Details

simplify6.3m

Calls

5535 calls:

Slowest
2.1s
(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)))
1.7s
(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)))
1.3s
(/ (* (* (* (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)))))
1.3s
(- (+ (/ (log (/ -1 x)) (* x (pow (- (log -1) (log (/ -1 x))) 2))) (/ 1 (* (pow x 2) (pow (- (log -1) (log (/ -1 x))) 2)))) (+ (/ (log (/ -1 x)) (- (log -1) (log (/ -1 x)))) (+ (/ (log (/ -1 x)) (* (pow x 2) (pow (- (log -1) (log (/ -1 x))) 3))) (+ (/ 1 (* x (- (log -1) (log (/ -1 x))))) (+ (* 1/2 (/ (log (/ -1 x)) (* (pow x 2) (pow (- (log -1) (log (/ -1 x))) 2)))) (* 1/2 (/ 1 (* (pow x 2) (- (log -1) (log (/ -1 x)))))))))))
1.0s
(fma (* (cbrt (+ (- (* x x) x) 2)) (cbrt (+ (- (* x x) x) 2))) (cbrt (+ (- (* x x) x) 2)) (- (* (- (* x x) x) 1)))

sample4.9m

Algorithm
56×intervals
16×halfpoints
Results
1.1m66524×body1280valid
39.0s17470×body2560valid
25.4s41703×body640valid
14.4s12861×body10240exit
10.9s94134×body80valid
8.2s63128×body80nan
8.0s21001×body320valid
3.9s10907×body160valid
2.7s47441×pre80true
796.0ms698×body1280nan
564.0ms456×body5120valid
481.0ms645×body640nan
181.0ms369×body320nan
57.0ms212×body160nan

prune1.5m

series25.0s

Calls

347 calls:

Slowest
877.0ms
(cbrt (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
776.0ms
(- (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))
428.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
421.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (tan x))
411.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* eps b)) (expm1 (* eps a))))

regimes3.6s

Accuracy

Total 24.7b remaining (18.4%)

4.7b82.9%quadm (p42, negative)
4.5b83.8%quadp (p42, positive)
4.0b71.4%2nthrt (problem 3.4.6)
3.1b0%expq3 (problem 3.4.2)
2.3b76.6%2tan (problem 3.3.2)

rewrite3.6s

Algorithm
113×rewrite-expression-head
Calls

347 calls:

Slowest
202.0ms
(/ (- (+ (- (* x x) x) 2) (- (* x x) x)) (* (fma x x x) (- x 1)))
126.0ms
(- (+ (- (* x x) x) 2) (- (* x x) x))
70.0ms
(* (* (cbrt (sqrt (fma 1/3 (* x x) 2))) (cbrt (sqrt (fma 1/3 (* x x) 2)))) (* (cbrt (sqrt (fma 1/3 (* x x) 2))) (* (sqrt (fma 1/3 (* x x) 2)) x)))
69.0ms
(- (cbrt (+ x 1)) (cbrt (* (* (cbrt x) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))) (cbrt x))))
67.0ms
(cbrt (* (* (cbrt x) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))) (cbrt x)))
Rules
1602×*-un-lft-identity
1567×add-sqr-sqrt
1380×add-cube-cbrt
751×pow1
748×prod-diff
647×add-exp-log
610×add-cbrt-cube
447×add-log-exp
437×times-frac
426×sqrt-prod
342×log1p-expm1-u
341×expm1-log1p-u
340×insert-posit16
284×associate-*l*
243×fma-neg
235×div-inv
207×associate-*r*
176×cbrt-prod
160×pow-prod-down
159×tan-quot
150×associate-/r*
147×associate-/r/
146×log-prod
131×associate-/l* unpow-prod-down prod-exp
124×cbrt-unprod
121×associate-*r/
120×flip3-- flip--
111×sqrt-div
108×frac-times
101×flip-+ flip3-+
83×associate-*l/
82×pow1/2
74×difference-of-squares
73×pow-prod-up
72×*-commutative
70×sub-neg
68×distribute-lft-out
62×fma-def
61×frac-2neg clear-num
60×exp-sum distribute-lft-out--
50×diff-log
44×pow-plus rem-sqrt-square
43×associate-/l/
41×div-exp
40×pow1/3 neg-mul-1
39×associate-+l+
37×cbrt-undiv
36×log-pow
34×fma-udef
33×pow2
22×pow-flip rec-exp
20×cbrt-div div-sub log-div
19×frac-sub
17×+-commutative
16×pow-unpow inv-pow
14×rem-log-exp
10×sum-log associate-+r+ sqrt-unprod
associate--l-
neg-sub0 exp-diff distribute-rgt-in distribute-lft-in frac-add
cube-prod associate--l+ pow-to-exp exp-prod log1p-udef
difference-of-sqr-1 rem-square-sqrt
pow-exp pow3 pow-pow associate-+l- un-div-inv sin-mult
expm1-log1p expm1-udef associate-+r- associate--r+ cos-sum rem-cbrt-cube
sin-sum log1p-def rem-cube-cbrt log1p-expm1 unpow3 distribute-frac-neg +.c-commutative cube-mult sqr-sin distribute-rgt-out-- tan-sum
diff-atan sub0-neg frac-2neg-c diff-sin diff-cos associate--r- expm1-def

bsearch3.1s

localize2.6s

end1.0ms