Details

sample99.0ms

Algorithm

intervals

Results

33.0ms	172×	body	80	valid
16.0ms	31×	body	2560	valid
15.0ms	35×	body	1280	valid
7.0ms	20×	body	640	valid
7.0ms	82×	body	80	nan
3.0ms	5×	body	5120	valid
2.0ms	7×	body	320	valid
1.0ms	3×	body	160	valid

simplify95.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	116
5	116
4	107
3	82
2	45
1	24
0	14

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (sqrt (- (* b b) (* (* c a) 4))) b) 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)))

rewrite186.0ms

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:

100.0ms	(/ (/ (- (sqrt (- (* b b) (* (* c a) 4))) b) 2) a)
15.0ms	(- (* b b) (* (* c a) 4))
51.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
14.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series486.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(/ (/ (- (sqrt (- (* b b) (* (* c a) 4))) b) 2) a)
83.0ms	(- (* b b) (* (* c a) 4))
121.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
122.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify2.4s

Counts

165 → 165

Iterations

Iter	Nodes
done	5002
2	2935
1	691
0	279

prune799.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

localize21.0ms

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)))

rewrite225.0ms

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:

160.0ms	(* (- (sqrt (- (* b b) (* (* c a) 4))) b) (/ 1/2 a))
7.0ms	(- (* b b) (* (* c a) 4))
48.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
8.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series368.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(* (- (sqrt (- (* b b) (* (* c a) 4))) b) (/ 1/2 a))
48.0ms	(- (* b b) (* (* c a) 4))
90.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
101.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify1.6s

Counts

97 → 97

Iterations

Iter	Nodes
done	5001
2	2366
1	460
0	177

prune542.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.9b

localize5.0ms

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

prune18.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.9b

localize66.0ms

Local error

Found 4 expressions with local error:

16.1b	(- (* (- (* b b) (* (* c a) 4)) (sqrt (- (* b b) (* (* c a) 4)))) (* (* b b) b))
17.2b	(/ (- (* (- (* b b) (* (* c a) 4)) (sqrt (- (* b b) (* (* c a) 4)))) (* (* b b) b)) (+ (+ (- (* b b) (* (* c a) 4)) (* b (sqrt (- (* b b) (* (* c a) 4))))) (* b b)))
22.2b	(sqrt (- (* b b) (* (* c a) 4)))
22.2b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite315.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac`
10×	`pow3`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `sqrt-prod` `add-log-exp`
5×	`difference-cubes`
4×	`flip3--` `sqrt-div` `insert-posit16` `flip--` `associate-/l*`
3×	`associate-/r*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `flip-+` `div-inv`

Counts

4 → 83

Calls

4 calls:

52.0ms	(- (* (- (* b b) (* (* c a) 4)) (sqrt (- (* b b) (* (* c a) 4)))) (* (* b b) b))
233.0ms	(/ (- (* (- (* b b) (* (* c a) 4)) (sqrt (- (* b b) (* (* c a) 4)))) (* (* b b) b)) (+ (+ (- (* b b) (* (* c a) 4)) (* b (sqrt (- (* b b) (* (* c a) 4))))) (* b b)))
14.0ms	(sqrt (- (* b b) (* (* c a) 4)))
14.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series792.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(- (* (- (* b b) (* (* c a) 4)) (sqrt (- (* b b) (* (* c a) 4)))) (* (* b b) b))
441.0ms	(/ (- (* (- (* b b) (* (* c a) 4)) (sqrt (- (* b b) (* (* c a) 4)))) (* (* b b) b)) (+ (+ (- (* b b) (* (* c a) 4)) (* b (sqrt (- (* b b) (* (* c a) 4))))) (* b b)))
98.0ms	(sqrt (- (* b b) (* (* c a) 4)))
96.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify2.4s

Counts

95 → 95

Iterations

Iter	Nodes
done	5001
2	3060
1	510
0	171

prune667.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.8b

regimes324.0ms

Accuracy

85.6% (4.1b remaining)

Error of 9.6b against oracle of 5.5b and baseline of 33.9b

bsearch170.0ms

Steps

Iters	Range		Point
6	1.6664801848567985e-94	1.3864776888564433e-93	1.3635892865650846e-93
7	-8.18523145413159e+143	-2.8208844788355687e+142	-3.0775171197265305e+143

simplify4.0ms

Iterations

Iter	Nodes
done	32
1	32
0	26

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.2s	978×	body	1280	valid
969.0ms	1056×	body	2560	valid
787.0ms	5744×	body	80	valid
427.0ms	2913×	body	80	nan
258.0ms	454×	body	640	valid
211.0ms	138×	body	5120	valid
90.0ms	257×	body	320	valid
29.0ms	119×	body	160	valid