Details

simplify24.7m

Calls

14769 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))))
1.8s
(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)))
1.6s
(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)))
1.6s
(/ (* (* (* 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
(/ (* (* 1 1) 1) (/ (* (* (* (* 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)))))

sample5.2m

Algorithm
56×intervals
16×halfpoints
Results
1.2m66856×body1280valid
40.1s17100×body2560valid
28.1s42520×body640valid
16.5s12688×body10240exit
13.2s94008×body80valid
9.0s20621×body320valid
7.1s62872×body80nan
2.8s47422×pre80true
2.7s10494×body160valid
1.2s647×body1280nan
653.0ms709×body640nan
542.0ms429×body5120valid
211.0ms361×body320nan
89.0ms176×body160nan

prune2.5m

series39.7s

Calls

357 calls:

Slowest
1.7s
(- (fma (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (fma (/ (sin x) (cos x)) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (+ (fma (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (* (cos eps) (cos eps)) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin eps) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin x) (cos x)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))))) (/ (sin x) (cos x)))
1.2s
(fma (/ (+ (tan x) (tan eps)) (- 1 (* (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* (tan eps) (tan x))))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x)))
788.0ms
(fma (- (/ (sqrt 2) (cbrt x))) (/ (sqrt 2) (* (cbrt x) (cbrt x))) (* (/ (sqrt 2) (cbrt x)) (/ (sqrt 2) (* (cbrt x) (cbrt x)))))
675.0ms
(fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x)))))
653.0ms
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))

rewrite8.4s

Algorithm
114×rewrite-expression-head
Calls

357 calls:

Slowest
208.0ms
(cbrt (* (* (* (expm1 (* a x)) (* (cbrt (expm1 (* a x))) (cbrt (expm1 (* a x))))) (cbrt (expm1 (* a x)))) (expm1 (* a x))))
203.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
202.0ms
(log (* (cbrt (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))) (cbrt (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))))
155.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (+ (fma (- (/ (sqrt 2) (cbrt x))) (/ (sqrt 2) (* (cbrt x) (cbrt x))) (* (/ (sqrt 2) (cbrt x)) (/ (sqrt 2) (* (cbrt x) (cbrt x))))) (/ 1 (- x 1))))
152.0ms
(* (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))) (sin (/ eps 2)))
Rules
7329×*-un-lft-identity
6818×add-sqr-sqrt
6738×times-frac
5412×add-cube-cbrt
3340×prod-diff
1835×sqrt-prod
1778×pow1
1239×add-exp-log
1040×add-cbrt-cube
708×associate-+l+
589×distribute-lft-out
537×add-log-exp
496×div-inv
465×difference-of-squares
443×associate-*l*
387×associate-*r*
378×distribute-lft-out--
368×pow-prod-down
354×log1p-expm1-u
349×expm1-log1p-u insert-posit16
348×prod-exp
344×pow-prod-up
309×fma-neg
291×cbrt-prod
287×associate-/l*
282×cbrt-unprod
273×associate-/r*
272×associate-/r/
233×div-exp
231×unpow-prod-down
220×pow-unpow pow-sqr
218×swap-sqr distribute-rgt-neg-in
181×flip-+ flip3-+
176×pow-plus
159×cbrt-undiv
148×unswap-sqr
146×sqrt-div
138×log-prod
131×distribute-lft-neg-in
130×pow2
125×fma-def
99×sqrt-pow1
95×tan-quot
93×flip3-- flip--
83×associate-*r/
77×*-commutative
75×sqr-pow
72×pow1/2
71×pow1/3
65×frac-times diff-log
62×exp-sum
59×sub-neg
57×associate-*l/
55×frac-2neg clear-num
45×neg-mul-1 log-pow fma-udef
44×1-exp
43×rec-exp
36×sum-log rem-sqrt-square
35×associate-/l/
29×pow-flip
23×exp-prod
20×+-commutative div-sub
18×inv-pow frac-add
17×frac-sub sin-mult
15×distribute-rgt-in distribute-lft-in
14×associate--l+ log-div
13×cbrt-div
12×rem-log-exp
10×pow-exp pow-pow pow-to-exp hypot-def
neg-sub0 associate--l-
neg-log
expm1-log1p expm1-udef sqrt-unprod sqr-sin
exp-diff cos-mult difference-of-sqr-1 associate--r+
associate-+r+ pow3 associate-+l-
sub-div rem-square-sqrt cos-sum rem-cbrt-cube
sin-sum log1p-def +.c-commutative frac-2neg-c tan-sum log1p-udef
diff-atan log1p-expm1 distribute-frac-neg un-div-inv exp-to-pow hypot-udef distribute-rgt-out-- rem-exp-log diff-sin diff-cos expm1-def

localize4.6s

regimes3.6s

Accuracy

Total 23.9b remaining (21.5%)

4.7b82.9%quadm (p42, negative)
4.5b83.5%quad2m (problem 3.2.1, negative)
4.3b84.8%quadp (p42, positive)
3.7b-11.7%expq3 (problem 3.4.2)
1.4b88.4%2nthrt (problem 3.4.6)

bsearch2.3s

end1.0ms