Details

sample122.0ms

Algorithm

intervals

Results

31.0ms	35×	body	2560	valid
29.0ms	194×	body	80	valid
20.0ms	28×	body	1280	valid
11.0ms	79×	body	80	nan
6.0ms	11×	body	640	valid
5.0ms	4×	body	5120	valid
2.0ms	5×	body	320	valid
1.0ms	4×	body	160	valid

simplify159.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

159.0ms

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize25.0ms

Local error

Found 4 expressions with local error:

22.3b	(sqrt (fma b b (* (* a c) -4)))
1.0b	(fma b b (* (* a c) -4))
1.0b	(- (sqrt (fma b b (* (* a c) -4))) b)
0.1b	(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 179

Calls

4 calls:

Slowest

34.0ms	(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)
8.0ms	(- (sqrt (fma b b (* (* a c) -4))) b)
1.0ms	(sqrt (fma b b (* (* a c) -4)))
0.0ms	(fma b b (* (* a c) -4))

series470.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

170.0ms	(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)
112.0ms	(- (sqrt (fma b b (* (* a c) -4))) b)
112.0ms	(sqrt (fma b b (* (* a c) -4)))
75.0ms	(fma b b (* (* a c) -4))

simplify15.4s

Counts

225 → 191

Calls

225 calls:

Slowest

371.0ms	(/ (/ (* (cbrt (- (sqrt (fma b b (* (* a c) -4))) b)) (cbrt (- (sqrt (fma b b (* (* a c) -4))) b))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
235.0ms	(- b (* 2 (/ (* a c) b)))
229.0ms	(/ (/ (* (cbrt (- (sqrt (fma b b (* (* a c) -4))) b)) (cbrt (- (sqrt (fma b b (* (* a c) -4))) b))) (sqrt 2)) (* (cbrt a) (cbrt a)))
198.0ms	(/ (/ (* (cbrt (- (sqrt (fma b b (* (* a c) -4))) b)) (cbrt (- (sqrt (fma b b (* (* a c) -4))) b))) (* (cbrt 2) (cbrt 2))) (sqrt a))
191.0ms	(/ (/ (* (* (- (sqrt (fma b b (* (* a c) -4))) b) (- (sqrt (fma b b (* (* a c) -4))) b)) (- (sqrt (fma b b (* (* a c) -4))) b)) (* (* 2 2) 2)) (* (* a a) a))

prune2.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.6b

localize33.0ms

Local error

Found 4 expressions with local error:

22.3b	(sqrt (fma b b (* (* a c) -4)))
5.6b	(- (/ (/ (sqrt (fma b b (* (* a c) -4))) 2) a) (/ (/ b 2) a))
1.0b	(fma b b (* (* a c) -4))
0.1b	(/ (/ (sqrt (fma b b (* (* a c) -4))) 2) a)

rewrite366.0ms

Algorithm

rewrite-expression-head

Rules

10113×	`times-frac`
5326×	`add-sqr-sqrt`
5300×	`*-un-lft-identity`
5274×	`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`
9×	`add-cbrt-cube` `add-exp-log`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `distribute-rgt-out--` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/r*` `div-exp`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `frac-sub` `fma-udef` `flip--` `sub-div` `associate-/l/`

Counts

4 → 3262

Calls

4 calls:

Slowest

76.0ms	(- (/ (/ (sqrt (fma b b (* (* a c) -4))) 2) a) (/ (/ b 2) a))
17.0ms	(/ (/ (sqrt (fma b b (* (* a c) -4))) 2) a)
3.0ms	(sqrt (fma b b (* (* a c) -4)))
0.0ms	(fma b b (* (* a c) -4))

series1.0s

Counts

4 → 12

Calls

4 calls:

Slowest

599.0ms	(- (/ (/ (sqrt (fma b b (* (* a c) -4))) 2) a) (/ (/ b 2) a))
195.0ms	(/ (/ (sqrt (fma b b (* (* a c) -4))) 2) a)
140.0ms	(sqrt (fma b b (* (* a c) -4)))
88.0ms	(fma b b (* (* a c) -4))