Details

sample358.0ms

Algorithm

intervals

Results

82.0ms	256×	body	80	nan
35.0ms	116×	body	320	valid
22.0ms	512×	pre	80	true
19.0ms	98×	body	160	valid
6.0ms	16×	body	640	valid
2.0ms	26×	body	80	valid

simplify113.0ms

Counts

1 → 1

Iterations

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.0b

localize21.0ms

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))
26.0b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite104.0ms

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:

7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(- (* b b) (* (* 4.0 a) c))
67.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
20.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series437.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
64.0ms	(- (* b b) (* (* 4.0 a) c))
174.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
106.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify918.0ms

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
2	1908
1	419
0	154

prune425.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

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))))
0.2b	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite247.0ms

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:

12.0ms	(- (* b b) (* (* 4.0 a) c))
36.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
120.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
68.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series699.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (* b b) (* (* 4.0 a) c))
112.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
224.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
289.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify1.9s

Counts

163 → 163

Iterations

Iter	Nodes
done	5000
2	3803
1	658
0	247

prune954.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (/ (* (- (- b) (sqrt (- (* b b) (* (* a c) 4.0)))) a) (* 4.0 a)))
0.1b	(- (* b b) (* (* a c) 4.0))
0.1b	(- (- b) (sqrt (- (* b b) (* (* a c) 4.0))))
0.1b	(/ (* (- (- b) (sqrt (- (* b b) (* (* a c) 4.0)))) a) (* 4.0 a))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-cbrt-cube` `add-exp-log`
20×	`times-frac`
18×	`add-sqr-sqrt` `*-un-lft-identity`
14×	`add-cube-cbrt`
13×	`cbrt-undiv` `div-exp`
10×	`add-log-exp`
8×	`prod-exp` `cbrt-unprod`
6×	`associate-/r*` `div-inv`
4×	`pow1` `associate-/l*`
3×	`flip3--` `diff-log` `flip--`
2×	`clear-num` `sub-neg` `frac-2neg` `associate-*l/` `distribute-lft-out--` `difference-of-squares` `associate-/l/`
1×	`associate--l-` `neg-sub0` `distribute-rgt-neg-in` `neg-log` `associate-/r/` `sqrt-prod`

Counts

4 → 97

Calls

4 calls:

40.0ms	(/ c (/ (* (- (- b) (sqrt (- (* b b) (* (* a c) 4.0)))) a) (* 4.0 a)))
6.0ms	(- (* b b) (* (* a c) 4.0))
25.0ms	(- (- b) (sqrt (- (* b b) (* (* a c) 4.0))))
54.0ms	(/ (* (- (- b) (sqrt (- (* b b) (* (* a c) 4.0)))) a) (* 4.0 a))

series602.0ms

Counts

4 → 12

Calls

4 calls:

243.0ms	(/ c (/ (* (- (- b) (sqrt (- (* b b) (* (* a c) 4.0)))) a) (* 4.0 a)))
69.0ms	(- (* b b) (* (* a c) 4.0))
138.0ms	(- (- b) (sqrt (- (* b b) (* (* a c) 4.0))))
152.0ms	(/ (* (- (- b) (sqrt (- (* b b) (* (* a c) 4.0)))) a) (* 4.0 a))

simplify1.5s

Counts

109 → 109

Iterations

Iter	Nodes
done	5000
2	3428
1	598
0	206

prune736.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

159×	`times-frac`
128×	`add-sqr-sqrt`
127×	`*-un-lft-identity`
75×	`add-cube-cbrt`
26×	`distribute-lft-out--` `difference-of-squares`
25×	`associate-/r*`
16×	`sqrt-prod`
13×	`distribute-rgt-neg-in`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `div-inv`
3×	`cbrt-undiv` `flip3--` `diff-log` `div-exp` `flip--` `associate-/l*`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `associate-/r/`

Counts

4 → 163

Calls

4 calls:

14.0ms	(sqrt (- (* b b) (* (* 4.0 c) a)))
70.0ms	(/ c (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 c) a)))) 4.0))
19.0ms	(- (* b b) (* (* 4.0 c) a))
35.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 c) a))))

series564.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(sqrt (- (* b b) (* (* 4.0 c) a)))
297.0ms	(/ c (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 c) a)))) 4.0))
65.0ms	(- (* b b) (* (* 4.0 c) a))
109.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 c) a))))

simplify1.8s

Counts

175 → 175

Iterations

Iter	Nodes
done	5001
2	3234
1	723
0	272

prune923.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes240.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	25
2	25
1	24
0	18

end0.0ms

sample5.1s

Algorithm

intervals

Results

1.2s	8098×	body	80	nan
1.2s	16098×	pre	80	true
1.1s	3577×	body	320	valid
555.0ms	3042×	body	160	valid
184.0ms	467×	body	640	valid
131.0ms	914×	body	80	valid