Details

simplify8.0m

Calls

4594 calls:

Slowest
3.5s
(/ (* (* (* (* a c) 4) (* (* a c) 4)) (* (* a c) 4)) (* (* (* (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))) (* (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c))))))) (* (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c))))))))
2.8s
(/ (* (* (* (* a c) 4) (* (* a c) 4)) (* (* a c) 4)) (* (* (* (* 2 a) (* 2 a)) (* 2 a)) (* (* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))) (- (- b) (sqrt (- (* b b) (* 4 (* a c))))))))
1.5s
(* (* (* (* (/ (* (cbrt (exp x)) (cbrt (exp x))) (+ (exp (+ (+ x x) x)) -1)) (+ (* (exp (+ (+ x x) x)) (exp (+ (+ x x) x))) (* (+ (exp x) 1) (* (+ (exp x) 1) (+ (exp x) 1))))) (* (/ (* (cbrt (exp x)) (cbrt (exp x))) (+ (exp (+ (+ x x) x)) -1)) (+ (* (exp (+ (+ x x) x)) (exp (+ (+ x x) x))) (* (+ (exp x) 1) (* (+ (exp x) 1) (+ (exp x) 1)))))) (* (/ (* (cbrt (exp x)) (cbrt (exp x))) (+ (exp (+ (+ x x) x)) -1)) (+ (* (exp (+ (+ x x) x)) (exp (+ (+ x x) x))) (* (+ (exp x) 1) (* (+ (exp x) 1) (+ (exp x) 1)))))) (/ (exp x) (* (* (- (* (+ 1 (exp x)) (+ 1 (exp x))) (+ (* (* (exp x) (exp x)) (- (exp x) (* (exp x) (exp x)))) (* (exp x) (exp x)))) (- (* (+ 1 (exp x)) (+ 1 (exp x))) (+ (* (* (exp x) (exp x)) (- (exp x) (* (exp x) (exp x)))) (* (exp x) (exp x))))) (- (* (+ 1 (exp x)) (+ 1 (exp x))) (+ (* (* (exp x) (exp x)) (- (exp x) (* (exp x) (exp x)))) (* (exp x) (exp 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)))
1.4s
(/ (* (* (+ (pow (/ (cos y) (exp x)) 3) (pow (* (cos y) (exp x)) 3)) (+ (pow (/ (cos y) (exp x)) 3) (pow (* (cos y) (exp x)) 3))) (+ (pow (/ (cos y) (exp x)) 3) (pow (* (cos y) (exp x)) 3))) (* (* (+ (* (/ (cos y) (exp x)) (/ (cos y) (exp x))) (- (* (* (cos y) (exp x)) (* (cos y) (exp x))) (* (/ (cos y) (exp x)) (* (cos y) (exp x))))) (+ (* (/ (cos y) (exp x)) (/ (cos y) (exp x))) (- (* (* (cos y) (exp x)) (* (cos y) (exp x))) (* (/ (cos y) (exp x)) (* (cos y) (exp x)))))) (+ (* (/ (cos y) (exp x)) (/ (cos y) (exp x))) (- (* (* (cos y) (exp x)) (* (cos y) (exp x))) (* (/ (cos y) (exp x)) (* (cos y) (exp x)))))))

sample5.0m

Algorithm
56×intervals
16×halfpoints
Results
1.1m66899×body1280valid
40.1s17018×body2560valid
25.3s42195×body640valid
12.8s12774×body10240exit
11.6s93914×body80valid
8.9s20421×body320valid
8.0s63024×body80nan
3.1s11084×body160valid
2.4s47503×pre80true
666.0ms616×body1280nan
572.0ms474×body5120valid
509.0ms610×body640nan
177.0ms299×body320nan
55.0ms190×body160nan

prune1.4m

series25.2s

Calls

389 calls:

Slowest
1.2s
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (/ (* (tan x) (sin eps)) (cos eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
812.0ms
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
441.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
338.0ms
(cbrt x)
331.0ms
(cbrt (- x))

rewrite7.2s

Algorithm
117×rewrite-expression-head
Calls

389 calls:

Slowest
2.3s
(- (* (* (* (* (cbrt (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (cbrt (sqrt (cbrt (+ x 1))))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1)))) (* (* (* (cbrt (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (cbrt (sqrt (cbrt (+ x 1))))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1))))) (* (sqrt x) (sqrt x)))
606.0ms
(* (+ (sqrt (- (* (* x x) -1/2) x)) 1) (* (* (cbrt (- (sqrt (- (* (* x x) -1/2) x)) 1)) (cbrt (- (sqrt (- (* (* x x) -1/2) x)) 1))) (cbrt (- (sqrt (- (* (* x x) -1/2) x)) 1))))
387.0ms
(* (* (/ (* (cbrt (exp x)) (cbrt (exp x))) (+ (exp (+ (+ x x) x)) -1)) (+ (* (exp (+ (+ x x) x)) (exp (+ (+ x x) x))) (* (+ (exp x) 1) (* (+ (exp x) 1) (+ (exp x) 1))))) (/ (cbrt (exp x)) (- (* (+ 1 (exp x)) (+ 1 (exp x))) (+ (* (* (exp x) (exp x)) (- (exp x) (* (exp x) (exp x)))) (* (exp x) (exp x))))))
161.0ms
(- (* (* (* (cbrt (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (cbrt (sqrt (cbrt (+ x 1))))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1)))) (sqrt x))
145.0ms
(/ (+ (pow (/ (cos y) (exp x)) 3) (pow (* (cos y) (exp x)) 3)) (+ (* (/ (cos y) (exp x)) (/ (cos y) (exp x))) (- (* (* (cos y) (exp x)) (* (cos y) (exp x))) (* (/ (cos y) (exp x)) (* (cos y) (exp x))))))
Rules
1235×add-sqr-sqrt
1166×*-un-lft-identity
941×add-cube-cbrt
689×add-exp-log
645×add-cbrt-cube
640×pow1
632×times-frac
551×add-log-exp
378×insert-posit16
317×flip3-- flip--
264×frac-times
236×associate-/l*
230×cbrt-div flip-+ associate-*r* flip3-+
214×associate-*r/
208×associate-/r/
185×div-inv
182×sqrt-prod
170×associate-/r* cbrt-prod
164×associate-*l/
161×associate-*l*
135×difference-of-squares
126×sqrt-div
112×prod-exp sub-neg
106×cbrt-unprod
100×frac-sub
96×distribute-lft-out--
94×log-prod
91×pow-prod-down
87×*-commutative
80×tan-quot
77×associate-/l/
75×frac-2neg clear-num
64×div-exp
62×distribute-lft-out
61×diff-log
58×cbrt-undiv
57×unpow-prod-down
53×cube-prod pow1/3
44×associate--l+
41×pow1/2
38×distribute-rgt-in distribute-lft-in
33×pow-prod-up
32×+-commutative
30×sum-log
29×difference-of-sqr-1
27×pow-plus
25×log-pow
24×div-sub
23×rem-sqrt-square
22×frac-add
21×cube-mult
20×pow2
19×log-div
18×pow-flip neg-sub0 rec-exp
17×difference-cubes
15×associate--r+
14×associate--l- rem-log-exp
13×complex-mul-def
12×inv-pow
pow-unpow
pow-exp associate-+l-
associate-+l+ rem-cube-cbrt associate-+r+ distribute-rgt-out-- pow-pow pow-to-exp
sqrt-unprod associate--r- distribute-lft-neg-in
unpow3 neg-mul-1 sum-cubes
*.c-commutative pow3 sin-mult distribute-rgt-neg-in +.c-commutative distribute-rgt-out
exp-diff sin-sum associate-+r- exp-neg complex-add-def sqr-sin rem-square-sqrt cos-sum tan-sum associate-*l*.c un-div-inv
diff-atan distribute-lft1-in distribute-frac-neg neg-log sub-div difference-of-sqr--1 frac-2neg-c distribute-neg-frac rem-exp-log diff-sin associate-+l+.c cube-div rem-cbrt-cube diff-cos unsub-neg exp-prod

regimes4.4s

Accuracy

Total 21.1b remaining (17.2%)

4.4b83.2%quad2p (problem 3.2.1, positive)
3.7b86.8%quadm (p42, negative)
3.6b61.7%expq3 (problem 3.4.2)
1.5b84.2%2nthrt (problem 3.4.6)
1.1b95.3%quadp (p42, positive)

localize3.4s

bsearch3.2s

end4.0ms