Details

sample1.7m (67.0%)

Algorithm
28×intervals
14×halfpoints
Results
1.4s2063×body1280valid
980.0ms548×body2560valid
493.0ms1251×body640valid
280.0ms409×body10240exit
181.0ms2956×body80valid
135.0ms614×body320valid
94.0ms1919×body80nan
81.0ms408×body160valid
31.0ms1471×pre80true
22.0ms23×body1280nan
11.0ms15×body640nan
5.0ms10×body5120valid
5.0ms12×body320nan
1.0msbody160nan

simplify43.0s (28.6%)

rewrite3.9s (2.6%)

Algorithm
37×rewrite-expression-head
Calls

93 calls:

442.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
148.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
124.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
121.0ms
(/ (- 1.0 (cos x)) (* x x))
116.0ms
(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
Rules
760×*-un-lft-identity
686×add-sqr-sqrt
435×times-frac
338×add-cube-cbrt
170×add-log-exp
154×distribute-lft-out--
151×add-exp-log
150×difference-of-squares
144×add-cbrt-cube
121×pow1
110×sqrt-prod
74×log-prod
72×associate-/l*
70×associate-*l*
64×distribute-lft-out
63×flip-- flip3--
61×associate-/r*
39×sub-neg diff-log
29×div-inv
26×pow-unpow
25×associate-*r*
23×div-exp
22×cbrt-undiv
20×associate-/r/ log-pow
18×associate-/l/
17×unpow-prod-down
16×distribute-rgt-in flip3-+ flip-+ clear-num frac-2neg distribute-lft-in
15×cbrt-prod
13×complex-mul-def prod-exp associate--l+ cbrt-unprod
11×sqrt-div log-div distribute-rgt-neg-in div-sub
10×unswap-sqr
associate-*l/ associate--r+
sqr-pow
*-commutative sum-log pow-prod-down frac-sub frac-add
rem-sqrt-square neg-sub0
associate--l- rem-log-exp pow1/2 sqrt-pow1
+-commutative tan-quot *.c-commutative frac-times associate-+l- associate-+l+
+.c-commutative neg-log
cos-sum exp-diff pow1/3 complex-add-def pow-pow associate-*r/ pow-to-exp tan-sum cbrt-div pow-exp exp-neg frac-2neg.c sin-sum
associate-+l+.c diff-cos rem-exp-log exp-prod diff-atan associate-*l*.c exp-to-pow diff-sin

localize1.3s (0.9%)

series969.0ms (0.6%)

Calls

14 calls:

21.0ms
(- (atan (+ N 1.0)) (atan N))
0.0ms
(*.c (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0)) (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0)))
0.0ms
(+.c (exp.c (complex xre xim)) (exp.c (neg.c (complex xre xim))))
0.0ms
(*.c (complex (/ (- 1.0) 2.0) (/ (sqrt 3.0) 2.0)) (complex (- (+ (/ 1.0 2.0) 2.0)) (+ (/ (sqrt 3.0) 2.0) 0.0)))
0.0ms
(+.c (exp.c (complex xre xim)) (exp.c (neg.c (complex xre xim))))

prune489.0ms (0.3%)

end0.0ms (0.0%)