Details

sample94.0ms

Algorithm

intervals

Results

34.0ms	267×	body	80	nan
15.0ms	163×	body	160	valid
11.0ms	523×	pre	80	true
7.0ms	50×	body	320	valid
2.0ms	43×	body	80	valid

simplify75.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	79	16
4	99	16
5	107	16
done	107	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 46.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
41.1b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite174.0ms

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:

20.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms	(- (* b b) (* (* 4.0 a) c))
111.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
25.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series361.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
51.0ms	(- (* b b) (* (* 4.0 a) c))
113.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
117.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.1s

Counts

82 → 82

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	154	1565
1	419	1461
2	1926	1245
done	5001	1239

prune282.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

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	(/ (+ 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))

rewrite267.0ms

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:

24.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(- (* b b) (* (* 4.0 a) c))
68.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
153.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series633.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
66.0ms	(- (* b b) (* (* 4.0 a) c))
206.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
243.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify2.4s

Counts

163 → 163

Iterations

Useful iterations: 2 (792.0ms)

Iter	Nodes	Cost
0	247	5048
1	658	4512
2	3777	4174
done	5001	4174

prune712.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite378.0ms

Algorithm

rewrite-expression-head

Rules

719×	`times-frac`
330×	`add-exp-log`
257×	`add-sqr-sqrt` `*-un-lft-identity`
214×	`div-exp`
185×	`add-cube-cbrt`
138×	`add-cbrt-cube`
83×	`prod-exp`
72×	`cbrt-undiv`
52×	`div-inv`
50×	`associate-/r/`
45×	`1-exp`
38×	`associate-/r*`
36×	`distribute-lft-out--` `difference-of-squares`
33×	`cbrt-unprod`
18×	`rec-exp` `flip3--` `distribute-rgt-neg-in` `sqrt-prod` `flip--`
15×	`associate-/l*`
6×	`add-log-exp`
4×	`pow1`
3×	`frac-2neg` `clear-num`
1×	`sub-neg` `diff-log` `associate-/l/`

Counts

4 → 457

Calls

4 calls:

9.0ms	(- (* b b) (* (* 4.0 a) c))
89.0ms	(/ (* 2.0 a) (/ (* (* a c) 4.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
97.0ms	(/ (/ 1 1) (/ (* 2.0 a) (/ (* (* a c) 4.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
121.0ms	(/ (* (* a c) 4.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series720.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* b b) (* (* 4.0 a) c))
133.0ms	(/ (* 2.0 a) (/ (* (* a c) 4.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
236.0ms	(/ (/ 1 1) (/ (* 2.0 a) (/ (* (* a c) 4.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
298.0ms	(/ (* (* a c) 4.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify2.4s

Counts

469 → 469

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	692	19688
1	2716	16622
done	5001	15148

prune906.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 (/ (* 2.0 a) (* (* a c) 4.0))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ 1 (/ (* 2.0 a) (* (* a c) 4.0)))
0.2b	(/ (* 2.0 a) (* (* a c) 4.0))

rewrite279.0ms

Algorithm

rewrite-expression-head

Rules

304×	`times-frac`
194×	`add-exp-log`
191×	`add-sqr-sqrt` `*-un-lft-identity`
107×	`add-cube-cbrt`
92×	`div-exp` `add-cbrt-cube`
63×	`prod-exp`
42×	`distribute-lft-out--` `difference-of-squares`
40×	`cbrt-undiv`
39×	`div-inv`
27×	`cbrt-unprod`
24×	`associate-/l*`
21×	`distribute-rgt-neg-in` `sqrt-prod`
14×	`rec-exp` `1-exp`
13×	`associate-/r*`
11×	`associate-/r/`
6×	`add-log-exp`
5×	`pow1`
3×	`frac-2neg` `clear-num`
2×	`flip3--` `flip--`
1×	`sub-neg` `pow-flip` `diff-log` `associate-/l/` `inv-pow`

Counts

4 → 311

Calls

4 calls:

123.0ms	(/ (/ 1 (/ (* 2.0 a) (* (* a c) 4.0))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
8.0ms	(- (* b b) (* (* 4.0 a) c))
73.0ms	(/ 1 (/ (* 2.0 a) (* (* a c) 4.0)))
45.0ms	(/ (* 2.0 a) (* (* a c) 4.0))

series295.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(/ (/ 1 (/ (* 2.0 a) (* (* a c) 4.0))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
48.0ms	(- (* b b) (* (* 4.0 a) c))
16.0ms	(/ 1 (/ (* 2.0 a) (* (* a c) 4.0)))
24.0ms	(/ (* 2.0 a) (* (* a c) 4.0))

simplify731.0ms

Counts

323 → 323

Iterations

Useful iterations: done (713.0ms)

Iter	Nodes	Cost
0	410	10830
1	1251	9955
done	5000	9336

prune820.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

regimes150.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.3s	4892×	body	160	valid
1.2s	16188×	pre	80	true
798.0ms	8188×	body	80	nan
358.0ms	1374×	body	320	valid
197.0ms	1734×	body	80	valid