Details

sample109.0ms

Algorithm

intervals

Results

24.0ms	189×	body	80	valid
23.0ms	30×	body	2560	valid
20.0ms	32×	body	1280	valid
14.0ms	99×	body	80	nan
7.0ms	15×	body	640	valid
2.0ms	4×	body	320	valid
1.0ms	5×	body	160	valid
1.0ms	1×	body	5120	valid

simplify180.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

180.0ms

(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.3b

localize30.0ms

Local error

Found 3 expressions with local error:

20.7b	(sqrt (fma c (* -4 a) (* b b)))
1.3b	(- (sqrt (fma c (* -4 a) (* b b))) b)
0.1b	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
134×	`add-sqr-sqrt`
107×	`*-un-lft-identity`
81×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`difference-of-squares`
22×	`associate-/l*`
18×	`prod-diff`
13×	`distribute-lft-out--`
8×	`add-cbrt-cube` `add-exp-log`
6×	`fma-neg`
5×	`div-inv` `add-log-exp`
4×	`pow1`
3×	`expm1-log1p-u` `cbrt-undiv` `associate-/r*` `div-exp` `insert-posit16` `log1p-expm1-u`
2×	`div-sub`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `flip--` `associate-/l/`

Counts

3 → 168

Calls

3 calls:

Slowest

39.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
15.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
3.0ms	(sqrt (fma c (* -4 a) (* b b)))

series296.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

104.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
101.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
90.0ms	(sqrt (fma c (* -4 a) (* b b)))

simplify14.2s

Counts

222 → 177

Calls

222 calls:

Slowest

412.0ms	(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
211.0ms	(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) (sqrt a))
210.0ms	(/ (* (* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (* (* a a) a))
188.0ms	(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (sqrt 2)) (* (cbrt a) (cbrt a)))
178.0ms	(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) 1)

prune2.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 27.7b

localize42.0ms

Local error

Found 3 expressions with local error:

20.7b	(sqrt (fma c (* -4 a) (* b b)))
5.7b	(- (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a) (/ (/ b 2) a))
0.1b	(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)

rewrite315.0ms

Algorithm

rewrite-expression-head

Rules

10113×	`times-frac`
5325×	`add-sqr-sqrt`
5299×	`*-un-lft-identity`
5273×	`add-cube-cbrt`
3010×	`prod-diff`
1230×	`sqrt-prod`
469×	`div-inv`
70×	`fma-neg`
22×	`associate-/l*`
13×	`distribute-lft-out--`
12×	`difference-of-squares`
8×	`add-cbrt-cube` `add-exp-log`
5×	`add-log-exp`
4×	`pow1` `distribute-rgt-out--`
3×	`expm1-log1p-u` `cbrt-undiv` `associate-/r*` `div-exp` `insert-posit16` `log1p-expm1-u`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `frac-sub` `flip--` `sub-div` `associate-/l/`

Counts

3 → 3251

Calls

3 calls:

Slowest

49.0ms	(- (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a) (/ (/ b 2) a))
17.0ms	(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)
1.0ms	(sqrt (fma c (* -4 a) (* b b)))

series392.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

142.0ms	(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)
126.0ms	(- (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a) (/ (/ b 2) a))
125.0ms	(sqrt (fma c (* -4 a) (* b b)))