Details

sample128.0ms

Algorithm

intervals

Results

30.0ms	189×	body	80	valid
26.0ms	30×	body	2560	valid
22.0ms	30×	body	1280	valid
11.0ms	19×	body	640	valid
10.0ms	79×	body	80	nan
3.0ms	3×	body	5120	valid
2.0ms	4×	body	320	valid
1.0ms	5×	body	160	valid

simplify164.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

164.0ms

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize32.0ms

Local error

Found 3 expressions with local error:

19.5b	(sqrt (fma c (* -4 a) (* b b)))
1.1b	(- (sqrt (fma c (* -4 a) (* b b))) b)
0.1b	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)

rewrite63.0ms

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

33.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
15.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
2.0ms	(sqrt (fma c (* -4 a) (* b b)))

series396.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

150.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
133.0ms	(sqrt (fma c (* -4 a) (* b b)))
113.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)

simplify13.3s

Counts

222 → 177

Calls

222 calls:

Slowest

380.0ms	(/ (/ (* (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)))
255.0ms	(/ (* (* (/ (- (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))
177.0ms	(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (sqrt 2)) (* (cbrt a) (cbrt a)))
176.0ms	(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) (sqrt a))
169.0ms	(/ (/ (* (* (- (sqrt (fma c (* -4 a) (* b b))) b) (- (sqrt (fma c (* -4 a) (* b b))) b)) (- (sqrt (fma c (* -4 a) (* b b))) b)) (* (* 2 2) 2)) (* (* a a) a))

prune2.1s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 26.8b

localize23.0ms

Local error

Found 3 expressions with local error:

19.5b	(sqrt (fma c (* -4 a) (* b b)))
1.1b	(- (sqrt (fma c (* -4 a) (* b b))) b)
0.2b	(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-sqr-sqrt`
45×	`*-un-lft-identity`
35×	`add-cube-cbrt`
34×	`times-frac`
25×	`add-exp-log`
22×	`associate-l`
19×	`sqrt-prod`
18×	`prod-diff`
15×	`add-cbrt-cube`
13×	`associate-r`
8×	`div-exp` `prod-exp` `difference-of-squares`
6×	`pow1` `fma-neg` `unswap-sqr`
5×	`add-log-exp`
4×	`cbrt-undiv` `cbrt-unprod` `distribute-lft-out--`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
2×	`rec-exp` `1-exp` `div-inv`
1×	`frac-times` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `pow-prod-down` `associate-l/` `associate-r/` `un-div-inv` `*-commutative` `flip--`

Counts

3 → 127

Calls

3 calls:

Slowest

49.0ms	(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
7.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms	(sqrt (fma c (* -4 a) (* b b)))

series375.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

143.0ms	(sqrt (fma c (* -4 a) (* b b)))
120.0ms	(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
112.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)

simplify6.6s

Counts

123 → 136

Calls

123 calls:

Slowest

308.0ms	(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
240.0ms	(* (/ (* (* (- (sqrt (fma c (* -4 a) (* b b))) b) (- (sqrt (fma c (* -4 a) (* b b))) b)) (- (sqrt (fma c (* -4 a) (* b b))) b)) (* (* 2 2) 2)) (/ (* (* 1 1) 1) (* (* a a) a)))
220.0ms	(+ (- (log (- (sqrt (fma c (* -4 a) (* b b))) b)) (log 2)) (- 0 (log a)))
216.0ms	(+ (- (log (- (sqrt (fma c (* -4 a) (* b b))) b)) (log 2)) (- (log 1) (log a)))
212.0ms	(* (* (* (/ (- (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)) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))

prune1.6s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 26.8b

localize23.0ms

Local error

Found 4 expressions with local error:

19.5b	(sqrt (fma c (* -4 a) (* b b)))
1.1b	(- (sqrt (fma c (* -4 a) (* b b))) b)
0.2b	(/ 1 (/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))
0.1b	(/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

831×	`times-frac`
563×	`add-sqr-sqrt`
464×	`*-un-lft-identity`
366×	`add-cube-cbrt`
98×	`difference-of-squares`
93×	`associate-/r*`
64×	`sqrt-prod`
49×	`distribute-lft-out--`
30×	`add-exp-log`
22×	`div-inv`
18×	`add-cbrt-cube` `div-exp` `prod-diff`
9×	`cbrt-undiv`
6×	`pow1` `fma-neg` `associate-/r/` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`rec-exp` `1-exp`
2×	`clear-num` `frac-2neg`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `pow-flip` `flip--` `inv-pow`

Counts

4 → 482

Calls

4 calls:

Slowest

30.0ms	(/ 1 (/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))
13.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
11.0ms	(/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))
1.0ms	(sqrt (fma c (* -4 a) (* b b)))

series662.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

265.0ms	(/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))
172.0ms	(/ 1 (/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))
113.0ms	(sqrt (fma c (* -4 a) (* b b)))
112.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)

simplify1.5m

Counts

733 → 494

Calls

733 calls:

Slowest

793.0ms	(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt a) (cbrt a)) (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) 1)))
579.0ms	(/ (sqrt 1) (/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) (cbrt 2))))
530.0ms	(/ (sqrt 1) (/ 1 (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2)))))
489.0ms	(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt a) (cbrt a)) (/ (+ (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt b)) (sqrt 2))))
462.0ms	(/ (* (cbrt a) (cbrt a)) (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (sqrt 2)))

prune4.8s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 11.7b

localize30.0ms

Local error

Found 3 expressions with local error:

19.5b	(sqrt (fma c (* -4 a) (* b b)))
4.3b	(- (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a) (/ (/ b 2) a))
0.1b	(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)

rewrite229.0ms

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

30.0ms	(- (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a) (/ (/ b 2) a))
15.0ms	(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)
1.0ms	(sqrt (fma c (* -4 a) (* b b)))

series318.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

131.0ms	(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)
94.0ms	(- (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a) (/ (/ b 2) a))
93.0ms	(sqrt (fma c (* -4 a) (* b b)))