Details

sample57.0ms

Algorithm

intervals

Results

15.0ms	168×	body	160	valid
10.0ms	517×	pre	80	true
9.0ms	261×	body	80	nan
4.0ms	34×	body	320	valid
2.0ms	54×	body	80	valid

simplify52.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	78	16
4	90	16
5	98	16
done	98	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
38.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
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×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms	(- (* b b) (* (* 4.0 a) c))
38.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series299.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
43.0ms	(- (* b b) (* (* 4.0 a) c))
105.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
81.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify719.0ms

Counts

82 → 82

Iterations

Useful iterations: done (717.0ms)

Iter	Nodes	Cost
0	154	1565
1	406	1461
2	1361	1245
done	5000	1235

prune202.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite111.0ms

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-exp-log` `add-cbrt-cube`
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×	`sub-neg` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `flip3-+` `neg-log` `flip-+`

Counts

4 → 151

Calls

4 calls:

14.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
49.0ms	(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
38.0ms	(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series421.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
49.0ms	(- (* b b) (* (* 4.0 a) c))
126.0ms	(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
170.0ms	(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify988.0ms

Counts

163 → 163

Iterations

Useful iterations: done (977.0ms)

Iter	Nodes	Cost
0	254	5790
1	670	5273
2	2388	4513
done	5000	4511

prune475.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (+ 0 (* 4.0 (* a c))))) (* 2.0 a))
0.2b	(/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (+ 0 (* 4.0 (* a c)))))
0.3b	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (+ 0 (* 4.0 (* a c))))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

560×	`times-frac`
346×	`add-sqr-sqrt` `*-un-lft-identity`
210×	`add-cube-cbrt`
96×	`associate-/l*`
68×	`distribute-lft-out--` `difference-of-squares`
62×	`add-exp-log`
36×	`div-exp`
34×	`distribute-rgt-neg-in` `sqrt-prod`
32×	`add-cbrt-cube`
31×	`associate-/r*`
25×	`associate-/r/`
16×	`cbrt-undiv`
15×	`div-inv`
11×	`flip3-+` `flip-+`
7×	`prod-exp`
6×	`rec-exp` `1-exp` `add-log-exp`
5×	`pow1`
3×	`frac-2neg` `clear-num` `cbrt-unprod` `associate-/l/`
2×	`flip3--` `flip--`
1×	`sub-neg` `pow-flip` `diff-log` `div-sub` `inv-pow`

Counts

4 → 396

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
59.0ms	(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (+ 0 (* 4.0 (* a c))))) (* 2.0 a))
28.0ms	(/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (+ 0 (* 4.0 (* a c)))))
36.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (+ 0 (* 4.0 (* a c))))

series449.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* b b) (* (* 4.0 a) c))
124.0ms	(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (+ 0 (* 4.0 (* a c))))) (* 2.0 a))
166.0ms	(/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (+ 0 (* 4.0 (* a c)))))
109.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (+ 0 (* 4.0 (* a c))))

simplify2.1s

Counts

408 → 408

Iterations

Useful iterations: 2 (1.2s)

Iter	Nodes	Cost
0	511	15423
1	1351	13396
2	4717	12076
done	5000	12076

prune729.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 (- (/ (- b) (* (* 4.0 a) c)) (/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b	(/ (- b) (* (* 4.0 a) c))
0.2b	(/ 1 (- (/ (- b) (* (* 4.0 a) c)) (/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* (* 4.0 a) c))))
0.3b	(/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* (* 4.0 a) c))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

160×	`times-frac`
111×	`*-un-lft-identity`
71×	`add-sqr-sqrt`
51×	`add-cube-cbrt` `associate-/l*`
48×	`add-exp-log`
36×	`add-cbrt-cube`
30×	`distribute-lft-out--`
26×	`div-inv`
20×	`div-exp`
16×	`distribute-rgt-neg-in`
13×	`cbrt-undiv`
12×	`associate-/r/`
11×	`associate-/r*`
10×	`distribute-rgt-out--` `prod-exp` `difference-of-squares`
8×	`cbrt-unprod`
6×	`distribute-lft-neg-in` `sqrt-prod`
5×	`pow1`
4×	`flip3--` `frac-2neg` `clear-num` `flip--` `add-log-exp`
3×	`rec-exp` `1-exp` `frac-sub` `associate-/l/` `sub-div`
2×	`neg-mul-1` `sqrt-div`
1×	`neg-sub0` `pow-flip` `div-sub` `distribute-frac-neg` `inv-pow`

Counts

4 → 213

Calls

4 calls:

88.0ms	(/ (/ 1 (- (/ (- b) (* (* 4.0 a) c)) (/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms	(/ (- b) (* (* 4.0 a) c))
52.0ms	(/ 1 (- (/ (- b) (* (* 4.0 a) c)) (/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* (* 4.0 a) c))))
16.0ms	(/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* (* 4.0 a) c))

series553.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(/ (/ 1 (- (/ (- b) (* (* 4.0 a) c)) (/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* (* 4.0 a) c)))) (* 2.0 a))
27.0ms	(/ (- b) (* (* 4.0 a) c))
205.0ms	(/ 1 (- (/ (- b) (* (* 4.0 a) c)) (/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* (* 4.0 a) c))))
137.0ms	(/ (sqrt (- (* b b) (* (* 4.0 a) c))) (* (* 4.0 a) c))

simplify1.5s

Counts

225 → 225

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	391	6973
1	1024	6567
2	3915	5886
done	5001	5883

prune460.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

regimes101.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	33
1	28	33
done	28	33

end0.0ms

sample1.5s

Algorithm

intervals

Results

344.0ms	4871×	body	160	valid
303.0ms	16451×	pre	80	true
287.0ms	8451×	body	80	nan
144.0ms	1368×	body	320	valid
62.0ms	1761×	body	80	valid