Details

simplify14.6m

Calls

10259 calls:

Slowest
2.1s
(/ (* (* (- (* 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))))
1.6s
(/ (* (* (* 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)))))))
1.6s
(/ (* (* (* (* x x) x) (* (* x x) x)) (* (* (+ 1 (cos x)) (+ 1 (cos x))) (+ 1 (cos x)))) (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin x) (sin x)) (sin x))))
1.5s
(/ (* (* (- (* 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))))
1.3s
(/ (* (* (* (* x x) (+ 1 (cos x))) (* (* x x) (+ 1 (cos x)))) (* (* x x) (+ 1 (cos x)))) (* (* (* (sin x) (sin x)) (* (sin x) (sin x))) (* (sin x) (sin x))))

sample5.1m

Algorithm
56×intervals
16×halfpoints
Results
1.1m66856×body1280valid
39.7s17100×body2560valid
26.5s42520×body640valid
14.2s12688×body10240exit
11.2s94008×body80valid
10.7s20621×body320valid
7.6s62872×body80nan
2.7s47422×pre80true
2.4s10494×body160valid
968.0ms429×body5120valid
766.0ms647×body1280nan
577.0ms709×body640nan
168.0ms361×body320nan
47.0ms176×body160nan

prune2.3m

series35.4s

Calls

384 calls:

Slowest
1.1s
(/ (* 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)))
523.0ms
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))))) (/ (sin x) (cos x)))
521.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
454.0ms
(log (+ 1 (* x (* x x))))
428.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite19.1s

Algorithm
118×rewrite-expression-head
Calls

384 calls:

Slowest
2.1s
(- (- 1 (+ (/ 1/6 (* n n)) (- (/ -1/2 n) (log n)))) 1)
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)))
751.0ms
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))))) (/ (sin x) (cos x)))
626.0ms
(/ (cbrt (- (* (* (* x x) 9/40) (* (* x x) 9/40)) (* (+ (* (* (* x x) (* x x)) 27/2800) 1/2) (+ (* (* (* x x) (* x x)) 27/2800) 1/2)))) (cbrt (+ (* (* x x) 9/40) (+ (* (* (* x x) (* x x)) 27/2800) 1/2))))
447.0ms
(* (* (* (* x x) (* x x)) (* x x)) 1/360)
Rules
4230×*-un-lft-identity
4082×times-frac
3970×add-sqr-sqrt
2746×add-cube-cbrt
1720×pow1
1628×add-exp-log
1614×sqrt-prod
1443×add-cbrt-cube
671×add-log-exp
600×pow-prod-down
599×prod-exp
580×associate-*l*
551×cbrt-unprod
506×distribute-lft-out
430×cbrt-prod
425×pow-unpow
393×associate-*r*
372×insert-posit16
371×difference-of-squares
319×associate-/l*
314×associate-/r*
289×div-inv
272×distribute-lft-out--
248×div-exp
188×flip-+
187×flip3-+
179×cbrt-undiv
178×pow-prod-up
176×unswap-sqr
165×unpow-prod-down
162×swap-sqr
149×log-prod
147×flip--
146×flip3--
144×associate-/r/
122×sqrt-div pow-sqr
110×cbrt-div
102×sqrt-pow1
99×diff-log
90×*-commutative
88×associate-*r/
84×sub-neg
76×pow-plus
75×associate-*l/
74×pow1/2
67×cube-prod
66×sum-log frac-2neg clear-num
65×pow1/3 exp-prod
61×associate-/l/
59×sqr-pow
57×pow2
52×log-pow
51×frac-times
39×pow-flip
35×1-exp rec-exp
34×+-commutative
32×frac-sub
31×log-div
30×distribute-rgt-neg-in
27×distribute-rgt-in distribute-lft-in
26×frac-add
25×associate--l+ pow-pow
22×rem-sqrt-square
19×pow-exp pow-to-exp
18×rem-log-exp
17×associate--r+ inv-pow
16×tan-quot div-sub
15×difference-of-sqr-1 sin-mult
13×complex-mul-def
12×cube-mult
10×associate--l- pow-div
associate-+l+
neg-sub0 distribute-rgt-out
exp-sum neg-log sqrt-unprod
cos-mult associate-+r+ distribute-lft1-in
distribute-rgt-out-- rem-cube-cbrt unpow3 sum-cubes associate-+l- rem-square-sqrt
associate-+r- *.c-commutative sub-div +.c-commutative sqr-sin associate--r-
sin-sum distribute-frac-neg neg-mul-1 tan-sum frac-2neg-c rem-exp-log cos-sum associate-*l*.c distribute-lft-neg-in complex-add-def
exp-diff diff-atan cube-unmult sub0-neg pow3 difference-cubes exp-to-pow associate-+l+.c diff-sin rem-cbrt-cube diff-cos distribute-rgt1-in

localize4.9s

regimes4.6s

Accuracy

Total 17.7b remaining (14.6%)

4.5b83.6%quad2m (problem 3.2.1, negative)
3.2b0%expq3 (problem 3.4.2)
1.4b94%quadp (p42, positive)
1.3b94.4%quadm (p42, negative)
1.2b86.1%2nthrt (problem 3.4.6)

bsearch2.4s

end1.0ms