Details

simplify8.4m

Calls

5567 calls:

Slowest
1.5s
(/ (* (* (* (+ (* (- x 1) (- (/ 1 (+ x 1)) (/ 2 x))) 1) (+ (/ 1 (+ x 1)) (/ 2 x))) (* (+ (* (- x 1) (- (/ 1 (+ x 1)) (/ 2 x))) 1) (+ (/ 1 (+ x 1)) (/ 2 x)))) (* (+ (* (- x 1) (- (/ 1 (+ x 1)) (/ 2 x))) 1) (+ (/ 1 (+ x 1)) (/ 2 x)))) (* (* (* (+ (/ 1 (+ x 1)) (/ 2 x)) (- x 1)) (* (+ (/ 1 (+ x 1)) (/ 2 x)) (- x 1))) (* (+ (/ 1 (+ x 1)) (/ 2 x)) (- x 1))))
1.2s
(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)))
1.1s
(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)))
1.1s
(/ (* (* (* eps (- (exp (* (+ a b) eps)) 1)) (* eps (- (exp (* (+ a b) eps)) 1))) (* eps (- (exp (* (+ a b) eps)) 1))) (* (* (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))))
1.0s
(cbrt (* (* (+ (pow (exp x) 3) (pow 1 3)) (- (* (exp x) (exp x)) (* 1 1))) (- (* (exp x) (exp x)) (* 1 1))))

sample5.1m

Algorithm
56×intervals
16×halfpoints
Results
1.1m66937×body1280valid
42.5s17805×body2560valid
27.1s41960×body640valid
14.7s12470×body10240exit
11.5s94031×body80valid
8.6s20299×body320valid
7.3s64141×body80nan
2.6s10402×body160valid
1.8s47376×pre80true
806.0ms667×body1280nan
609.0ms693×body640nan
518.0ms488×body5120valid
155.0ms336×body320nan
53.0ms192×body160nan

prune1.5m

series23.4s

Calls

388 calls:

Slowest
441.0ms
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))))) (/ (sin x) (cos x)))
423.0ms
(- (/ (+ (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))
381.0ms
(+ 1 (- (log n) (/ 1/6 (* n n))))
356.0ms
(- x (sin x))

regimes4.4s

Accuracy

Total 18.8b remaining (15.6%)

4.0b85.6%quad2p (problem 3.2.1, positive)
3.3b88%quadp (p42, positive)
3.3b0%expq3 (problem 3.4.2)
1.5b83.3%2nthrt (problem 3.4.6)
1.0b95.8%quadm (p42, negative)

rewrite4.2s

Algorithm
121×rewrite-expression-head
Calls

388 calls:

Slowest
208.0ms
(/ (- (- (- (* -1/2 (pow x 4)) (* x x)) (* (pow x 6) 1/3)) (log (+ 1 x))) (log (+ 1 x)))
203.0ms
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))))) (/ (sin x) (cos x)))
176.0ms
(- (+ (+ 1 (- (log n) (/ 1/6 (* n n)))) (/ 1/2 n)) 1)
119.0ms
(- (* (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1)))) (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))))) (* (sqrt x) (sqrt x)))
107.0ms
(* (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1)))) (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1)))))
Rules
3104×cbrt-div
2368×frac-times
2348×sqrt-div
1714×flip-+ flip3-+
1046×*-un-lft-identity
987×add-sqr-sqrt
909×associate-*l/
799×add-cube-cbrt
668×add-exp-log
663×pow1
603×add-cbrt-cube
560×associate-*r/
527×add-log-exp
377×insert-posit16
356×times-frac
205×div-inv
204×associate-/r*
184×flip3-- associate-*l* flip-- associate-*r*
176×associate-/r/
155×associate-/l*
119×cbrt-prod
104×sqrt-prod distribute-lft-out--
92×associate-/l/
90×log-pow sub-neg
89×log-prod prod-exp
82×frac-2neg clear-num
80×cbrt-unprod
79×pow-prod-down *-commutative
78×distribute-lft-out
74×difference-of-squares
67×pow1/3
60×div-exp
54×cbrt-undiv
52×frac-sub
51×pow1/2
48×diff-log
44×log-div
39×pow-prod-up
37×frac-add
35×pow-flip
32×+-commutative
29×sum-log rec-exp
24×distribute-rgt-in inv-pow distribute-lft-in rem-sqrt-square
23×pow-plus
22×pow2
21×difference-of-sqr-1 exp-prod
20×pow-unpow
19×rem-log-exp
18×div-sub
17×tan-quot associate--l+
16×unpow-prod-down
13×complex-mul-def
11×un-div-inv
associate--l- sin-mult associate--r-
associate-+l+ cube-prod
associate-+r+ pow3 sqrt-unprod associate--r+
pow-to-exp rem-exp-log cube-mult
sin-sum difference-cubes
neg-sub0 cos-mult exp-sum associate-+l-
associate-+r- pow-exp *.c-commutative pow-pow +.c-commutative rem-square-sqrt
distribute-lft1-in exp-diff neg-mul-1 sqr-sin tan-sum complex-add-def cos-sum associate-*l*.c rem-cbrt-cube
remove-posit16 diff-atan distribute-rgt-out-- rem-cube-cbrt sin-cos-mult unpow3 frac-2neg-c associate-+l+.c diff-sin diff-cos distribute-rgt-out

localize3.9s

bsearch2.1s

end1.0ms