Details

simplify17.0m

Calls

11571 calls:

Slowest
1.7s
(/ (* (* (- 0 (* a c)) (- 0 (* a c))) (- 0 (* a c))) (* (* a a) a))
1.4s
(/ (* (* (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1)) (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))) (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))) (* (* (* (* (+ x 1) (+ x 1)) (+ x 1)) (* (* x x) x)) (* (* (- x 1) (- x 1)) (- x 1))))
1.4s
(im (+.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
(* (* (/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (cos eps) (cos eps)) (cos eps)))) (* (* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))))
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)))

sample5.1m

Algorithm
56×intervals
16×halfpoints
Results
1.1m66345×body1280valid
41.9s18017×body2560valid
27.5s42393×body640valid
13.9s12720×body10240exit
10.7s20654×body320valid
10.5s93427×body80valid
6.3s63700×body80nan
3.0s10654×body160valid
2.1s47219×pre80true
803.0ms699×body1280nan
623.0ms445×body5120valid
476.0ms625×body640nan
165.0ms347×body320nan
75.0ms176×body160nan

prune2.2m

series39.3s

Calls

387 calls:

Slowest
1.8s
(/ (* 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)))))))))
1.1s
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
823.0ms
(- (pow (exp (* (cbrt x) (cbrt x))) (* (cbrt x) 3)) (pow 1 3))
495.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
466.0ms
(sqrt (- (* b_2 b_2) (* a c)))

rewrite15.4s

Algorithm
119×rewrite-expression-head
Calls

387 calls:

Slowest
1.9s
(- (- 1 (+ (/ 1/6 (* n n)) (- (/ -1/2 n) (log n)))) 1)
357.0ms
(* (* (* (* x x) (* x x)) (* x x)) 1/360)
307.0ms
(* (sqrt (- (- (exp x) 2) (/ -1 (exp x)))) (sqrt (- (- (exp x) 2) (/ -1 (exp x)))))
305.0ms
(/ (sqrt (+ (exp (+ x (+ x x))) 1)) (sqrt (+ (* (exp x) (exp x)) (- (* 1 1) (* (exp x) 1)))))
293.0ms
(/ 1 (* (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt (+ x 1))))))
Rules
4865×*-un-lft-identity
4111×add-sqr-sqrt
3997×times-frac
2729×add-cube-cbrt
2077×pow1
1948×add-exp-log
1884×sqrt-prod
1737×add-cbrt-cube
808×distribute-lft-out
764×prod-exp
720×pow-prod-down
681×cbrt-unprod
674×add-log-exp
558×associate-*l*
517×difference-of-squares
502×associate-*r*
375×insert-posit16
358×associate-/l*
331×div-exp
330×log-prod
326×associate-/r*
319×cbrt-prod
305×distribute-lft-out--
303×div-inv
298×swap-sqr
274×sqrt-div
262×cbrt-undiv
259×pow-prod-up
251×frac-times flip-+ flip3-+
229×associate-*l/
223×unpow-prod-down
219×associate-*r/
203×flip3-- flip--
182×unswap-sqr
181×pow-sqr
173×associate-/r/
133×exp-prod
128×sqr-pow
113×sqrt-pow1 pow-plus
110×cube-prod
106×pow-unpow diff-log
105×*-commutative
99×sub-neg
90×associate-/l/
89×pow1/2
85×cbrt-div
80×pow2
76×frac-sub frac-add
70×frac-2neg clear-num log-pow
63×distribute-rgt-neg-in
59×tan-quot
58×pow-flip
57×pow1/3
55×sum-log
43×distribute-lft-neg-in
42×1-exp rec-exp
32×distribute-rgt-in distribute-lft-in
31×pow-pow
28×pow-exp difference-of-sqr-1 +-commutative
27×associate--l+
25×rem-log-exp
24×rem-sqrt-square
22×inv-pow
20×un-div-inv
19×pow-to-exp div-sub
16×log-div
15×distribute-rgt-out
14×associate--l- distribute-lft1-in associate--r+
13×complex-mul-def
11×associate-+l+
10×neg-sub0 cube-mult
neg-mul-1
rem-cube-cbrt
neg-log rem-exp-log
pow-div sqrt-unprod difference-cubes rem-square-sqrt e-exp-1
sin-sum
associate-+r+ unpow3 sin-mult associate-+l- distribute-rgt1-in
distribute-rgt-out-- exp-sum *.c-commutative distribute-frac-neg +.c-commutative
associate-+r- sin-cos-mult sub-div sqr-sin tan-sum frac-2neg-c exp-to-pow cos-sum cube-div associate-*l*.c associate--r- complex-add-def
quot-tan exp-diff diff-atan sqrt-undiv sub0-neg pow3 distribute-neg-frac diff-sin associate-+l+.c diff-cos

localize4.8s

regimes4.5s

Accuracy

Total 19.4b remaining (18%)

4.3b84.7%quadp (p42, positive)
3.2b0%expq3 (problem 3.4.2)
1.7b93.1%quad2p (problem 3.2.1, positive)
1.6b93.2%quadm (p42, negative)
1.6b93.3%quad2m (problem 3.2.1, negative)

bsearch1.7s

end1.0ms