Details

simplify5.8m

Calls

4026 calls:

Slowest
1.8s
(/ (* (* (* (- (/ 1 N) (/ -1/2 (* N N))) (+ (+ 1 (/ (* N -1/2) (* N N))) (/ 1/3 (* N N)))) (* (- (/ 1 N) (/ -1/2 (* N N))) (+ (+ 1 (/ (* N -1/2) (* N N))) (/ 1/3 (* N N))))) (* (- (/ 1 N) (/ -1/2 (* N N))) (+ (+ 1 (/ (* N -1/2) (* N N))) (/ 1/3 (* N N))))) (* (* (* (- (/ 1 N) (/ -1/2 (* N N))) N) (* (- (/ 1 N) (/ -1/2 (* N N))) N)) (* (- (/ 1 N) (/ -1/2 (* N N))) N)))
1.4s
(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)))
1.4s
(/ (* (* (+ (* (- (* 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))))
1.3s
(/ (/ (* (* (* (sin eps) (+ (/ (* (sin x) (sin x)) (cos x)) (cos x))) (* (sin eps) (+ (/ (* (sin x) (sin x)) (cos x)) (cos x)))) (* (sin eps) (+ (/ (* (sin x) (sin x)) (cos x)) (cos x)))) (* (* (cos eps) (cos eps)) (cos eps))) (* (* (* (- 1 (* (tan x) (tan eps))) (cos x)) (* (- 1 (* (tan x) (tan eps))) (cos x))) (* (- 1 (* (tan x) (tan eps))) (cos x))))
1.3s
(/ (/ (* (* (* (sin eps) (sin eps)) (sin eps)) (* (* (+ (/ (* (sin x) (sin x)) (cos x)) (cos x)) (+ (/ (* (sin x) (sin x)) (cos x)) (cos x))) (+ (/ (* (sin x) (sin x)) (cos x)) (cos x)))) (* (* (cos eps) (cos eps)) (cos eps))) (* (* (* (- 1 (* (tan x) (tan eps))) (cos x)) (* (- 1 (* (tan x) (tan eps))) (cos x))) (* (- 1 (* (tan x) (tan eps))) (cos x))))

sample5.0m

Algorithm
56×intervals
16×halfpoints
Results
1.1m67314×body1280valid
39.2s17433×body2560valid
25.9s41943×body640valid
13.0s12693×body10240exit
12.6s93816×body80valid
9.0s20435×body320valid
6.9s63373×body80nan
3.5s10580×body160valid
1.9s47371×pre80true
817.0ms693×body1280nan
632.0ms447×body5120valid
583.0ms629×body640nan
208.0ms327×body320nan
50.0ms189×body160nan

prune1.3m

series35.5s

Calls

378 calls:

Slowest
1.0s
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (+ (* (* (* a eps) (* (* a eps) (* a eps))) 1/6) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))) (- (exp (* b eps)) 1)))
732.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
528.0ms
(+ 1 (- (log n) (/ 1/6 (* n n))))
479.0ms
(- (* (* x x) 9/40) (- (* (pow x 4) 27/2800) -1/2))
472.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

regimes4.1s

Accuracy

Total 24.3b remaining (21.6%)

4.6b82.4%quadm (p42, negative)
4.2b82%quad2m (problem 3.2.1, negative)
4.2b84.7%quadp (p42, positive)
3.3b0%expq3 (problem 3.4.2)
1.2b85.9%2nthrt (problem 3.4.6)

rewrite4.1s

Algorithm
118×rewrite-expression-head
Calls

378 calls:

Slowest
204.0ms
(* (+ (+ (* (* (* a eps) (* (* a eps) (* a eps))) 1/6) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))) (- (exp (* b eps)) 1))
174.0ms
(- (+ (+ 1 (- (log n) (/ 1/6 (* n n)))) (/ 1/2 n)) 1)
108.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (+ (* (* (* a eps) (* (* a eps) (* a eps))) 1/6) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))) (- (exp (* b eps)) 1)))
61.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
57.0ms
(* (+ (sqrt (exp x)) 1) (* (+ (* x (+ (* 1/48 x) 1/8)) 1/2) x))
Rules
1002×*-un-lft-identity
954×add-sqr-sqrt
807×add-cube-cbrt
644×add-exp-log
615×pow1
584×add-cbrt-cube
521×add-log-exp
367×insert-posit16
347×times-frac
256×flip-+ flip3-+
246×associate-*l/
240×associate-*l*
232×associate-*r*
195×flip3-- flip--
171×sqrt-prod
162×cbrt-div
148×frac-times
140×associate-/r/
139×associate-/l*
135×associate-/r*
134×sqrt-div
132×div-inv
127×log-prod
126×cbrt-prod associate-*r/
99×sub-neg
94×*-commutative
82×prod-exp
80×associate-/l/
75×pow-prod-down
72×cbrt-unprod
65×frac-2neg clear-num
64×distribute-lft-out--
63×difference-of-squares
61×distribute-lft-out
60×div-exp
57×frac-add
56×pow1/3 pow1/2
55×log-pow
51×cbrt-undiv
48×diff-log
34×tan-quot
32×+-commutative log-div
31×sum-log
30×distribute-rgt-in distribute-lft-in
28×pow-prod-up
27×rem-sqrt-square
23×difference-of-sqr-1
22×unpow-prod-down
21×frac-sub pow-flip
19×rec-exp rem-log-exp
18×pow2 pow-plus
16×div-sub
13×inv-pow complex-mul-def
12×pow-unpow cube-prod
11×associate-+l+ exp-sum associate--l+
exp-diff sqrt-unprod exp-prod cube-mult
neg-sub0 associate-+r+ pow-to-exp
associate--l- pow-exp pow-pow associate-+l-
sin-sum sin-mult rem-exp-log
distribute-rgt-out-- rem-cube-cbrt unpow3 sum-cubes rem-square-sqrt
quot-tan pow-div *.c-commutative associate--r+ sqr-sin +.c-commutative
associate-*l*.c associate-+r- exp-neg pow3 un-div-inv neg-mul-1 complex-add-def cos-sum tan-sum rem-cbrt-cube
distribute-lft1-in diff-atan cos-mult sin-cos-mult sub0-neg distribute-frac-neg frac-2neg-c associate-+l+.c diff-sin diff-cos associate--r-

localize3.1s

bsearch2.0s

end19.0ms