Details

sample51.0ms

Algorithm

intervals

Results

19.0ms	256×	body	80	valid
6.0ms	256×	pre	80	true

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
3	1807
2	295
1	60
0	17

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.8b

localize40.0ms

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))))
37.1b	(/ (/ (* (* 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))
45.5b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite871.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-cbrt-cube` `add-exp-log`
58×	`times-frac`
54×	`flip3-+` `flip-+`
50×	`associate-/r/`
44×	`add-sqr-sqrt`
36×	`frac-times`
30×	`associate-*r/`
28×	`*-un-lft-identity` `add-cube-cbrt`
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` `clear-num` `frac-2neg` `distribute-lft-in` `*-commutative`
1×	`pow2` `pow-plus` `flip3--` `pow-sqr` `pow-prod-up` `flip--` `unswap-sqr`

Counts

4 → 208

Calls

4 calls:

206.0ms	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
130.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
328.0ms	(/ (/ (* (* 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))
191.0ms	(/ (* (* 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:

76.0ms	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
141.0ms	(* (* 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))
272.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify1.7s

Counts

220 → 220

Iterations

Iter	Nodes
done	5002
1	1372
0	366

prune1.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 35.4b

localize83.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.1b	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
35.6b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
36.1b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

366×	`times-frac`
300×	`add-sqr-sqrt`
235×	`*-un-lft-identity`
155×	`add-cube-cbrt`
96×	`associate-r`
70×	`add-cbrt-cube` `add-exp-log`
62×	`difference-of-squares`
44×	`associate-/r/`
42×	`associate-l`
33×	`cbrt-undiv` `div-exp`
31×	`sqrt-prod` `distribute-lft-out--`
22×	`flip3-+` `flip-+` `div-inv`
19×	`associate-/l*`
16×	`prod-exp` `cbrt-unprod`
12×	`associate-/r*`
9×	`distribute-lft-out`
6×	`pow1` `unswap-sqr`
5×	`associate-/l/`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-*r/`
2×	`flip3--` `flip--`
1×	`frac-times` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 372

Calls

4 calls:

282.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
998.0ms	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
70.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
158.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series4.1s

Counts

4 → 12

Calls

4 calls:

478.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
3.3s	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
131.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
221.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify2.3s

Counts

384 → 384

Iterations

Iter	Nodes
done	5001
1	1811
0	509

prune2.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 35.3b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.1b	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))
35.6b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
36.1b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

85×	`add-cbrt-cube` `add-exp-log`
79×	`times-frac`
63×	`*-un-lft-identity`
61×	`add-sqr-sqrt`
42×	`associate-l`
41×	`add-cube-cbrt`
40×	`cbrt-undiv` `div-exp`
21×	`prod-exp` `cbrt-unprod`
18×	`associate-/r/`
15×	`associate-r`
12×	`associate-/r*`
10×	`flip3-+` `flip-+`
9×	`div-inv` `distribute-lft-out`
7×	`associate-/l/`
6×	`pow1`
5×	`associate-/l*`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u` `add-log-exp` `difference-of-squares` `unswap-sqr`
3×	`clear-num` `frac-2neg`
2×	`frac-times` `associate-*l/` `sqrt-prod` `distribute-lft-out--`
1×	`flip3--` `pow-prod-down` `*-commutative` `flip--`

Counts

4 → 199

Calls

4 calls:

394.0ms	(/ (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
537.0ms	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))
75.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
121.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series4.5s

Counts

4 → 12

Calls

4 calls:

3.4s	(/ (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
866.0ms	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))
129.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
192.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify1.5s

Counts

211 → 211

Iterations

Iter	Nodes
done	5001
1	1208
0	347

prune1.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 35.3b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))
0.1b	(/ (* (/ (/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.1b	(* (/ (/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))
36.1b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

759×	`times-frac`
636×	`*-un-lft-identity`
336×	`add-sqr-sqrt`
296×	`add-cube-cbrt`
278×	`associate-l`
188×	`distribute-lft-out`
82×	`add-cbrt-cube` `add-exp-log`
43×	`cbrt-undiv` `div-exp`
38×	`associate-/r/`
21×	`div-inv`
18×	`flip3-+` `flip-+`
16×	`prod-exp` `cbrt-unprod`
15×	`associate-r`
14×	`associate-/r*`
8×	`unswap-sqr`
7×	`associate-/l*` `associate-/l/`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`clear-num` `frac-2neg`
2×	`frac-times` `associate-l/` `associate-r/` `sqrt-prod` `distribute-lft-out--`
1×	`flip3--` `pow-prod-down` `*-commutative` `flip--`

Counts

4 → 453

Calls

4 calls:

96.0ms	(/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))
289.0ms	(/ (* (/ (/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
617.0ms	(* (/ (/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))
529.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series4.4s

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))
3.4s	(/ (* (/ (/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
801.0ms	(* (/ (/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))
176.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify2.6s

Counts

465 → 465

Iterations

Iter	Nodes
done	5001
1	2191
0	637

prune3.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.9b

regimes319.0ms

Accuracy

41% (9.5b remaining)

Error of 11.4b against oracle of 1.9b and baseline of 18.0b

bsearch151.0ms

Steps

Iters	Range		Point
8	2.3380853692493277e+111	8.290998643302116e+113	1.8735013853412201e+112

simplify15.0ms

Iterations

Iter	Nodes
done	47
1	47
0	35

end0.0ms

sample1.7s

Algorithm

intervals

Results

872.0ms	8000×	body	80	valid
364.0ms	8000×	pre	80	true