Details

sample161.0ms

Algorithm

intervals

Results

45.0ms	172×	body	80	valid
29.0ms	31×	body	2560	valid
28.0ms	35×	body	1280	valid
13.0ms	20×	body	640	valid
12.0ms	82×	body	80	nan
6.0ms	5×	body	5120	valid
3.0ms	7×	body	320	valid
1.0ms	3×	body	160	valid

simplify107.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	116
5	116
4	108
3	86
2	45
1	24
0	14

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) 2) a)
0.4b	(- (* b b) (* (* 4 a) c))
0.9b	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
22.2b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 153

Calls

4 calls:

71.0ms	(/ (/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) 2) a)
14.0ms	(- (* b b) (* (* 4 a) c))
36.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
7.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series414.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ (/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) 2) a)
81.0ms	(- (* b b) (* (* 4 a) c))
107.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
84.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.9s

Counts

165 → 165

Iterations

Iter	Nodes
done	5000
2	2973
1	686
0	279

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.9b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- (sqrt (- (* b b) (* c (* a 4)))) b) (/ 1/2 a))
0.4b	(- (* b b) (* c (* a 4)))
0.9b	(- (sqrt (- (* b b) (* c (* a 4)))) b)
22.2b	(sqrt (- (* b b) (* c (* a 4))))

rewrite237.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

129.0ms	(* (- (sqrt (- (* b b) (* c (* a 4)))) b) (/ 1/2 a))
17.0ms	(- (* b b) (* c (* a 4)))
73.0ms	(- (sqrt (- (* b b) (* c (* a 4)))) b)
16.0ms	(sqrt (- (* b b) (* c (* a 4))))

series429.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(* (- (sqrt (- (* b b) (* c (* a 4)))) b) (/ 1/2 a))
66.0ms	(- (* b b) (* c (* a 4)))
141.0ms	(- (sqrt (- (* b b) (* c (* a 4)))) b)
105.0ms	(sqrt (- (* b b) (* c (* a 4))))

simplify1.5s

Counts

97 → 97

Iterations

Iter	Nodes
done	5002
2	2384
1	455
0	177

prune523.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.9b

localize35.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
0.9b	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
22.2b	(sqrt (- (* b b) (* (* 4 a) c)))
22.2b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`sqrt-prod` `add-log-exp`
6×	`pow1` `add-cube-cbrt`
4×	`flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

39.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
38.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
11.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
15.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series438.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
121.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
116.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
94.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.6s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
3	4459
2	788
1	202
0	82

prune371.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.9b

localize6.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune0.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.9b

regimes260.0ms

Accuracy

85.5% (4.1b remaining)

Error of 9.5b against oracle of 5.4b and baseline of 33.9b

bsearch163.0ms

Steps

Iters	Range		Point
6	1.6664801848567985e-94	1.3864776888564433e-93	1.3635892865650846e-93
7	-8.18523145413159e+143	-2.8208844788355687e+142	-5.517926393801403e+142

simplify4.0ms

Iterations

Iter	Nodes
done	28
1	28
0	24

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.0s	978×	body	1280	valid
963.0ms	1056×	body	2560	valid
856.0ms	5744×	body	80	valid
533.0ms	257×	body	320	valid
405.0ms	2913×	body	80	nan
256.0ms	454×	body	640	valid
150.0ms	138×	body	5120	valid
28.0ms	119×	body	160	valid