Details

sample121.0ms

Algorithm

intervals

Results

32.0ms	189×	body	80	valid
32.0ms	41×	body	2560	valid
17.0ms	25×	body	1280	valid
12.0ms	91×	body	80	nan
5.0ms	11×	body	640	valid
4.0ms	10×	body	320	valid
1.0ms	4×	body	160	valid

simplify201.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

201.0ms

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize40.0ms

Local error

Found 4 expressions with local error:

21.6b	(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)
0.0b	(fma c (* -4 a) (* b b))

rewrite56.0ms

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

32.0ms	(/ (/ (- (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)))
0.0ms	(fma c (* -4 a) (* b b))

series447.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

139.0ms	(sqrt (fma c (* -4 a) (* b b)))
119.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
115.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
75.0ms	(fma c (* -4 a) (* b b))

simplify20.2s

Counts

282 → 191

Calls

282 calls:

Slowest

607.0ms	(- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b))
578.0ms	(* (* (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a) (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)) (/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a))
459.0ms	(/ (/ (* (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)))
427.0ms	(/ (/ (+ (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt b)) 1) (* (cbrt a) (cbrt a)))
319.0ms	(- (pow (sqrt (fma c (* -4 a) (* b b))) 3) (pow b 3))

prune2.3s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 28.6b

localize29.0ms

Local error

Found 4 expressions with local error:

21.6b	(sqrt (fma c (* -4 a) (* b b)))
1.3b	(- (sqrt (fma c (* -4 a) (* b b))) b)
0.2b	(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
0.0b	(fma c (* -4 a) (* b b))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
36×	`add-cube-cbrt`
34×	`times-frac`
26×	`add-exp-log`
22×	`associate-l`
19×	`sqrt-prod`
18×	`prod-diff`
16×	`add-cbrt-cube`
13×	`associate-r`
8×	`div-exp` `prod-exp` `difference-of-squares`
7×	`pow1`
6×	`fma-neg` `add-log-exp` `unswap-sqr`
4×	`expm1-log1p-u` `cbrt-undiv` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
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` `fma-udef` `flip--`

Counts

4 → 138

Calls

4 calls:

Slowest

28.0ms	(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
7.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
6.0ms	(fma c (* -4 a) (* b b))
1.0ms	(sqrt (fma c (* -4 a) (* b b)))

series403.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

124.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
104.0ms	(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
96.0ms	(sqrt (fma c (* -4 a) (* b b)))
78.0ms	(fma c (* -4 a) (* b b))

simplify22.0s

Counts

178 → 150

Calls

178 calls:

Slowest

673.0ms	(- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b))
442.0ms	(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 (* (cbrt a) (cbrt a))))
420.0ms	(* (/ (- (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt b)) (sqrt 2)) (/ 1 a))
411.0ms	(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) (cbrt 2)) (/ 1 a))
410.0ms	(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ (* (cbrt 1) (cbrt 1)) (sqrt a)))

prune1.9s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 28.6b

localize55.0ms

Local error

Found 4 expressions with local error:

21.6b	(sqrt (fma c (* -4 a) (* b b)))
1.3b	(- (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))

rewrite65.0ms

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

24.0ms	(/ 1 (/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))
15.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
11.0ms	(/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))
3.0ms	(sqrt (fma c (* -4 a) (* b b)))

series679.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

290.0ms	(/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))
173.0ms	(/ 1 (/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))
118.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
98.0ms	(sqrt (fma c (* -4 a) (* b b)))

simplify2.4m

Counts

797 → 494

Calls

797 calls:

Slowest

1.4s	(* (* (/ 1 (/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))) (/ 1 (/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))) (/ 1 (/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))))
1.1s	(- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b))
771.0ms	(/ (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)))))
753.0ms	(/ (cbrt 1) (/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) (sqrt 2))))
748.0ms	(/ 1 (/ a (/ (- (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt b)) (sqrt 2))))

prune7.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.8b

localize36.0ms

Local error

Found 4 expressions with local error:

21.6b	(sqrt (fma c (* -4 a) (* b b)))
6.8b	(- (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a) (/ (/ b 2) a))
0.1b	(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)
0.0b	(fma c (* -4 a) (* b b))

rewrite333.0ms

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

42.0ms	(- (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a) (/ (/ b 2) a))
16.0ms	(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)
3.0ms	(sqrt (fma c (* -4 a) (* b b)))
0.0ms	(fma c (* -4 a) (* b b))

series437.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

155.0ms	(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)
131.0ms	(- (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a) (/ (/ b 2) a))
93.0ms	(sqrt (fma c (* -4 a) (* b b)))
58.0ms	(fma c (* -4 a) (* b b))