Details

simplify17.5m

Calls

12202 calls:

Slowest
1.5s
(/ (* (* (* c c) c) (* (* a a) a)) (* (* a a) a))
1.4s
(/ (* (* (* (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)))))
1.4s
(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)))
1.3s
(/ (* (* (* (/ (sin x) x) (sin x)) (* (/ (sin x) x) (sin x))) (* (/ (sin x) x) (sin x))) (* (* (* (+ (cos x) 1) x) (* (+ (cos x) 1) x)) (* (+ (cos x) 1) x)))
1.3s
(* (* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x))) (* (* (* x x) (* x x)) (* x x)))

sample5.2m

Algorithm
56×intervals
16×halfpoints
Results
1.2m66512×body1280valid
40.0s16978×body2560valid
29.6s42491×body640valid
14.5s12661×body10240exit
11.6s93713×body80valid
10.2s21110×body320valid
7.3s63554×body80nan
2.9s10954×body160valid
2.3s47441×pre80true
1.1s621×body1280nan
614.0ms478×body5120valid
518.0ms679×body640nan
182.0ms388×body320nan
77.0ms196×body160nan

prune2.5m

series37.1s

Calls

383 calls:

Slowest
1.0s
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))) (- (exp (* b eps)) 1)))
719.0ms
(log (exp (* (cbrt (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))) (cbrt (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))))
552.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
529.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (log (exp (* (tan x) (tan eps)))))) (tan x))
480.0ms
(log (- 1 (* x (* x x))))

rewrite19.1s

Algorithm
118×rewrite-expression-head
Calls

383 calls:

Slowest
3.5s
(* (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))) (- (exp (* b eps)) 1))
1.6s
(- (- 1 (+ (/ 1/6 (* n n)) (- (/ -1/2 n) (log n)))) 1)
878.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))) (- (exp (* b eps)) 1)))
481.0ms
(/ (+ (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (* (* (cbrt (- (* 1 1) (* (exp x) 1))) (cbrt (- (* 1 1) (* (exp x) 1)))) (cbrt (- (* 1 1) (* (exp x) 1))))))
359.0ms
(- (* b b) (* 4 (* a c)))
Rules
5849×times-frac
5487×*-un-lft-identity
4839×add-sqr-sqrt
3461×add-cube-cbrt
2948×sqrt-prod
2437×pow1
1612×add-exp-log
1425×add-cbrt-cube
862×associate-*l*
701×distribute-lft-out
688×add-log-exp
651×pow-prod-down
561×pow-prod-up
560×prod-exp
520×difference-of-squares
501×cbrt-unprod
448×associate-*r*
416×associate-/l*
373×insert-posit16
317×distribute-lft-out--
304×associate-/r*
286×div-inv
266×pow-sqr
264×div-exp
253×flip-+ flip3-+
241×sqrt-div
239×unpow-prod-down
238×pow-plus
221×log-prod
203×swap-sqr
196×cbrt-undiv
184×associate-*l/
180×associate-/r/
179×flip3-- flip--
166×unswap-sqr
156×pow2
150×frac-times
128×sqrt-pow1
119×cube-prod
118×sqr-pow
116×associate-*r/
108×sub-neg
106×diff-log
100×pow1/2 log-pow
98×*-commutative
76×cbrt-prod
74×pow-unpow
70×exp-prod
67×distribute-rgt-neg-in
60×frac-2neg clear-num
55×cbrt-div
54×sum-log associate-/l/
49×pow-flip
41×1-exp difference-of-sqr-1
40×log-div
38×rec-exp
35×tan-quot frac-add
31×distribute-rgt-in distribute-lft-in
29×+-commutative
28×rem-sqrt-square distribute-lft-neg-in
26×pow1/3 inv-pow rem-log-exp
20×associate--l+
17×neg-sub0
16×exp-sum div-sub
14×associate--r+
13×associate-+l+ pow-pow exp-to-pow complex-mul-def
12×cube-mult associate-+l-
11×frac-sub pow-exp neg-log pow-to-exp
10×exp-diff pow-div associate--l-
sqrt-unprod
sum-cubes rem-exp-log
pow3
difference-cubes
sin-sum distribute-rgt-out-- distribute-lft1-in rem-cbrt-cube distribute-rgt-out
exp-neg neg-mul-1 sin-mult rem-square-sqrt un-div-inv
rem-cube-cbrt associate-+r+ *.c-commutative unpow3 +.c-commutative
associate-*l*.c associate-+r- sin-cos-mult sqr-sin tan-sum complex-add-def cos-sum associate--r-
diff-atan cos-mult exp-sqrt cube-unmult distribute-frac-neg sub-div distribute-neg-frac associate-+l+.c cube-div diff-sin diff-cos

regimes5.0s

Accuracy

Total 19.1b remaining (15.7%)

3.8b-20.5%expq3 (problem 3.4.2)
3.5b87.7%quadp (p42, positive)
3.3b88.2%quad2p (problem 3.2.1, positive)
1.3b84.3%2nthrt (problem 3.4.6)
1.2b95.2%quad2m (problem 3.2.1, negative)

localize4.8s

bsearch2.8s

end6.0ms