 2.0 i (+ alpha beta)))
167.0ms	(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

simplify1.7s

Counts

242 → 242

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	356	9313
1	897	9060
2	2895	8621
done	5000	8620

prune1.3s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 35.1b

regimes295.0ms

Accuracy

33.4% (2.6b remaining)

Error of 36.2b against oracle of 33.6b and baseline of 37.5b

bsearch77.0ms

Steps

Iters	Range		Point
8	5.1017931923025254e+200	4.847911097173389e+204	6.006963476966066e+202

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	58
1	31	58
done	31	58

end0.0ms

sample2.2s

Algorithm

intervals

Results

908.0ms	8000×	body	80	valid
843.0ms	8000×	pre	80	true