Details

sample53.0ms

Algorithm

intervals

Results

27.0ms	256×	body	80	valid
11.0ms	256×	pre	80	true

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	2093
4	2093
3	1567
2	267
1	58
0	17

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.7b

localize51.0ms

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))))
34.9b	(/ (/ (* (* 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))
46.2b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

rewrite653.0ms

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:

117.0ms	(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
91.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
283.0ms	(/ (/ (* (* 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))
157.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

series1.4s

Counts

4 → 12

Calls

4 calls:

79.0ms	(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
122.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
974.0ms	(/ (/ (* (* 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))
231.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

simplify1.3s

Counts

216 → 216

Iterations

Iter	Nodes
done	2012
2	2012
1	1313
0	360

prune2.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 34.5b

localize49.0ms

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))))
34.5b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
34.8b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite1.1s

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:

215.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
639.0ms	(* (/ (/ (* 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))))
65.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
152.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series3.4s

Counts

4 → 12

Calls

4 calls:

460.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
2.7s	(* (/ (/ (* 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))))
126.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
153.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify1.7s

Counts

380 → 380

Iterations

Iter	Nodes
done	2002
2	2002
1	1707
0	503

prune5.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 34.4b

localize96.0ms

Local error

Found 4 expressions with local error:

34.5b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
34.5b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
34.8b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
34.8b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite391.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac` `add-cube-cbrt`
18×	`add-cbrt-cube` `add-exp-log`
12×	`associate-/r*`
8×	`flip3-+` `associate-/r/` `flip-+` `associate-/l*` `associate-/l/`
6×	`cbrt-undiv` `div-exp`
4×	`pow1` `clear-num` `frac-2neg` `associate-*r/` `insert-posit16` `div-inv` `add-log-exp`
2×	`prod-exp` `cbrt-unprod`

Counts

4 → 116

Calls

4 calls:

61.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
72.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
121.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
136.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series577.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
115.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
156.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
164.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify1.5s

Counts

128 → 128

Iterations

Iter	Nodes
done	2017
3	2017
2	1825
1	381
0	126

prune2.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 34.4b

localize79.0ms

Local error

Found 4 expressions with local error:

34.5b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
34.5b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
34.8b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
34.8b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite385.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac` `add-cube-cbrt`
18×	`add-cbrt-cube` `add-exp-log`
12×	`associate-/r*`
8×	`flip3-+` `associate-/r/` `flip-+` `associate-/l*` `associate-/l/`
6×	`cbrt-undiv` `div-exp`
4×	`pow1` `clear-num` `frac-2neg` `associate-*r/` `insert-posit16` `div-inv` `add-log-exp`
2×	`prod-exp` `cbrt-unprod`

Counts

4 → 116

Calls

4 calls:

62.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
56.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
140.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
124.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series595.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
134.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
150.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
198.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify1.6s

Counts

128 → 128

Iterations

Iter	Nodes
done	2017
3	2017
2	1825
1	381
0	126

prune2.7s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 34.4b

regimes228.0ms

Accuracy

0% (2.5b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	34
1	34
0	25

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.9s	8000×	body	80	valid
403.0ms	8000×	pre	80	true