Details

simplify6.4m

Calls

4758 calls:

Slowest
1.2s
(/ (* (* (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1)) (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))) (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))) (* (* (* (* (+ x 1) x) (* (+ x 1) x)) (* (+ x 1) x)) (* (* (- x 1) (- x 1)) (- x 1))))
1.1s
(/ (* (* (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1)) (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))) (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))) (* (* (* (* (+ x 1) x) (- x 1)) (* (* (+ x 1) x) (- x 1))) (* (* (+ x 1) x) (- x 1))))
1.1s
(/ (* (* (* (sin x) (sin x)) (* (sin x) (sin x))) (* (sin x) (sin x))) (* (* (* (* x x) (* x x)) (* x x)) (* (* (+ 1 (cos x)) (+ 1 (cos x))) (+ 1 (cos x)))))
1.1s
(/ (* (+ (pow (exp x) 2) (+ (exp x) 1)) (exp x)) (- (pow (exp x) 3) 1))
1.0s
(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)))

sample5.0m

Algorithm
56×intervals
16×halfpoints
Results
1.0m66345×body1280valid
40.4s18017×body2560valid
25.0s42393×body640valid
15.4s12720×body10240exit
11.9s93427×body80valid
9.2s20654×body320valid
5.7s63700×body80nan
2.6s10654×body160valid
2.2s47219×pre80true
800.0ms699×body1280nan
549.0ms445×body5120valid
457.0ms625×body640nan
162.0ms347×body320nan
74.0ms176×body160nan

prune1.4m

series41.8s

Calls

390 calls:

Slowest
1.8s
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (+ (* eps b) (+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* (* (* eps b) (* eps b)) (* eps b)))))))
1.7s
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (/ (* (* (tan x) (tan eps)) (* (sin x) (sin eps))) (* (cos x) (cos eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
1.2s
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
500.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
491.0ms
(+ 1 (- (log n) (/ 1/6 (* n n))))

regimes4.3s

Accuracy

Total 23.6b remaining (18.7%)

5.5b80.7%quad2m (problem 3.2.1, negative)
4.3b84.7%quadp (p42, positive)
3.2b0%expq3 (problem 3.4.2)
1.7b93.1%quad2p (problem 3.2.1, positive)
1.6b93.2%quadm (p42, negative)

localize3.9s

rewrite3.8s

Algorithm
119×rewrite-expression-head
Calls

390 calls:

Slowest
204.0ms
(- (+ (+ 1 (- (log n) (/ 1/6 (* n n)))) (/ 1/2 n)) 1)
62.0ms
(/ 1 (* (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt (+ x 1))))))
60.0ms
(* (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt (+ x 1)))))
52.0ms
(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
51.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
Rules
1197×*-un-lft-identity
1189×add-sqr-sqrt
942×add-cube-cbrt
745×pow1
672×add-exp-log
606×add-cbrt-cube
540×add-log-exp
486×times-frac
378×insert-posit16
272×flip-+ flip3-+
268×sqrt-div
262×associate-*l*
244×sqrt-prod
238×associate-*r*
217×div-inv
212×associate-*l/
210×associate-/r*
208×associate-*r/
206×frac-times
184×flip3-- flip-- associate-/r/
169×associate-/l*
160×cbrt-prod
118×pow-prod-down
116×log-prod
113×difference-of-squares
110×prod-exp
100×log-pow
95×*-commutative
94×cbrt-div distribute-lft-out-- sub-neg
93×cbrt-unprod
91×associate-/l/
88×distribute-lft-out
76×frac-add
72×tan-quot
71×frac-2neg clear-num
60×pow1/2
57×pow1/3 diff-log
53×frac-sub
49×pow-prod-up
42×div-exp
37×cbrt-undiv
35×pow-flip
34×unpow-prod-down
32×rem-sqrt-square
31×pow-unpow pow-plus +-commutative
29×rec-exp exp-prod
28×log-div
27×sum-log distribute-rgt-in distribute-lft-in
25×div-sub
24×pow2
21×inv-pow
20×difference-of-sqr-1 un-div-inv
19×cube-prod
18×rem-log-exp
17×associate--l+
16×pow-pow
14×cube-mult
13×pow-to-exp complex-mul-def
11×associate-+l+ associate--l- difference-cubes
10×neg-sub0
pow-exp
associate-+r+ distribute-rgt1-in
rem-cube-cbrt sin-sum sqrt-unprod neg-mul-1 sin-mult associate-+l- rem-square-sqrt
associate--r+ distribute-rgt-neg-in distribute-lft-neg-in
pow-div exp-sum *.c-commutative unpow3 distribute-frac-neg +.c-commutative rem-exp-log
quot-tan associate-+r- sin-cos-mult distribute-lft1-in pow3 sqr-sin tan-sum frac-2neg-c cos-sum associate-*l*.c complex-add-def
exp-diff diff-atan sub0-neg sub-div sum-cubes distribute-neg-frac distribute-rgt-out-- associate-+l+.c diff-sin diff-cos

bsearch2.0s

end1.0ms