Details

sample246.0ms

Algorithm

intervals

Results

27.0ms	182×	body	80	valid
25.0ms	35×	body	1280	valid
22.0ms	26×	body	2560	valid
11.0ms	91×	body	80	nan
8.0ms	15×	body	640	valid
4.0ms	4×	body	5120	valid
3.0ms	8×	body	320	valid
1.0ms	2×	body	160	valid

simplify87.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	44
4	44
3	41
2	32
1	18
0	10

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.6b	(- (* b_2 b_2) (* a c))
24.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `insert-posit16` `flip--`
3×	`associate-/r*` `diff-log`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `div-inv`

Counts

4 → 95

Calls

4 calls:

80.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
42.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
15.0ms	(- (* b_2 b_2) (* a c))
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series420.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
124.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
44.0ms	(- (* b_2 b_2) (* a c))
122.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify874.0ms

Counts

107 → 107

Iterations

Iter	Nodes
3	2560
2	1015
1	388
0	162

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.7b

localize25.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* b_2 b_2) (* a c))
4.0b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.6b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
24.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
146×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
81×	`add-cube-cbrt`
32×	`difference-of-squares`
27×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-lft-out--`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp` `insert-posit16`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg` `sqrt-div`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 188

Calls

4 calls:

15.0ms	(- (* b_2 b_2) (* a c))
97.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
48.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series617.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- (* b_2 b_2) (* a c))
209.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
254.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
100.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify883.0ms

Counts

200 → 200

Iterations

Iter	Nodes
2	2201
1	733
0	306

prune2.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.7b

localize23.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* b_2 b_2) (* a c))
4.0b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.6b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
24.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite624.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
146×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
81×	`add-cube-cbrt`
32×	`difference-of-squares`
27×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-lft-out--`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp` `insert-posit16`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg` `sqrt-div`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 188

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
532.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
66.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series584.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- (* b_2 b_2) (* a c))
199.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
259.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
76.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify802.0ms

Counts

200 → 200

Iterations

Iter	Nodes
2	2201
1	733
0	306

prune2.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.7b

localize79.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* b_2 b_2) (* a c))
5.1b	(* (/ a (cbrt a)) (/ c (cbrt a)))
5.8b	(* (* (/ a (cbrt a)) (/ c (cbrt a))) (/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (cbrt a)))
24.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

300×	`times-frac`
243×	`add-sqr-sqrt`
176×	`*-un-lft-identity`
170×	`associate-r`
140×	`add-cube-cbrt`
131×	`add-exp-log`
96×	`cbrt-prod`
59×	`add-cbrt-cube`
54×	`div-exp`
49×	`prod-exp`
36×	`difference-of-squares`
31×	`cbrt-undiv` `cbrt-unprod`
23×	`associate-l`
21×	`sqrt-prod`
18×	`distribute-lft-out--`
12×	`pow1` `associate-/r/`
9×	`div-inv` `unswap-sqr`
8×	`flip3--` `flip--`
6×	`frac-times` `associate-*l/` `add-log-exp`
5×	`rec-exp` `1-exp`
4×	`pow-prod-down` `associate-*r/` `insert-posit16`
2×	`sqrt-div` `*-commutative`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 310

Calls

4 calls:

8.0ms	(- (* b_2 b_2) (* a c))
17.0ms	(* (/ a (cbrt a)) (/ c (cbrt a)))
102.0ms	(* (* (/ a (cbrt a)) (/ c (cbrt a))) (/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (cbrt a)))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series594.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (* b_2 b_2) (* a c))
161.0ms	(* (/ a (cbrt a)) (/ c (cbrt a)))
281.0ms	(* (* (/ a (cbrt a)) (/ c (cbrt a))) (/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (cbrt a)))
87.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.3s

Counts

322 → 322

Iterations

Iter	Nodes
2	6194
1	1809
0	529

prune3.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.7b

regimes488.0ms

Accuracy

90.8% (2.3b remaining)

Error of 8.1b against oracle of 5.8b and baseline of 30.5b

bsearch307.0ms

Steps

Iters	Range		Point
6	2.332248586404817e+54	2.734436825826664e+55	2.6656023684116586e+55
10	-2.41525809068359e-149	-7.408643487586304e-161	-7.54129264686236e-161
10	-5.8265675171318085e+48	-9.838122626960614e+38	-4.293594559701796e+48

simplify26.0ms

Iterations

Iter	Nodes
2	41
1	41
0	33

end0.0ms

sample3.8s

Algorithm

intervals

Results

929.0ms	1042×	body	2560	valid
766.0ms	5889×	body	80	valid
711.0ms	2911×	body	80	nan
646.0ms	935×	body	1280	valid
262.0ms	475×	body	640	valid
88.0ms	110×	body	5120	valid
69.0ms	207×	body	320	valid
22.0ms	107×	body	160	valid