Details

simplify15.9m

Calls

11598 calls:

Slowest
2.3s
(/ (* (* (- (* a c)) (- (* a c))) (- (* a c))) (* (* (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))) (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))))
1.9s
(/ (* (* (* (/ (sin eps) (cos eps)) (+ (/ (sin x) (/ (cos x) (sin x))) (cos x))) (* (/ (sin eps) (cos eps)) (+ (/ (sin x) (/ (cos x) (sin x))) (cos x)))) (* (/ (sin eps) (cos eps)) (+ (/ (sin x) (/ (cos x) (sin x))) (cos x)))) (* (* (* (- 1 (* (tan x) (tan eps))) (- 1 (* (tan x) (tan eps)))) (- 1 (* (tan x) (tan eps)))) (* (* (cos x) (cos x)) (cos x))))
1.6s
(/ (* (* (- (* a c)) (- (* a c))) (- (* a c))) (* (* (* a a) a) (* (* (+ (sqrt (- (* b_2 b_2) (* a c))) b_2) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))))
1.6s
(/ (* (* (* a a) a) (* (* c c) c)) (* (* (* a (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (* a (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) (* a (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))))
1.5s
(/ (* (* (* a c) (* a c)) (* a c)) (* (* (* a (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (* a (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) (* a (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))))

sample5.1m

Algorithm
56×intervals
16×halfpoints
Results
1.2m66475×body1280valid
42.8s17763×body2560valid
28.9s41579×body640valid
13.9s12253×body10240exit
11.6s94162×body80valid
8.7s20902×body320valid
7.5s64708×body80nan
2.7s10452×body160valid
2.0s47299×pre80true
924.0ms728×body1280nan
686.0ms489×body5120valid
597.0ms630×body640nan
173.0ms358×body320nan
91.0ms195×body160nan

prune2.4m

series41.8s

Calls

404 calls:

Slowest
2.1s
(/ (* 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)))))))))
1.0s
(/ (* 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)))
791.0ms
(/ (* (/ (sin eps) (cos eps)) (+ (/ (sin x) (/ (cos x) (sin x))) (cos x))) (* (- 1 (* (tan x) (tan eps))) (cos x)))
667.0ms
(- (* (* (cbrt (pow (+ x 1) (/ 1 n))) (cbrt (pow (+ x 1) (/ 1 n)))) (cbrt (* (pow (sqrt (+ x 1)) (/ 1 n)) (pow (sqrt (+ x 1)) (/ 1 n))))) (pow x (/ 1 n)))
512.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite18.7s

Algorithm
120×rewrite-expression-head
Calls

404 calls:

Slowest
1.8s
(/ (+ (pow (+ (* a x) (* x (* (* a 1/6) (* (* a x) (* a x))))) 3) (pow (* (* 1/2 (* a x)) (* a x)) 3)) (+ (* (+ (* a x) (* x (* (* a 1/6) (* (* a x) (* a x))))) (+ (* a x) (* x (* (* a 1/6) (* (* a x) (* a x)))))) (- (* (* (* 1/2 (* a x)) (* a x)) (* (* 1/2 (* a x)) (* a x))) (* (+ (* a x) (* x (* (* a 1/6) (* (* a x) (* a x))))) (* (* 1/2 (* a x)) (* a x))))))
1.1s
(- (+ (/ 1/2 n) (+ 1 (+ (log n) (/ -1/6 (* n n))))) 1)
888.0ms
(/ (* 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)))
651.0ms
(* (- (exp (* a eps)) 1) (+ (* eps b) (+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* eps (* b (* (* eps b) (* eps b))))))))
405.0ms
(/ 1 (sqrt (sqrt 2)))
Rules
4992×*-un-lft-identity
4591×add-sqr-sqrt
4451×times-frac
2847×add-cube-cbrt
2667×pow1
2272×sqrt-prod
1798×add-exp-log
1593×add-cbrt-cube
829×pow-prod-down
705×prod-exp
703×difference-of-squares
675×add-log-exp
636×cbrt-unprod
571×distribute-lft-out--
557×log-prod
549×associate-*l*
512×cbrt-prod
498×associate-*r*
493×distribute-lft-out
471×pow-prod-up
392×insert-posit16
367×associate-/r*
303×flip3-- flip--
295×associate-/l*
266×associate-*l/
265×flip-+ flip3-+
248×div-exp
234×pow-sqr
209×div-inv
207×associate-/r/
203×pow-plus
192×frac-times
190×swap-sqr
188×log-pow
185×unswap-sqr
180×cbrt-undiv
168×sqrt-div
164×associate-*r/
148×cbrt-div
136×pow-unpow
131×pow2
111×sub-neg
108×*-commutative diff-log
93×associate-/l/
91×frac-add
89×unpow-prod-down
78×sqrt-pow1
72×frac-sub associate--l+ log-div
68×frac-2neg clear-num exp-prod
65×pow1/2
56×sum-log
49×pow1/3
44×1-exp rec-exp
43×pow-flip associate--r+
41×distribute-rgt-in distribute-lft-in
40×difference-of-sqr-1
34×+-commutative
32×tan-quot
26×rem-sqrt-square
25×sqr-pow
21×rem-log-exp div-sub
20×exp-sum
19×cube-prod associate--r-
18×inv-pow
17×pow-pow
15×pow-exp pow-to-exp
13×complex-mul-def
12×distribute-rgt-neg-in
11×associate--l-
10×pow-div
associate-+l+ sin-mult sum-cubes
distribute-rgt-out--
neg-sub0 cos-mult sin-sum distribute-lft1-in sqrt-unprod cube-mult distribute-rgt-out
pow3 neg-log sub-div
exp-diff associate-+r+ *.c-commutative un-div-inv +.c-commutative rem-exp-log associate-+l- cos-sum rem-cbrt-cube
associate-*l*.c sin-cos-mult sub0-neg distribute-frac-neg neg-mul-1 sqr-sin frac-2neg-c complex-add-def rem-square-sqrt tan-sum e-exp-1 distribute-lft-neg-in
remove-posit16 diff-atan rem-cube-cbrt unpow3 sqrt-pow2 exp-to-pow exp-neg diff-sin associate-+l+.c unpow1/3 diff-cos

localize4.8s

regimes4.8s

Accuracy

Total 15.8b remaining (14.9%)

3.3b0%expq3 (problem 3.4.2)
2.0b76.9%2nthrt (problem 3.4.6)
1.5b93.5%quad2p (problem 3.2.1, positive)
1.3b94.3%quadp (p42, positive)
1.2b95%quadm (p42, negative)

bsearch1.7s

end1.0ms