Details

sample56.0ms

Algorithm

intervals

Results

16.0ms	187×	body	80	valid
11.0ms	40×	body	2560	valid
4.0ms	23×	body	1280	valid
4.0ms	86×	body	80	nan
3.0ms	16×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	2×	body	5120	valid
0.0ms	5×	body	160	valid

simplify44.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	12	17
1	21	17
2	41	16
3	76	16
4	90	16
5	98	16
done	98	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.8b	(- (* b b) (* (* 3.0 a) c))
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
21.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite53.0ms

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:

35.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
2.0ms	(- (* b b) (* (* 3.0 a) c))
11.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series305.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
48.0ms	(- (* b b) (* (* 3.0 a) c))
80.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify490.0ms

Counts

82 → 82

Iterations

Useful iterations: done (488.0ms)

Iter	Nodes	Cost
0	154	1565
1	408	1463
2	1403	1247
done	5000	1237

prune243.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.6b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
6.0b	(/ (/ (+ (* b (- b b)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
8.8b	(/ (+ (* b (- b b)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
21.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 154

Calls

4 calls:

11.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
48.0ms	(/ (/ (+ (* b (- b b)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
32.0ms	(/ (+ (* b (- b b)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series442.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
131.0ms	(/ (/ (+ (* b (- b b)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
166.0ms	(/ (+ (* b (- b b)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify691.0ms

Counts

166 → 166

Iterations

Useful iterations: done (680.0ms)

Iter	Nodes	Cost
0	262	5855
1	675	5308
2	2499	4562
done	5000	4560

prune464.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* 3.0 a) c)
0.8b	(- (* b b) (* (* 3.0 a) c))
1.3b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
21.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod`
3×	`flip3--` `associate-r` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

6.0ms	(* (* 3.0 a) c)
2.0ms	(- (* b b) (* (* 3.0 a) c))
17.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
7.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series216.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
44.0ms	(- (* b b) (* (* 3.0 a) c))
80.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
72.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify421.0ms

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	120	1001
1	283	903
2	1068	825