Details

simplify6.1m

Calls

4221 calls:

Slowest
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
(/ (* (* (* (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)))))
1.1s
(+ (* (* (- (pow (* 1 x) 3) (pow (* (+ x 1) 2) 3)) (- (* x x) (* 1 1))) (+ (* x x) (- (* 1 1) (* x 1)))) (* (* (+ (* (* 1 x) (* 1 x)) (+ (* (* (+ x 1) 2) (* (+ x 1) 2)) (* (* 1 x) (* (+ x 1) 2)))) (+ x 1)) (* (* (+ (pow x 3) (pow 1 3)) x) 1)))
1.0s
(* (+ (exp (* a eps)) 1) (+ (* (* eps b) (* eps b)) (- (* (+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* (* (* eps b) (* eps b)) (* eps b)))) (+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* (* (* eps b) (* eps b)) (* eps b))))) (* (* eps b) (+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* (* (* eps b) (* eps b)) (* eps b))))))))

sample5.1m

Algorithm
56×intervals
16×halfpoints
Results
1.1m66524×body1280valid
40.6s17470×body2560valid
27.3s41703×body640valid
14.8s12861×body10240exit
11.7s94134×body80valid
9.6s21001×body320valid
7.1s63128×body80nan
2.8s10907×body160valid
2.0s47441×pre80true
804.0ms698×body1280nan
482.0ms456×body5120valid
466.0ms645×body640nan
172.0ms369×body320nan
86.0ms212×body160nan

prune1.4m

series30.0s

Calls

402 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)))))))
1.3s
(cbrt (* (* 1/2 c) (/ 4 (- (sqrt (+ (* c (* -4 a)) (* b b))) b))))
1.1s
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
1.0s
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (/ (* (* (tan x) (sin eps)) (* (tan x) (sin eps))) (* (cos eps) (cos eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
941.0ms
(cbrt (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))

rewrite4.7s

Algorithm
121×rewrite-expression-head
Calls

402 calls:

Slowest
279.0ms
(* (+ (+ (* (* (* a eps) (* (* a eps) (* a eps))) 1/6) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))) (- (exp (* b eps)) 1))
204.0ms
(- (+ (+ 1 (- (log n) (/ 1/6 (* n n)))) (/ 1/2 n)) 1)
118.0ms
(+ (+ (* (* (* a eps) (* (* a eps) (* a eps))) 1/6) (* a eps)) (* 1/2 (* (* a eps) (* a eps))))
80.0ms
(+ (+ (* (exp x) (- (* (exp x) (exp x)) 4)) 2) (exp x))
75.0ms
(cbrt (+ (+ (* (* (* a eps) (* (* a eps) (* a eps))) 1/6) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))))
Rules
1022×add-sqr-sqrt
1007×*-un-lft-identity
827×add-cube-cbrt
794×pow1
640×add-exp-log
608×add-cbrt-cube
559×add-log-exp
391×insert-posit16
283×times-frac
236×associate-*r*
223×flip-+ flip3-+
217×associate-*l*
189×flip3-- flip--
186×associate-*l/
160×sqrt-prod
158×associate-/r/
144×log-prod
142×associate-/r*
138×cbrt-prod div-inv
126×pow-prod-down associate-/l*
125×sqrt-div associate-*r/
114×frac-times
113×log-pow
109×sub-neg
100×cbrt-div
98×*-commutative prod-exp
91×cbrt-unprod
81×difference-of-squares
79×distribute-lft-out--
72×tan-quot
65×pow-prod-up
64×pow1/3
61×frac-2neg clear-num associate-/l/
60×pow1/2
57×diff-log
51×log-div
42×distribute-lft-out
40×pow-plus
39×+-commutative
37×frac-add
36×div-exp
35×pow2
34×sum-log
32×cbrt-undiv rem-sqrt-square
30×distribute-rgt-in distribute-lft-in
29×associate--l+
26×rem-log-exp
23×exp-prod
22×unpow-prod-down
20×frac-sub associate-+r+ difference-of-sqr-1
19×pow-flip div-sub
18×rec-exp
17×associate-+l+
16×pow-unpow
13×inv-pow complex-mul-def associate-+l-
11×exp-sum
exp-diff associate--l-
sqrt-unprod sin-mult
pow-to-exp
associate-+r-
neg-sub0 pow-exp pow-pow rem-square-sqrt
*.c-commutative cube-prod +.c-commutative distribute-rgt-out--
associate-*l*.c cos-mult sin-sum distribute-lft1-in associate--r+ sqr-sin un-div-inv complex-add-def cos-sum tan-sum
diff-atan rem-cube-cbrt cube-unmult sub0-neg pow3 unpow3 distribute-frac-neg frac-2neg-c exp-to-pow rem-exp-log unpow1/3 sqr-cos associate-+l+.c diff-sin cube-mult rem-cbrt-cube diff-cos associate--r-

regimes4.5s

Accuracy

Total 17.6b remaining (14.3%)

4.3b84.5%quadp (p42, positive)
2.4b0%expq3 (problem 3.4.2)
1.6b81.2%2nthrt (problem 3.4.6)
1.3b94.4%quadm (p42, negative)
1.1b95.3%quad2m (problem 3.2.1, negative)

localize3.2s

bsearch2.5s

end1.0ms