Details

simplify15.3m

Calls

10089 calls:

Slowest
1.6s
(* (* (* (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))) (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps))))) (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps))))) (* (* (- (exp (* b eps)) 1) (- (exp (* b eps)) 1)) (- (exp (* b eps)) 1)))
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 1)) (+ x 1)) (* (* x x) x)) (* (* (- x 1) (- x 1)) (- x 1))))
1.3s
(/ (* (* (- 0 (* a c)) (- 0 (* a c))) (- 0 (* a c))) (* (* a a) a))
1.3s
(/ (* (* (+ (* (- (* 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))))
1.3s
(* (* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x))) (* (* (* x x) (* x x)) (* x x)))

sample4.9m

Algorithm
56×intervals
16×halfpoints
Results
1.0m66365×body1280valid
39.4s17581×body2560valid
26.8s42516×body640valid
12.3s12771×body10240exit
11.0s94012×body80valid
8.6s20524×body320valid
7.2s63432×body80nan
2.8s10653×body160valid
2.5s47339×pre80true
923.0ms695×body640nan
797.0ms645×body1280nan
487.0ms479×body5120valid
193.0ms354×body320nan
53.0ms192×body160nan

prune2.0m

series33.4s

Calls

390 calls:

Slowest
1.3s
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
674.0ms
(* n (log n))
524.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
407.0ms
(- (* b b) (* 4 (* a c)))
388.0ms
(cbrt (+ (+ (* a x) (* x (* (* a 1/6) (* (* a x) (* a x))))) (* (* 1/2 (* a x)) (* a x))))

rewrite17.3s

Algorithm
119×rewrite-expression-head
Calls

390 calls:

Slowest
3.8s
(* (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))) (- (exp (* b eps)) 1))
944.0ms
(- (+ (/ 1/2 n) (+ 1 (+ (log n) (/ -1/6 (* n n))))) 1)
473.0ms
(- (* (* (cos y) (exp x)) (* (cos y) (exp x))) (* (/ (cos y) (exp x)) (* (cos y) (exp x))))
259.0ms
(* eps (* (* 1/6 a) (* (* a eps) (* a eps))))
246.0ms
(/ (log (exp (+ (* (- (* (exp x) (exp x)) 3) (exp x)) 2))) (* (+ (exp x) 2) (exp x)))
Rules
3822×*-un-lft-identity
3492×add-sqr-sqrt
3253×times-frac
2506×pow1
2268×add-cube-cbrt
1956×add-exp-log
1840×add-cbrt-cube
986×sqrt-prod
793×prod-exp
776×pow-prod-down
749×cbrt-unprod
703×add-log-exp
697×associate-*l*
524×distribute-lft-out
507×pow-prod-up
421×associate-*r*
404×difference-of-squares
379×insert-posit16
323×div-exp
317×associate-/l*
291×associate-/r*
283×cbrt-undiv
256×pow-sqr
254×distribute-lft-out--
233×unpow-prod-down
222×pow-plus
221×associate-*l/
205×log-prod
203×div-inv
197×flip3-- flip--
188×flip-+ flip3-+
172×unswap-sqr
156×cbrt-prod
153×frac-times
144×pow2
128×associate-*r/
126×cube-prod
122×associate-/r/
119×swap-sqr
107×sub-neg
102×sqrt-div *-commutative
101×diff-log
84×pow-unpow exp-prod
79×associate-/l/
71×sum-log
65×distribute-rgt-neg-in
64×frac-2neg clear-num
61×sqr-pow
59×tan-quot
55×log-pow
50×sqrt-pow1 pow1/2
46×distribute-rgt-in distribute-lft-in
45×frac-add
43×distribute-lft-neg-in
40×+-commutative
37×log-div
35×associate--l+
32×cbrt-div
31×difference-of-sqr-1
30×cube-mult
28×sum-cubes
26×associate--r+ rem-sqrt-square
25×1-exp rec-exp
24×pow-flip
23×rem-log-exp
21×pow1/3
20×div-sub
16×frac-sub
15×associate-+l+ pow-exp
13×associate--l- pow-to-exp complex-mul-def
12×neg-sub0
11×exp-sum inv-pow
neg-mul-1 pow-pow
associate-+r+ neg-log
distribute-rgt-out
distribute-lft1-in rem-exp-log associate-+l- distribute-rgt-out--
sin-sum
rem-cube-cbrt distribute-frac-neg sqrt-unprod sin-mult un-div-inv associate--r- distribute-rgt1-in
*.c-commutative exp-to-pow +.c-commutative
exp-diff cos-mult exp-neg sub0-neg pow3 unpow3 sub-div sqr-sin complex-add-def rem-square-sqrt cos-sum tan-sum associate-*l*.c e-exp-1
diff-atan sin-cos-mult associate-+r- frac-2neg-c distribute-neg-frac diff-sin associate-+l+.c cube-div rem-cbrt-cube diff-cos

localize4.6s

regimes4.5s

Accuracy

Total 20.3b remaining (13.2%)

4.9b56.3%2nthrt (problem 3.4.6)
4.5b49.7%expq3 (problem 3.4.2)
1.6b93.6%quadp (p42, positive)
1.4b94.3%quad2p (problem 3.2.1, positive)
1.3b94.4%quadm (p42, negative)

bsearch2.6s

end1.0ms