Details

sample172.0ms

Algorithm

intervals

Results

63.0ms	41×	body	2560	valid
32.0ms	179×	body	80	valid
22.0ms	27×	body	1280	valid
16.0ms	95×	body	80	nan
8.0ms	12×	body	640	valid
5.0ms	4×	body	5120	valid
4.0ms	8×	body	320	valid
1.0ms	3×	body	160	valid

simplify161.0ms

Calls

1 calls:

Slowest

161.0ms

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

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 35.4b

localize24.0ms

Local error

Found 3 expressions with local error:

25.6b	(sqrt (fma c (* -4 a) (* b b)))
1.0b	(- (sqrt (fma c (* -4 a) (* b b))) b)
0.1b	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

3 calls:

Slowest

45.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
13.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms	(sqrt (fma c (* -4 a) (* b b)))

series338.0ms

Calls

3 calls:

Slowest

137.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
116.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
84.0ms	(sqrt (fma c (* -4 a) (* b b)))

simplify15.0s

Calls

232 calls:

Slowest

538.0ms	(/ (/ (- (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt b)) (sqrt 2)) (sqrt a))
512.0ms	(- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b))
403.0ms	(/ (/ (* (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)))
345.0ms	(- (pow (sqrt (fma c (* -4 a) (* b b))) 3) (pow b 3))
233.0ms	(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (sqrt 2)) (* (cbrt a) (cbrt a)))

prune2.1s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 29.7b

localize42.0ms

Local error

Found 3 expressions with local error:

25.6b	(sqrt (fma c (* -4 a) (* b b)))
6.2b	(- (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a) (/ (/ b 2) a))
0.1b	(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)

rewrite385.0ms

Algorithm

rewrite-expression-head

Rules

10977×	`times-frac`
6208×	`add-sqr-sqrt`
6186×	`*-un-lft-identity`
6156×	`add-cube-cbrt`
3010×	`prod-diff`
1569×	`sqrt-prod`
1454×	`associate-/l*`
1120×	`frac-sub`
722×	`associate-/l/`
539×	`div-inv`
430×	`associate-/r*`
142×	`frac-2neg`
138×	`clear-num`
70×	`fma-neg`
15×	`sub-div`
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` `div-exp` `insert-posit16` `log1p-expm1-u`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `flip--`

Calls

3 calls:

Slowest

55.0ms	(- (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a) (/ (/ b 2) a))
16.0ms	(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)
1.0ms	(sqrt (fma c (* -4 a) (* b b)))

series350.0ms

Calls

3 calls:

Slowest

139.0ms	(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)
110.0ms	(sqrt (fma c (* -4 a) (* b b)))
101.0ms	(- (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a) (/ (/ b 2) a))