Details

simplify7.2m

Calls

4405 calls:

Slowest
1.9s
(/ (* (* (* (sin x) (sin x)) (* (sin x) (sin x))) (* (sin x) (sin x))) (/ (* (* (* (* x x) (+ (pow 1 3) (pow (cos x) 3))) (* (* x x) (+ (pow 1 3) (pow (cos x) 3)))) (* (* x x) (+ (pow 1 3) (pow (cos x) 3)))) (* (* (+ 1 (- (* (cos x) (cos x)) (cos x))) (+ 1 (- (* (cos x) (cos x)) (cos x)))) (+ 1 (- (* (cos x) (cos x)) (cos x))))))
1.5s
(* (* (* (/ (- (exp x) (exp (- x))) 2) (/ (- (exp x) (exp (- x))) 2)) (/ (- (exp x) (exp (- x))) 2)) (* (* (sin y) (sin y)) (sin y)))
1.3s
(/ (* (* (* (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)))))
1.2s
(* (* (* (* x x) (* x x)) (* x x)) (* (* (+ 1 (cos x)) (+ 1 (cos x))) (+ 1 (cos x))))
1.1s
(* (* (* (/ 1 a) (/ 1 a)) (/ 1 a)) (* (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))

sample5.2m

Algorithm
56×intervals
16×halfpoints
Results
1.1m66717×body1280valid
42.2s17445×body2560valid
26.2s42249×body640valid
14.1s12614×body10240exit
11.5s93619×body80valid
9.2s20720×body320valid
7.8s62794×body80nan
3.1s10575×body160valid
1.8s47386×pre80true
793.0ms628×body1280nan
558.0ms439×body5120valid
538.0ms672×body640nan
197.0ms362×body320nan
58.0ms193×body160nan

prune1.4m

series27.3s

Calls

380 calls:

Slowest
1.4s
(/ (* 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)))))))
945.0ms
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
649.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
427.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
423.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

regimes5.1s

Accuracy

Total 20.7b remaining (16.7%)

4.5b84%quad2p (problem 3.2.1, positive)
4.3b84.5%quadp (p42, positive)
3.2b0%expq3 (problem 3.4.2)
1.4b83.9%2nthrt (problem 3.4.6)
0.8b96.5%quadm (p42, negative)

rewrite4.0s

Algorithm
118×rewrite-expression-head
Calls

380 calls:

Slowest
132.0ms
(- (+ (+ 1 (- (log n) (/ 1/6 (* n n)))) (/ 1/2 n)) 1)
106.0ms
(/ (- (* (- (* (pow eps 5) -2/5) (* 2 eps)) (- (* (pow eps 5) -2/5) (* 2 eps))) (* (* (* eps eps) (* eps 2/3)) (* (* eps eps) (* eps 2/3)))) (+ (- (* (pow eps 5) -2/5) (* 2 eps)) (* (* eps eps) (* eps 2/3))))
67.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
65.0ms
(/ (+ (pow (/ 1 a) 3) (pow (/ 1 b) 3)) (+ (* (/ 1 a) (/ 1 a)) (- (* (/ 1 b) (/ 1 b)) (* (/ 1 a) (/ 1 b)))))
62.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))
Rules
1040×*-un-lft-identity
924×add-sqr-sqrt
744×add-cube-cbrt
632×add-exp-log
629×pow1
582×add-log-exp add-cbrt-cube
399×associate-*l/
396×associate-*r/
370×insert-posit16
322×times-frac
301×frac-times
280×frac-add
277×flip-+ flip3-+
265×associate-/r/
258×frac-sub
254×flip3-- flip--
226×div-inv
204×associate-*l*
196×associate-*r*
168×un-div-inv
144×associate-/r*
141×distribute-lft-out
139×cbrt-div
130×associate-/l* sqrt-prod
105×sub-neg
102×cbrt-prod
95×sqrt-div
94×associate-/l/
93×unpow-prod-down
89×*-commutative
86×cube-prod
82×prod-exp
79×difference-of-squares
78×pow-prod-down
77×distribute-lft-out--
75×cbrt-unprod
71×log-prod
66×log-pow
64×tan-quot
63×diff-log
59×frac-2neg clear-num
56×sub-div
53×pow1/3 div-exp
50×pow1/2
47×sum-log
46×cbrt-undiv
36×+-commutative
29×log-div
27×pow-prod-up
25×rec-exp
24×rem-sqrt-square
23×div-sub
22×distribute-rgt-in distribute-lft-in
21×difference-of-sqr-1
19×pow-flip
18×associate--l+ pow-plus
17×associate-+r+ pow2
14×rem-log-exp
13×inv-pow complex-mul-def
12×sin-mult pow-unpow
10×neg-sub0 associate--l-
exp-prod
associate-+l+
distribute-lft1-in sqrt-unprod
cos-mult associate--r+ sum-cubes associate-+l-
associate-+r- pow-to-exp rem-exp-log
sqr-sin rem-square-sqrt cube-div
exp-diff distribute-rgt-out-- pow-exp *.c-commutative cube-mult pow-pow +.c-commutative cos-sum
sin-sum rem-cube-cbrt exp-sum unpow3 neg-mul-1 exp-neg tan-sum associate-*l*.c complex-add-def
remove-posit16 diff-atan sqr-cos associate-+l+.c diff-sin diff-cos associate--r-

localize3.2s

bsearch2.2s

end1.0ms