Details

simplify38.7m

Calls

20380 calls:

Slowest

3.3s	(- (+ (* 4/9 (* (/ (pow (log -1) 3) (pow x 2)) (pow (/ 1 (* (log (/ -1 x)) (pow (- (log -1) (log (/ -1 x))) 14))) 1/3))) (+ (* 8/3 (* (/ (pow (log -1) 5) (pow x 2)) (pow (/ (pow (log (/ -1 x)) 5) (pow (- (log -1) (log (/ -1 x))) 26)) 1/3))) (+ (* 2/3 (* (/ 1 x) (pow (/ (pow (log (/ -1 x)) 5) (pow (- (log -1) (log (/ -1 x))) 8)) 1/3))) (+ (* 5/9 (* (/ 1 (pow x 2)) (pow (/ (pow (log (/ -1 x)) 8) (pow (- (log -1) (log (/ -1 x))) 14)) 1/3))) (+ (pow (/ (pow (log (/ -1 x)) 2) (pow (- (log -1) (log (/ -1 x))) 2)) 1/3) (+ (* 1/3 (* (/ 1 (pow x 2)) (pow (/ (pow (log (/ -1 x)) 5) (pow (- (log -1) (log (/ -1 x))) 8)) 1/3))) (+ (* 2/3 (* (/ 1 x) (pow (/ (pow (log (/ -1 x)) 11) (pow (- (log -1) (log (/ -1 x))) 14)) 1/3))) (+ (* 2 (* (/ (pow (log -1) 2) x) (pow (/ (pow (log (/ -1 x)) 5) (pow (- (log -1) (log (/ -1 x))) 14)) 1/3))) (+ (* 80/9 (* (/ (pow (log -1) 3) (pow x 2)) (pow (/ (pow (log (/ -1 x)) 11) (pow (- (log -1) (log (/ -1 x))) 26)) 1/3))) (+ (* (/ (log -1) (pow x 2)) (pow (/ (pow (log (/ -1 x)) 8) (pow (- (log -1) (log (/ -1 x))) 14)) 1/3)) (+ (* 1/3 (* (/ (pow (log -1) 2) (pow x 2)) (pow (/ 1 (* (log (/ -1 x)) (pow (- (log -1) (log (/ -1 x))) 8))) 1/3))) (+ (* 8/3 (* (/ (log -1) (pow x 2)) (pow (/ (pow (log (/ -1 x)) 17) (pow (- (log -1) (log (/ -1 x))) 26)) 1/3))) (+ (* 2/3 (* (/ (pow (log -1) 2) x) (pow (/ 1 (* (log (/ -1 x)) (pow (- (log -1) (log (/ -1 x))) 8))) 1/3))) (+ (* 1/3 (* (/ (pow (log -1) 3) (pow x 2)) (pow (/ (pow (log (/ -1 x)) 2) (pow (- (log -1) (log (/ -1 x))) 14)) 1/3))) (+ (* 4/9 (* (/ 1 (pow x 2)) (pow (/ (pow (log (/ -1 x)) 14) (pow (- (log -1) (log (/ -1 x))) 20)) 1/3))) (+ (* (/ (pow (log -1) 2) (pow x 2)) (pow (/ (pow (log (/ -1 x)) 2) (pow (- (log -1) (log (/ -1 x))) 14)) 1/3)) (+ (* 1/3 (* (/ (pow (log -1) 2) (pow x 2)) (pow (/ 1 (* (pow (log (/ -1 x)) 4) (pow (- (log -1) (log (/ -1 x))) 8))) 1/3))) (+ (* 1/3 (* (/ 1 (pow x 2)) (pow (/ (pow (log (/ -1 x)) 2) (pow (- (log -1) (log (/ -1 x))) 8)) 1/3))) (+ (* 8/9 (* (/ (pow (log -1) 5) (pow x 2)) (pow (/ 1 (* (log (/ -1 x)) (pow (- (log -1) (log (/ -1 x))) 20))) 1/3))) (* 32/9 (* (/ (pow (log -1) 3) (pow x 2)) (pow (/ (pow (log (/ -1 x)) 5) (pow (- (log -1) (log (/ -1 x))) 20)) 1/3)))))))))))))))))))))) (+ (* 4/9 (* (/ (pow (log -1) 6) (pow x 2)) (pow (/ (pow (log (/ -1 x)) 2) (pow (- (log -1) (log (/ -1 x))) 26)) 1/3))) (+ (* (/ (pow (log -1) 2) (pow x 2)) (pow (/ (pow (log (/ -1 x)) 5) (pow (- (log -1) (log (/ -1 x))) 14)) 1/3)) (+ (* 20/3 (* (/ (pow (log -1) 4) (pow x 2)) (pow (/ (pow (log (/ -1 x)) 8) (pow (- (log -1) (log (/ -1 x))) 26)) 1/3))) (+ (* 28/9 (* (/ (pow (log -1) 4) (pow x 2)) (pow (/ (pow (log (/ -1 x)) 2) (pow (- (log -1) (log (/ -1 x))) 20)) 1/3))) (+ (* 4/9 (* (/ (pow (log -1) 4) (pow x 2)) (pow (/ 1 (* (pow (log (/ -1 x)) 4) (pow (- (log -1) (log (/ -1 x))) 14))) 1/3))) (+ (* 20/3 (* (/ (pow (log -1) 2) (pow x 2)) (pow (/ (pow (log (/ -1 x)) 14) (pow (- (log -1) (log (/ -1 x))) 26)) 1/3))) (+ (* 4/9 (* (/ 1 (pow x 2)) (pow (/ (pow (log (/ -1 x)) 20) (pow (- (log -1) (log (/ -1 x))) 26)) 1/3))) (+ (* 1/3 (* (/ 1 (pow x 2)) (pow (/ (pow (log (/ -1 x)) 11) (pow (- (log -1) (log (/ -1 x))) 14)) 1/3))) (+ (* 2/3 (* (/ (pow (log -1) 3) x) (pow (/ (pow (log (/ -1 x)) 2) (pow (- (log -1) (log (/ -1 x))) 14)) 1/3))) (+ (* 4/3 (* (/ (log -1) x) (pow (/ (pow (log (/ -1 x)) 2) (pow (- (log -1) (log (/ -1 x))) 8)) 1/3))) (+ (* 8/9 (* (/ (log -1) (pow x 2)) (pow (/ (pow (log (/ -1 x)) 11) (pow (- (log -1) (log (/ -1 x))) 20)) 1/3))) (+ (* 14/9 (* (/ (log -1) (pow x 2)) (pow (/ (pow (log (/ -1 x)) 5) (pow (- (log -1) (log (/ -1 x))) 14)) 1/3))) (+ (* 2/3 (* (/ (log -1) (pow x 2)) (pow (/ 1 (* (log (/ -1 x)) (pow (- (log -1) (log (/ -1 x))) 8))) 1/3))) (+ (* 8/9 (* (/ (pow (log -1) 2) (pow x 2)) (pow (/ (pow (log (/ -1 x)) 8) (pow (- (log -1) (log (/ -1 x))) 20)) 1/3))) (+ (* 2/3 (* (/ (log -1) (pow x 2)) (pow (/ (pow (log (/ -1 x)) 2) (pow (- (log -1) (log (/ -1 x))) 8)) 1/3))) (* 2 (* (/ (log -1) x) (pow (/ (pow (log (/ -1 x)) 8) (pow (- (log -1) (log (/ -1 x))) 14)) 1/3)))))))))))))))))))
2.2s	(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)))
2.0s	(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)))
1.6s	(/ (* (* (- 0 (* a c)) (- 0 (* a c))) (- 0 (* a c))) (* (* a a) a))
1.2s	(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin x) (sin x)) (sin x))) (* (* (* (* x x) (+ 1 (cos x))) (* (* x x) (+ 1 (cos x)))) (* (* x x) (+ 1 (cos x)))))

sample5.1m

Algorithm

56×	intervals
16×	halfpoints

Results

1.2m	66837×	body	1280	valid
41.9s	17222×	body	2560	valid
29.2s	42464×	body	640	valid
13.0s	12436×	body	10240	exit
12.1s	94230×	body	80	valid
8.0s	20162×	body	320	valid
6.7s	63339×	body	80	nan
3.1s	10638×	body	160	valid
1.9s	47310×	pre	80	true
771.0ms	645×	body	1280	nan
527.0ms	385×	body	5120	valid
520.0ms	659×	body	640	nan
168.0ms	355×	body	320	nan
59.0ms	212×	body	160	nan

prune3.0m

series37.6s

Calls

353 calls:

Slowest

780.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))
719.0ms	(fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x)))))
588.0ms	(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
543.0ms	(* (cbrt (/ (log1p (- x)) (log1p x))) (cbrt (/ (log1p (- x)) (log1p x))))
499.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite8.4s

Algorithm

112×	rewrite-expression-head

Calls

353 calls:

Slowest

190.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
157.0ms	(+ (- (/ 1 (+ x 1)) (/ 2 x)) (+ (fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))) (/ 1 (- x 1))))
131.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
122.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
116.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

Rules

12896×	`times-frac`
11447×	`*-un-lft-identity`
10080×	`add-sqr-sqrt`
8320×	`add-cube-cbrt`
4469×	`prod-diff`
3439×	`sqrt-prod`
1454×	`pow1`
1239×	`add-exp-log`
1216×	`distribute-lft-out`
992×	`add-cbrt-cube`
900×	`div-inv`
713×	`associate-l`
629×	`difference-of-squares`
628×	`cbrt-prod`
551×	`unpow-prod-down`
538×	`associate-+l+`
537×	`add-log-exp`
462×	`fma-neg`
451×	`associate-/r*`
434×	`distribute-lft-out--`
390×	`associate-/r/`
369×	`associate-/l*`
366×	`log-prod`
354×	`associate-r`
347×	`log1p-expm1-u`
346×	`expm1-log1p-u`
345×	`insert-posit16`
295×	`cube-prod`
289×	`div-exp` `prod-exp`
263×	`pow-prod-up`
258×	`pow-prod-down`
255×	`swap-sqr`
219×	`cbrt-unprod`
187×	`cbrt-undiv`
180×	`flip3--` `flip--`
170×	`flip-+` `flip3-+`
166×	`unswap-sqr`
165×	`pow-sqr`
153×	`distribute-rgt-neg-in`
152×	`pow-flip`
150×	`fma-def`
143×	`sqr-pow`
132×	`distribute-lft-neg-in`
131×	`associate-+r+`
130×	`pow-plus`
116×	`sqrt-div`
98×	`sqrt-pow1` `pow-unpow`
95×	`pow2`
80×	`frac-times`
77×	`associate-*l/`
76×	`frac-2neg` `clear-num`
75×	`cbrt-div`
73×	`tan-quot`
71×	`log-pow`
66×	`pow1/3` `diff-log`
61×	`*-commutative` `pow1/2`
60×	`1-exp` `rec-exp` `associate-*r/` `sub-neg`
58×	`associate-/l/`
46×	`frac-sub`
45×	`exp-prod`
44×	`neg-mul-1`
43×	`inv-pow`
40×	`unpow3` `cube-mult`
39×	`fma-udef`
38×	`sum-log`
30×	`exp-sum`
29×	`log-div`
24×	`+-commutative`
23×	`rem-sqrt-square`
21×	`un-div-inv`
19×	`rem-log-exp`
18×	`div-sub`
17×	`frac-add`
15×	`unpow-prod-up`
14×	`pow-div`
13×	`associate--l+`
10×	`pow-exp` `pow-pow`
9×	`distribute-rgt-in` `difference-of-sqr-1` `pow-to-exp` `distribute-lft-in`
8×	`associate--l-`
7×	`neg-sub0` `neg-log`
6×	`exp-diff` `rem-exp-log` `associate-+l-` `hypot-def`
5×	`log-rec` `associate--r+`
4×	`expm1-udef` `associate-+r-` `sin-mult`
3×	`expm1-log1p` `distribute-rgt-out--`
2×	`sin-sum` `log1p-def` `+.c-commutative` `sqr-sin` `tan-sum` `frac-2neg-c` `cos-sum` `pow-sub` `log1p-udef`
1×	`remove-posit16` `diff-atan` `rem-cube-cbrt` `distribute-neg-out` `log1p-expm1` `pow3` `distribute-frac-neg` `sub0-neg` `distribute-lft-neg-out` `hypot-udef` `sub-div` `diff-sin` `difference-cubes` `diff-cos` `unsub-neg` `expm1-def` `e-exp-1`

regimes4.3s

Accuracy

Total 19.7b remaining (13.4%)

4.2b	84.6%	quadp (p42, positive)
3.7b	-5.4%	expq3 (problem 3.4.2)
3.2b	88.3%	quadm (p42, negative)
1.6b	87.4%	2nthrt (problem 3.4.6)
1.1b	95.4%	quad2p (problem 3.2.1, positive)

Details

simplify38.7m

sample5.1m

prune3.0m

series37.6s

rewrite8.4s

regimes4.3s

localize4.2s

bsearch3.8s

end1.0ms