Details

simplify33.8m

Calls

18458 calls:

Slowest
1.9s
(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)))
1.8s
(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)))
1.2s
(/ (* (* (* (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)))))
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)))))
1.1s
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin x) (sin x)) (sin x))) (* (* (* (* x x) (* x x)) (* x x)) (* (* (+ 1 (cos x)) (+ 1 (cos x))) (+ 1 (cos x)))))

sample5.0m

Algorithm
56×intervals
16×halfpoints
Results
1.1m67025×body1280valid
38.0s17549×body2560valid
27.0s41666×body640valid
13.0s12910×body10240exit
11.3s93927×body80valid
8.9s21014×body320valid
6.7s62901×body80nan
2.8s10717×body160valid
1.9s47530×pre80true
1.0s631×body1280nan
628.0ms467×body5120valid
525.0ms658×body640nan
175.0ms369×body320nan
53.0ms192×body160nan

prune2.8m

series41.6s

Calls

353 calls:

Slowest
945.0ms
(- (fma (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (* (tan x) (tan eps)) (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))))) (tan x))
861.0ms
(/ (expm1 (* eps b)) (/ (cbrt (expm1 (* (+ a b) eps))) (/ (cbrt (expm1 (* eps a))) eps)))
790.0ms
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
748.0ms
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
722.0ms
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))

rewrite8.6s

Algorithm
114×rewrite-expression-head
Calls

353 calls:

Slowest
406.0ms
(pow (+ x 1) (/ 1 n))
229.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
217.0ms
(- (+ (/ -1/2 (* N N)) (/ 1 N)) (/ -1/3 (* (* N N) N)))
168.0ms
(+ (- (/ 1 (+ 1 x)) (/ 2 x)) (+ (fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))) (/ 1 (- x 1))))
142.0ms
(- (/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c))))) (/ b_2 a))
Rules
10917×times-frac
9532×*-un-lft-identity
9176×add-sqr-sqrt
7685×add-cube-cbrt
4266×prod-diff
2157×sqrt-prod
1270×pow1
1071×add-exp-log
1053×cbrt-prod
945×add-cbrt-cube
663×div-inv
595×distribute-lft-out
535×add-log-exp
521×difference-of-squares
472×associate-+l+
438×associate-/r*
435×associate-*l*
433×fma-neg
432×associate-*r*
362×associate-/r/
354×associate-/l*
350×log1p-expm1-u
347×expm1-log1p-u
346×insert-posit16
334×unpow-prod-down
324×distribute-lft-out--
277×pow-prod-down
246×prod-exp
243×swap-sqr
225×cbrt-unprod
216×sqrt-div
213×pow-unpow
199×div-exp
173×distribute-rgt-neg-in
167×pow-prod-up
164×tan-quot
163×flip-+ unswap-sqr flip3-+
150×cbrt-undiv
145×flip3-- flip--
133×distribute-lft-neg-in
120×fma-def
115×pow-sqr
113×associate-*r/
108×log-prod
103×frac-times
98×sqr-pow
87×pow-plus
80×pow1/3
78×associate-*l/
75×*-commutative
68×diff-log
67×sqrt-pow1
64×pow2 pow1/2
63×sub-neg
59×frac-2neg clear-num
44×neg-mul-1
40×cbrt-div associate-/l/
37×log-pow
33×sum-log
30×rem-sqrt-square fma-udef
28×pow-flip div-sub
26×1-exp rec-exp
23×frac-sub
19×+-commutative
15×associate--l+ distribute-rgt-in distribute-lft-in frac-add
14×inv-pow rem-log-exp
13×pow-exp exp-sum pow-to-exp
11×exp-prod
10×difference-of-sqr-1 associate--r+ hypot-def log-div
expm1-udef pow-pow
associate--l-
neg-sub0 neg-log
sqrt-unprod
expm1-log1p
associate-+r+ distribute-neg-frac log1p-def sin-mult
pow3 sub-div associate-+l- rem-square-sqrt
cos-mult sin-sum log1p-udef +.c-commutative sqr-sin un-div-inv tan-sum cos-sum rem-cbrt-cube expm1-def e-exp-1
remove-posit16 exp-diff diff-atan log1p-expm1 log-rec distribute-lft-neg-out frac-2neg-c hypot-udef distribute-rgt-out-- diff-sin diff-cos

localize4.3s

regimes4.2s

Accuracy

Total 25.2b remaining (18.7%)

4.7b83.5%quad2p (problem 3.2.1, positive)
4.6b83.4%quadp (p42, positive)
4.5b84.1%quadm (p42, negative)
3.3b0%expq3 (problem 3.4.2)
2.2b75.8%2tan (problem 3.3.2)

bsearch2.4s

end1.0ms