Details

sample64.0ms

Algorithm

intervals

Results

13.0ms	112×	body	320	valid
10.0ms	277×	body	80	nan
10.0ms	533×	pre	80	true
8.0ms	98×	body	160	valid
3.0ms	19×	body	640	valid
1.0ms	27×	body	80	valid

simplify57.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	45	16
3	87	16
4	105	16
5	113	16
done	113	16

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.9b

localize12.0ms

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))
28.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms	(- (* b b) (* (* 4.0 a) c))
35.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series310.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
45.0ms	(- (* b b) (* (* 4.0 a) c))
109.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
82.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify728.0ms

Counts

102 → 102

Iterations

Useful iterations: done (726.0ms)

Iter	Nodes	Cost
0	167	1697
1	436	1584
2	1482	1361
done	5000	1351

prune248.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

123×	`add-sqr-sqrt` `*-un-lft-identity`
90×	`times-frac`
79×	`add-cube-cbrt`
61×	`prod-diff`
41×	`sqrt-prod`
32×	`distribute-rgt-neg-in`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
11×	`fma-neg`
10×	`add-log-exp`
8×	`associate-/r*`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`flip3--` `flip--`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`diff-log` `associate-/l/`
2×	`sub-neg` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `flip3-+` `neg-log` `flip-+`

Counts

4 → 231

Calls

4 calls:

16.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
39.0ms	(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
55.0ms	(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series479.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms	(- (* b b) (* (* 4.0 a) c))
192.0ms	(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
161.0ms	(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify1.0s

Counts

243 → 243

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	341	10754
1	833	8177
2	2856	6648
done	5000	6646

prune607.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ (+ (* 4.0 (* a c)) (* b (- b b))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
53×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
48×	`add-cube-cbrt`
34×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`add-exp-log` `add-cbrt-cube`
11×	`fma-neg`
10×	`add-log-exp`
7×	`neg-mul-1`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`cbrt-undiv` `times-frac` `diff-log` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`sub-neg` `sqrt-div` `associate-*r/` `associate-/r/` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `clear-num` `associate-/r*` `flip-+` `div-inv`

Counts

4 → 152

Calls

4 calls:

4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
16.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
35.0ms	(/ (+ (* 4.0 (* a c)) (* b (- b b))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series355.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
81.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms	(- (* b b) (* (* 4.0 a) c))
155.0ms	(/ (+ (* 4.0 (* a c)) (* b (- b b))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify905.0ms

Counts

164 → 164

Iterations

Useful iterations: done (897.0ms)

Iter	Nodes	Cost
0	265	7046
1	672	4933
2	2474	3810
done	5001	3809

prune398.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

107×	`add-sqr-sqrt` `*-un-lft-identity`
76×	`times-frac`
71×	`add-cube-cbrt`
61×	`prod-diff`
39×	`sqrt-prod`
30×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
11×	`fma-neg`
10×	`div-inv` `associate-/l*` `add-log-exp`
8×	`associate-/r*`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `diff-log` `flip--`
2×	`sub-neg` `frac-2neg` `prod-exp` `clear-num` `associate-/r/` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `neg-log` `associate-/l/`

Counts

4 → 213

Calls

4 calls:

26.0ms	(/ (/ (fma 4.0 (* a c) 0) (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
16.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
3.0ms	(/ (fma 4.0 (* a c) 0) (* 2.0 a))

series413.0ms

Counts

4 → 12

Calls

4 calls:

236.0ms	(/ (/ (fma 4.0 (* a c) 0) (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
81.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms	(- (* b b) (* (* 4.0 a) c))
50.0ms	(/ (fma 4.0 (* a c) 0) (* 2.0 a))

simplify906.0ms

Counts

225 → 225

Iterations

Useful iterations: done (898.0ms)

Iter	Nodes	Cost
0	314	9204
1	738	7212
2	2449	5980
done	5001	5979

prune500.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

regimes109.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	17
1	17	17
done	17	17

end0.0ms

sample1.8s

Algorithm

intervals

Results

435.0ms	3624×	body	320	valid
313.0ms	8210×	body	80	nan
313.0ms	16210×	pre	80	true
241.0ms	2991×	body	160	valid
77.0ms	472×	body	640	valid
36.0ms	913×	body	80	valid