Details

sample207.0ms

Algorithm

intervals

Results

61.0ms	17×	body	640	valid
23.0ms	109×	body	320	valid
17.0ms	256×	body	80	nan
16.0ms	512×	pre	80	true
14.0ms	96×	body	160	valid
2.0ms	34×	body	80	valid

simplify82.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	111
5	111
4	102
3	78
2	44
1	24
0	14

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
26.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`neg-sub0` `cbrt-undiv` `sum-log` `flip3-+` `flip3--` `sqrt-div` `div-exp` `associate-+l-` `flip-+` `flip--` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `associate-/r*` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms	(- (* b b) (* (* 4.0 a) c))
117.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
20.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series427.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
64.0ms	(- (* b b) (* (* 4.0 a) c))
159.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
112.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify879.0ms

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
2	1908
1	419
0	154

prune460.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 4.0 a) c))
0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
82×	`add-sqr-sqrt` `*-un-lft-identity`
38×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-cbrt-cube` `add-exp-log`
11×	`distribute-rgt-neg-in` `sqrt-prod`
10×	`add-log-exp`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`flip3--` `flip--`
4×	`pow1` `div-inv`
3×	`diff-log` `associate-/l/`
2×	`clear-num` `sub-neg` `frac-2neg` `prod-exp` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `flip3-+` `neg-log` `flip-+`

Counts

4 → 151

Calls

4 calls:

6.0ms	(- (* b b) (* (* 4.0 a) c))
19.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
52.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
96.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series656.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- (* b b) (* (* 4.0 a) c))
124.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
268.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
210.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify1.9s

Counts

163 → 163

Iterations

Iter	Nodes
done	5001
2	3812
1	657
0	247

prune835.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 c) a))))
0.3b	(/ 1 (* (* (/ 2.0 4.0) (/ a (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 c) a))))))
0.3b	(/ a (* a c))
0.3b	(* (* (/ 2.0 4.0) (/ a (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 c) a)))))

rewrite365.0ms

Algorithm

rewrite-expression-head

Rules

136×	`add-exp-log`
76×	`add-cbrt-cube`
61×	`prod-exp`
46×	`div-exp`
31×	`cbrt-unprod`
24×	`cbrt-undiv`
18×	`frac-times`
17×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`pow1`
12×	`associate-*l/`
11×	`associate-/r/`
10×	`associate-*r/`
9×	`flip3--` `add-cube-cbrt` `flip--`
8×	`rec-exp` `1-exp` `add-log-exp`
7×	`associate-r`
6×	`times-frac` `pow-prod-down` `associate-/l*`
4×	`distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `pow-flip`
2×	`distribute-rgt-in` `clear-num` `associate-/r*` `distribute-rgt-neg-in` `frac-2neg` `distribute-lft-in` `diff-log` `sqrt-prod` `div-inv`
1×	`associate--l-` `neg-sub0` `associate-l` `neg-log` `*-commutative` `inv-pow`

Counts

4 → 150

Calls

4 calls:

18.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 c) a))))
179.0ms	(/ 1 (* (* (/ 2.0 4.0) (/ a (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 c) a))))))
7.0ms	(/ a (* a c))
156.0ms	(* (* (/ 2.0 4.0) (/ a (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 c) a)))))

series489.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 c) a))))
246.0ms	(/ 1 (* (* (/ 2.0 4.0) (/ a (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 c) a))))))
12.0ms	(/ a (* a c))
128.0ms	(* (* (/ 2.0 4.0) (/ a (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 c) a)))))

simplify456.0ms

Counts

162 → 162

Iterations

Iter	Nodes
done	5000
1	866
0	269

prune810.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (* b b) (* (* 4.0 c) a)))
0.1b	(/ (/ (* 1 c) (/ 2.0 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 c) a)))))
0.1b	(- (* b b) (* (* 4.0 c) a))
0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 c) a))))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

302×	`times-frac`
169×	`add-sqr-sqrt`
168×	`*-un-lft-identity`
88×	`add-cube-cbrt`
40×	`distribute-lft-out--` `difference-of-squares`
29×	`add-exp-log`
23×	`sqrt-prod`
22×	`add-cbrt-cube`
20×	`distribute-rgt-neg-in`
18×	`associate-/l*`
17×	`div-inv`
16×	`div-exp`
11×	`cbrt-undiv`
10×	`associate-/r/` `add-log-exp`
7×	`associate-/r*`
5×	`pow1`
4×	`flip3--` `prod-exp` `flip--`
3×	`diff-log`
2×	`sub-neg` `sqrt-div` `1-exp` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 221

Calls

4 calls:

7.0ms	(sqrt (- (* b b) (* (* 4.0 c) a)))
62.0ms	(/ (/ (* 1 c) (/ 2.0 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 c) a)))))
6.0ms	(- (* b b) (* (* 4.0 c) a))
19.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 c) a))))

series502.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(sqrt (- (* b b) (* (* 4.0 c) a)))
244.0ms	(/ (/ (* 1 c) (/ 2.0 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 c) a)))))
64.0ms	(- (* b b) (* (* 4.0 c) a))
108.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 c) a))))

simplify2.1s

Counts

233 → 233

Iterations

Iter	Nodes
done	5002
2	4986
1	1077
0	383

prune1.2s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes226.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	23
2	23
1	22
0	17

end0.0ms

sample5.3s

Algorithm

intervals

Results

1.6s	3662×	body	320	valid
1.3s	16233×	pre	80	true
778.0ms	8233×	body	80	nan
570.0ms	2940×	body	160	valid
190.0ms	471×	body	640	valid
119.0ms	927×	body	80	valid