Details

sample110.0ms

Algorithm

intervals

Results

69.0ms	256×	body	80	valid
15.0ms	256×	pre	80	true

simplify856.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2046
3	1567
2	267
1	58
0	17

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 55.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
0.1b	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
38.8b	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
48.4b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

rewrite579.0ms

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×	`associate-l` `pow-prod-down` `insert-posit16` `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 → 204

Calls

4 calls:

123.0ms	(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
72.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
238.0ms	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
140.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

series1.8s

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
115.0ms	(* (* 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 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
261.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

simplify916.0ms

Counts

216 → 216

Iterations

Iter	Nodes
done	2012
1	1313
0	360

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 34.7b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
0.1b	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
35.0b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
35.4b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite1.0s

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×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-*r/`
2×	`flip3--` `flip--`
1×	`frac-times` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 368

Calls

4 calls:

206.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
638.0ms	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
44.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
109.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series3.6s

Counts

4 → 12

Calls

4 calls:

383.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
2.9s	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
131.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
178.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify1.4s

Counts

380 → 380

Iterations

Iter	Nodes
done	2001
1	1707
0	503

prune2.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 34.7b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b	(* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))))
0.0b	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
0.1b	(* (/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
35.4b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

329×	`times-frac`
285×	`add-sqr-sqrt`
226×	`*-un-lft-identity`
147×	`add-cube-cbrt`
117×	`associate-r`
70×	`add-cbrt-cube` `add-exp-log`
62×	`difference-of-squares`
36×	`associate-/r/`
31×	`sqrt-prod` `distribute-lft-out--`
29×	`cbrt-undiv` `div-exp`
20×	`prod-exp` `cbrt-unprod`
18×	`div-inv` `associate-/l*`
17×	`flip3-+` `flip-+`
13×	`associate-l`
10×	`distribute-lft-out`
9×	`associate-/r*`
8×	`pow1`
5×	`unswap-sqr`
4×	`insert-posit16` `add-log-exp`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `pow-prod-down` `associate-r/` `-commutative` `flip--`
1×	`frac-times` `associate-*l/`

Counts

4 → 348

Calls

4 calls:

98.0ms	(* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))))
233.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
657.0ms	(* (/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
120.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series3.4s

Counts

4 → 12

Calls

4 calls:

102.0ms	(* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))))
397.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
2.8s	(* (/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
151.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify1.5s

Counts

360 → 360

Iterations

Iter	Nodes
done	2002
1	1571
0	470

prune2.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.5b

localize71.0ms

Local error

Found 3 expressions with local error:

0.0b

(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))

0.0b

(/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))

0.0b

(* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))))

rewrite401.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
35×	`times-frac`
30×	`add-sqr-sqrt`
25×	`add-cube-cbrt`
23×	`distribute-lft-out`
21×	`associate-r`
19×	`add-cbrt-cube` `add-exp-log`
7×	`associate-/r*`
6×	`cbrt-undiv` `div-exp` `associate-/r/` `associate-/l*`
5×	`pow1`
4×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+`
3×	`associate-l` `insert-posit16` `div-inv` `add-log-exp` `associate-/l/`
2×	`clear-num` `frac-2neg` `associate-*r/` `unswap-sqr`
1×	`pow-prod-down` `*-commutative`

Counts

3 → 110

Calls

3 calls:

102.0ms

(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))

163.0ms

(/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))

134.0ms

(* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))))

series561.0ms

Counts

3 → 9

Calls

3 calls:

99.0ms

(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))

359.0ms

(/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))

102.0ms

(* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))))

simplify599.0ms

Counts

119 → 119

Iterations

Iter	Nodes
done	2000
1	483
0	165

prune695.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.5b

regimes351.0ms

Accuracy

45.5% (8.8b remaining)

Error of 10.8b against oracle of 2.0b and baseline of 18.1b

bsearch101.0ms

Steps

Iters	Range		Point
4	1.068852210417882e+133	1.6844947560592646e+133	1.6205126458778218e+133

simplify24.0ms

Iterations

Iter	Nodes
done	60
1	60
0	43

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.4s	8000×	body	80	valid
817.0ms	8000×	pre	80	true