Details

sample41.0ms

Algorithm

intervals

Results

9.0ms	39×	body	2560	valid
7.0ms	183×	body	80	valid
4.0ms	24×	body	1280	valid
3.0ms	84×	body	80	nan
2.0ms	14×	body	640	valid
1.0ms	13×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	1×	body	160	valid

simplify77.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	28	17
2	63	17
3	114	17
4	131	17
5	137	17
6	140	17
done	140	17

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

37.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms	(- (* b b) (* 4.0 (* a c)))
13.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series284.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
47.0ms	(- (* b b) (* 4.0 (* a c)))
76.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
68.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify450.0ms

Counts

89 → 89

Iterations

Useful iterations: done (447.0ms)

Iter	Nodes	Cost
0	157	1750
1	412	1650
2	1385	1474
done	5001	1465

prune242.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) a)
0.8b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite70.0ms

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-/l*`
16×	`sqrt-prod`
13×	`distribute-rgt-neg-in`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `div-inv`
3×	`cbrt-undiv` `flip3--` `diff-log` `div-exp` `associate-/r*` `flip--`
2×	`sub-neg` `sqrt-div` `div-sub`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 164

Calls

4 calls:

41.0ms	(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) a)
3.0ms	(- (* b b) (* 4.0 (* a c)))
13.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series281.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) a)
43.0ms	(- (* b b) (* 4.0 (* a c)))
75.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify177.0ms

Iterations

Useful iterations: 1 (58.0ms)

Iter	Nodes	Cost
0	283	4621
1	690	4441