Details

sample114.0ms

Algorithm

intervals

Results

29.0ms	39×	body	2560	valid
24.0ms	180×	body	80	valid
19.0ms	29×	body	1280	valid
10.0ms	21×	body	640	valid
9.0ms	70×	body	80	nan
2.0ms	7×	body	320	valid
0.0ms	1×	body	160	valid

simplify118.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	93
7	93
6	92
5	90
4	82
3	66
2	40
1	21
0	12

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
1.0b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
1.0b	(- (* b b) (* (* 3 a) c))
19.1b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

90.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
49.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
15.0ms	(- (* b b) (* (* 3 a) c))
15.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series386.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
92.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
56.0ms	(- (* b b) (* (* 3 a) c))
109.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.1s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	1267
1	395
0	157

prune506.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3 a) c)
1.0b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
1.0b	(- (* b b) (* (* 3 a) c))
19.1b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod` `insert-posit16`
3×	`flip3--` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

20.0ms	(* (* 3 a) c)
66.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
14.0ms	(- (* b b) (* (* 3 a) c))
15.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series295.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (* 3 a) c)
111.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
57.0ms	(- (* b b) (* (* 3 a) c))
85.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify2.3s

Counts

76 → 76

Iterations

Iter	Nodes
done	5002
3	3467
2	910
1	297
0	123

prune474.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b b) (* (* 3 a) c))) b) (/ 1 (* 3 a)))
1.0b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
1.0b	(- (* b b) (* (* 3 a) c))
19.1b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite224.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
19×	`add-sqr-sqrt`
13×	`add-cbrt-cube`
12×	`*-un-lft-identity`
10×	`prod-exp`
8×	`add-cube-cbrt` `add-log-exp`
7×	`pow1` `associate-r`
6×	`associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`div-exp` `cbrt-unprod` `insert-posit16` `difference-of-squares`
3×	`times-frac`
2×	`frac-times` `cbrt-undiv` `rec-exp` `sub-neg` `sqrt-div` `diff-log` `1-exp` `associate-*l/` `distribute-lft-out--`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

149.0ms	(* (- (sqrt (- (* b b) (* (* 3 a) c))) b) (/ 1 (* 3 a)))
43.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
18.0ms	(- (* b b) (* (* 3 a) c))
12.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series424.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(* (- (sqrt (- (* b b) (* (* 3 a) c))) b) (/ 1 (* 3 a)))
107.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
71.0ms	(- (* b b) (* (* 3 a) c))
89.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify2.1s

Counts

97 → 97

Iterations

Iter	Nodes
done	5009
2	1714
1	466
0	183

prune596.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
1.0b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
1.0b	(- (* b b) (* (* 3 a) c))
19.1b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

81.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
46.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
13.0ms	(- (* b b) (* (* 3 a) c))
7.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series445.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
104.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
82.0ms	(- (* b b) (* (* 3 a) c))
90.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.3s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	1267
1	395
0	157

prune442.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.2b

regimes657.0ms

Accuracy

84.6% (4.2b remaining)

Error of 10.0b against oracle of 5.7b and baseline of 33.2b

bsearch251.0ms

Steps

Iters	Range		Point
9	1.542649851819534e-86	4.188981380654902e-77	5.930445637544082e-86
10	-9.235597319251238e+162	-1.2115114540629089e+151	-2.1550838670737497e+152

simplify9.0ms

Iterations

Iter	Nodes
done	31
1	31
0	26

end1.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	1057×	body	2560	valid
853.0ms	5901×	body	80	valid
640.0ms	895×	body	1280	valid
464.0ms	2938×	body	80	nan
270.0ms	456×	body	640	valid
132.0ms	106×	body	5120	valid
102.0ms	211×	body	320	valid
23.0ms	94×	body	160	valid