Details

simplify26.8m

Calls

15449 calls:

Slowest

1.8s	(im (+.c (+.c (+.c (+.c (+.c (+.c (.c (.c (.c (.c (.c (complex -1 1) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1)) (.c (.c (.c (.c (.c (complex 6 0) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1))) (.c (.c (.c (.c (complex 15 0) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1))) (.c (.c (.c (complex 20 0) (complex -1 1)) (complex -1 1)) (complex -1 1))) (.c (.c (complex 15 0) (complex -1 1)) (complex -1 1))) (.c (complex 6 0) (complex -1 1))) (complex 1 0)))
1.7s	(re (+.c (+.c (+.c (+.c (+.c (+.c (.c (.c (.c (.c (.c (complex -1 1) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1)) (.c (.c (.c (.c (.c (complex 6 0) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1))) (.c (.c (.c (.c (complex 15 0) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1))) (.c (.c (.c (complex 20 0) (complex -1 1)) (complex -1 1)) (complex -1 1))) (.c (.c (complex 15 0) (complex -1 1)) (complex -1 1))) (.c (complex 6 0) (complex -1 1))) (complex 1 0)))
1.6s	(/ (* (* (* a c) (* a c)) (* a c)) (* (* (* a (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (* a (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) (* a (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))))
1.5s	(/ (* (* (- 0 (* a c)) (- 0 (* a c))) (- 0 (* a c))) (* (* a a) a))
1.5s	(/ (/ (* (* (+ (+ (sqrt (fma (* -4 c) a (* b b))) (- b)) (+ (- b) b)) (+ (+ (sqrt (fma (* -4 c) a (* b b))) (- b)) (+ (- b) b))) (+ (+ (sqrt (fma (* -4 c) a (* b b))) (- b)) (+ (- b) b))) (* (* 2 2) 2)) (* (* a a) a))

sample5.1m

Algorithm

56×	intervals
16×	halfpoints

Results

1.1m	66535×	body	1280	valid
36.5s	17389×	body	2560	valid
27.3s	42048×	body	640	valid
15.6s	12964×	body	10240	exit
11.3s	93830×	body	80	valid
10.4s	21104×	body	320	valid
6.9s	62744×	body	80	nan
3.4s	10560×	body	160	valid
2.1s	47555×	pre	80	true
902.0ms	699×	body	1280	nan
522.0ms	692×	body	640	nan
486.0ms	398×	body	5120	valid
213.0ms	398×	body	320	nan
52.0ms	183×	body	160	nan

prune2.5m

series34.4s

Calls

346 calls:

Slowest

782.0ms	(/ 1 (+ (hypot (sqrt x) 1) (sqrt x)))
686.0ms	(fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x)))))
649.0ms	(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
624.0ms	(* (- c) (/ 1 (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)))
502.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite9.2s

Algorithm

111×	rewrite-expression-head

Calls

346 calls:

Slowest

690.0ms	(/ (/ (+ (+ (- (- b) (sqrt (fma b b (* (* -4 c) a)))) (+ (- b) b)) 0) 2) a)
454.0ms	(- (+ (log (exp (/ -1/2 (* N N)))) (/ 1 N)) (/ -1/3 (* (* N N) N)))
260.0ms	(/ (/ (+ (+ (sqrt (fma (* -4 c) a (* b b))) (- b)) (+ (- b) b)) 2) a)
237.0ms	(- (+ (/ -1/2 (* N N)) (/ 1 N)) (/ -1/3 (* (* N N) N)))
206.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

Rules

8718×	`*-un-lft-identity`
7640×	`times-frac`
7209×	`add-sqr-sqrt`
5636×	`add-cube-cbrt`
3175×	`prod-diff`
1815×	`sqrt-prod`
1244×	`pow1`
1229×	`distribute-lft-out`
1026×	`add-exp-log`
927×	`add-cbrt-cube`
551×	`difference-of-squares` `distribute-lft-out--` `add-log-exp`
524×	`div-inv`
483×	`associate-+l+`
412×	`associate-l`
384×	`associate-r`
381×	`associate-/l*`
350×	`associate-/r/`
342×	`log1p-expm1-u`
339×	`expm1-log1p-u` `insert-posit16`
338×	`cbrt-prod`
332×	`fma-neg`
331×	`distribute-rgt-neg-in`
321×	`associate-/r*`
310×	`pow-unpow`
306×	`unpow-prod-down`
233×	`pow-prod-down`
220×	`pow-prod-up`
216×	`prod-exp`
208×	`div-exp`
203×	`swap-sqr`
200×	`cbrt-unprod`
182×	`flip-+` `flip3-+`
177×	`fma-def`
163×	`cbrt-undiv`
148×	`sqrt-pow1`
147×	`unswap-sqr`
138×	`flip3--` `flip--`
135×	`sqrt-div`
126×	`pow-sqr`
114×	`distribute-lft-neg-in`
103×	`pow1/2`
92×	`pow-plus`
89×	`sqr-pow`
68×	`log-prod` `pow2`
67×	`diff-log`
66×	`-commutative` `associate-r/`
62×	`sub-neg`
61×	`frac-2neg` `clear-num`
50×	`log-pow`
49×	`fma-udef`
47×	`sum-log`
46×	`associate-*l/`
40×	`pow1/3`
38×	`associate-/l/`
37×	`exp-prod`
35×	`tan-quot`
34×	`neg-mul-1`
33×	`rem-sqrt-square`
30×	`div-sub`
28×	`cube-prod` `frac-times`
27×	`cbrt-div` `+-commutative`
26×	`1-exp` `rec-exp`
24×	`frac-add`
23×	`pow-flip`
17×	`distribute-rgt-in` `distribute-lft-in`
16×	`frac-sub`
14×	`neg-sub0` `inv-pow`
13×	`associate-+l-`
12×	`pow-exp` `pow-to-exp` `hypot-def`
11×	`pow-pow`
9×	`neg-log` `difference-of-sqr-1` `sqrt-unprod` `log-div`
8×	`associate-+r+` `rem-log-exp`
7×	`associate-+r-` `sin-mult` `sum-cubes` `cube-mult`
6×	`associate--l-`
5×	`log1p-def`
4×	`exp-sum` `associate--l+` `associate--r+` `sqr-sin` `distribute-rgt-out--` `rem-square-sqrt` `unsub-neg`
3×	`expm1-log1p` `expm1-udef`
2×	`exp-diff` `sin-sum` `sub-div` `+.c-commutative` `un-div-inv` `tan-sum` `cos-sum` `exp-neg` `log1p-udef`
1×	`distribute-lft-neg-out` `diff-atan` `cos-mult` `sqrt-undiv` `log1p-expm1` `pow3` `distribute-frac-neg` `frac-2neg-c` `hypot-udef` `hypot-1-def` `sub0-neg` `diff-sin` `diff-cos` `expm1-def`

localize4.2s

regimes4.1s

Accuracy

Total 22.7b remaining (18.4%)

4.4b	84.1%	quadm (p42, negative)
4.1b	82.6%	quad2m (problem 3.2.1, negative)
4.0b	85.4%	quadp (p42, positive)
3.3b	0%	expq3 (problem 3.4.2)
1.6b	86.4%	2nthrt (problem 3.4.6)

Details

simplify26.8m

sample5.1m

prune2.5m

series34.4s

rewrite9.2s

localize4.2s

regimes4.1s

bsearch2.8s

end1.0ms