Details

simplify15.5m

Calls

11666 calls:

Slowest
1.5s
(* (- (/ (/ 1 n) x) 0) (* n x))
1.3s
(/ (* (* (- 0 (* a c)) (- 0 (* a c))) (- 0 (* a c))) (* (* a a) a))
1.3s
(* (* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x))) (* (* (* x x) (* x x)) (* x x)))
1.3s
(/ (* (* (* (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)))))
1.2s
(/ (* (* (* (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)))))

sample5.0m

Algorithm
55×intervals
16×halfpoints
Results
1.1m65121×body1280valid
41.0s17222×body2560valid
28.5s41197×body640valid
13.8s12436×body10240exit
10.9s90116×body80valid
9.3s19576×body320valid
7.0s55295×body80nan
3.2s10321×body160valid
2.0s47310×pre80true
816.0ms645×body1280nan
596.0ms659×body640nan
507.0ms385×body5120valid
181.0ms355×body320nan
65.0ms212×body160nan

prune2.1m

series37.4s

Calls

392 calls:

Slowest
2.0s
(/ (* 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)))))))))
1.2s
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
797.0ms
(* (cbrt (/ 1/2 (sqrt 2))) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))
501.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
478.0ms
(- (* b_2 b_2) (* a c))

rewrite17.0s

Algorithm
119×rewrite-expression-head
Calls

392 calls:

Slowest
2.0s
(- (- 1 (+ (/ 1/6 (* n n)) (- (/ -1/2 n) (log n)))) 1)
775.0ms
(- (* (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))) (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))))) (* (sqrt x) (sqrt x)))
661.0ms
(* (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))) (* (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))))
397.0ms
(- (* b b) (* 4 (* c a)))
254.0ms
(* x (* (* a 1/6) (* (* a x) (* a x))))
Rules
40904×sqrt-div
35043×cbrt-div
28587×frac-times
17722×flip-+ flip3-+
7393×associate-*l/
7380×associate-*r/
5568×*-un-lft-identity
4947×times-frac
4313×add-sqr-sqrt
3148×pow1
2950×add-cube-cbrt
1733×add-exp-log
1522×add-cbrt-cube
1445×sqrt-prod
1083×distribute-lft-out
1076×pow-prod-down
737×pow-prod-up
697×add-log-exp
633×sqrt-pow1
607×prod-exp
546×cbrt-unprod
518×associate-*l*
466×difference-of-squares
433×associate-*r*
412×associate-/r*
381×div-inv
380×insert-posit16
379×log-prod
364×pow-sqr
342×pow-plus
323×div-exp
319×distribute-lft-out--
308×associate-/l*
276×cbrt-prod
249×swap-sqr
235×cbrt-undiv
221×flip3-- flip--
210×associate-/r/
191×unswap-sqr
185×pow2
143×pow1/3
137×associate-+r+
135×unpow-prod-down
112×exp-prod
105×diff-log
104×frac-sub
99×pow1/2
98×*-commutative
95×log-pow
93×sub-neg
89×pow-flip
88×pow-unpow
70×frac-2neg clear-num
67×associate-/l/
63×sum-log frac-add
60×distribute-lft1-in distribute-rgt-out
59×tan-quot sqr-pow
57×1-exp
53×rec-exp
51×associate-+l+
45×cube-prod
38×inv-pow log-div
37×+-commutative
31×distribute-rgt-in distribute-lft-in
30×distribute-rgt-neg-in
28×difference-of-sqr-1
26×exp-sum
23×rem-sqrt-square
22×associate--l+
21×un-div-inv
20×rem-log-exp
19×div-sub
15×unpow-prod-up
14×pow-exp
13×associate--l- associate--r+ pow-pow complex-mul-def pow-to-exp
distribute-rgt-out-- rem-exp-log
neg-sub0 neg-log
sqrt-unprod
exp-diff associate-+r-
sin-sum log-rec exp-to-pow
sin-mult associate-+l-
*.c-commutative +.c-commutative rem-square-sqrt
rem-cube-cbrt pow-div pow3 unpow3 sub-div sqr-sin tan-sum frac-2neg-c sub0-neg complex-add-def cos-sum associate-*l*.c cube-mult pow-sub
distribute-lft-neg-out diff-atan cos-mult sin-cos-mult cube-unmult distribute-neg-out distribute-frac-neg difference-cubes associate-+l+.c diff-sin rem-cbrt-cube diff-cos unsub-neg associate--r- e-exp-1

localize5.0s

regimes4.2s

Accuracy

Total 19.4b remaining (18%)

4.1b85.1%quad2m (problem 3.2.1, negative)
3.4b0%expq3 (problem 3.4.2)
3.3b88.2%quadm (p42, negative)
1.8b80.9%2nthrt (problem 3.4.6)
1.1b95.4%quad2p (problem 3.2.1, positive)

bsearch2.2s

end1.0ms