Details

sample34.0ms

Algorithm

intervals

Results

14.0ms	282×	body	80	valid
4.0ms	86×	body	80	nan

simplify91.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	20	38
1	36	38
2	66	37
3	122	37
4	151	37
5	165	37
6	166	37
done	166	37

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.4b

localize120.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
58×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
50×	`add-cube-cbrt`
37×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
24×	`distribute-lft-neg-in`
12×	`add-log-exp`
10×	`fma-def` `fma-neg`
8×	`neg-mul-1`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `sum-log` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `associate--l-` `associate-+l-` `sub-neg` `flip3-+` `flip-+`

Counts

4 → 151

Calls

4 calls:

17.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series296.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
79.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify581.0ms

Counts

163 → 163

Iterations

Useful iterations: done (571.0ms)

Iter	Nodes	Cost
0	179	6238
1	429	4258
2	1314	3343
done	5001	3332

prune443.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 7.1b

localize118.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.3b	(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
4.5b	(/ (* a c) b)
21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

62×	`*-un-lft-identity`
60×	`prod-diff`
55×	`add-sqr-sqrt`
50×	`add-cube-cbrt`
34×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
14×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg`
8×	`times-frac` `add-log-exp`
7×	`neg-mul-1`
6×	`associate-/l*`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-/r*` `log1p-expm1-u` `distribute-lft-out`
2×	`neg-sub0` `flip3--` `frac-2neg` `sqrt-div` `diff-log` `div-sub` `prod-exp` `clear-num` `flip--` `cbrt-unprod` `div-inv` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `associate-+l-` `associate-+r-` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 161

Calls

4 calls:

17.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
65.0ms	(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
3.0ms	(/ (* a c) b)
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series224.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
58.0ms	(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
19.0ms	(/ (* a c) b)
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify173.0ms

Iterations

Useful iterations: 1 (56.0ms)

Iter	Nodes	Cost
0	265	6492
1	665	4520