Details

simplify6.7m

Calls

5069 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)))
1.5s	(/ (* (* (- (* a c)) (- (* a c))) (- (* a c))) (* (* (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))) (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))))
1.1s	(/ (* (* (/ 1 (log1p x)) (/ 1 (log1p x))) (/ 1 (log1p x))) (* (* (/ 1 (log1p (- x))) (/ 1 (log1p (- x)))) (/ 1 (log1p (- x)))))
983.0ms	(- (+ (/ (log (/ -1 x)) (* x (pow (- (log -1) (log (/ -1 x))) 2))) (/ 1 (* (pow x 2) (pow (- (log -1) (log (/ -1 x))) 2)))) (+ (/ (log (/ -1 x)) (- (log -1) (log (/ -1 x)))) (+ (/ (log (/ -1 x)) (* (pow x 2) (pow (- (log -1) (log (/ -1 x))) 3))) (+ (/ 1 (* x (- (log -1) (log (/ -1 x))))) (+ (* 1/2 (/ (log (/ -1 x)) (* (pow x 2) (pow (- (log -1) (log (/ -1 x))) 2)))) (* 1/2 (/ 1 (* (pow x 2) (- (log -1) (log (/ -1 x)))))))))))

sample5.0m

Algorithm

56×	intervals
16×	halfpoints

Results

1.1m	66899×	body	1280	valid
37.0s	17018×	body	2560	valid
27.3s	42195×	body	640	valid
13.7s	12774×	body	10240	exit
10.8s	93914×	body	80	valid
10.6s	20421×	body	320	valid
6.9s	63024×	body	80	nan
3.1s	11084×	body	160	valid
2.1s	47503×	pre	80	true
950.0ms	474×	body	5120	valid
680.0ms	616×	body	1280	nan
462.0ms	610×	body	640	nan
151.0ms	299×	body	320	nan
58.0ms	190×	body	160	nan

prune1.4m

series25.7s

Calls

342 calls:

Slowest

724.0ms	(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
497.0ms	(cbrt (* (cbrt x) (cbrt x)))
464.0ms	(/ (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* eps b)) (expm1 (* eps a))))
440.0ms	(cbrt (* (cbrt x) (cbrt x)))
440.0ms	(cbrt (* (cbrt x) (cbrt x)))

regimes4.2s

Accuracy

Total 25.7b remaining (16.7%)

4.6b	83.4%	quadm (p42, negative)
4.5b	83%	quad2p (problem 3.2.1, positive)
4.1b	85.3%	quadp (p42, positive)
3.4b	0%	expq3 (problem 3.4.2)
1.7b	85.5%	2nthrt (problem 3.4.6)

bsearch3.5s

localize2.7s

rewrite2.4s

Algorithm

111×	rewrite-expression-head

Calls

342 calls:

Slowest

75.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
48.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
47.0ms	(* (sqrt (sqrt (fma 1/3 (* x x) 2))) (* (sqrt (sqrt (fma 1/3 (* x x) 2))) (* (sqrt (fma 1/3 (* x x) 2)) x)))
44.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
41.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

Rules

1473×	`*-un-lft-identity`
1459×	`add-sqr-sqrt`
1306×	`add-cube-cbrt`
798×	`prod-diff`
562×	`add-exp-log`
534×	`pow1`
509×	`add-cbrt-cube`
441×	`add-log-exp`
436×	`times-frac`
338×	`log1p-expm1-u`
336×	`expm1-log1p-u`
335×	`insert-posit16`
276×	`div-inv`
271×	`sqrt-prod`
216×	`associate-l`
215×	`cbrt-prod`
191×	`fma-neg`
182×	`associate-/r/`
167×	`associate-r`
166×	`associate-/l*`
160×	`unpow-prod-down`
144×	`cube-prod` `associate-/r*`
119×	`flip3--` `flip--`
103×	`flip-+` `flip3-+`
86×	`log-prod`
75×	`frac-2neg` `clear-num`
73×	`pow-prod-down`
71×	`prod-exp` `associate-*r/`
69×	`tan-quot`
66×	`cbrt-unprod` `sqrt-div`
65×	`fma-def`
61×	`difference-of-squares` `sub-neg`
58×	`pow1/3`
52×	`distribute-lft-out--`
50×	`*-commutative`
46×	`distribute-lft-out`
45×	`div-exp` `neg-mul-1`
44×	`frac-times`
43×	`associate-/l/` `associate-*l/`
41×	`diff-log`
38×	`pow1/2`
35×	`cbrt-undiv`
31×	`cbrt-div` `unpow3` `fma-udef` `cube-mult`
28×	`associate-+l+`
27×	`rec-exp`
24×	`pow-flip` `log-pow` `rem-sqrt-square`
23×	`distribute-lft-neg-in`
22×	`+-commutative`
21×	`distribute-rgt-neg-in` `exp-prod` `pow-prod-up`
20×	`pow-unpow`
18×	`div-sub`
17×	`inv-pow`
15×	`sum-log` `frac-sub`
14×	`pow2` `pow-plus` `rem-log-exp`
13×	`neg-sub0`
12×	`frac-add`
11×	`log-div`
8×	`exp-sum`
7×	`pow-to-exp`
6×	`expm1-log1p` `associate--l-` `associate-+r+`
5×	`expm1-udef` `difference-of-sqr-1`
4×	`log1p-def` `associate--l+` `sqrt-unprod` `pow-pow` `distribute-rgt-out--` `rem-exp-log` `associate-+l-`
3×	`pow-exp` `distribute-rgt-in` `un-div-inv` `distribute-lft-in` `sin-mult` `distribute-rgt-out` `log1p-udef`
2×	`exp-diff` `sin-sum` `rem-cube-cbrt` `distribute-frac-neg` `+.c-commutative` `associate-+r-` `sqr-sin` `exp-neg` `cos-sum` `tan-sum`
1×	`diff-atan` `log1p-expm1` `neg-log` `sub-div` `associate--r+` `difference-cubes` `frac-2neg-c` `distribute-neg-frac` `rem-square-sqrt` `diff-sin` `diff-cos` `unsub-neg` `associate--r-` `expm1-def`

Details

simplify6.7m

sample5.0m

prune1.4m

series25.7s

regimes4.2s

bsearch3.5s

localize2.7s

rewrite2.4s

end2.0ms