Details

simplify5.2m (43.4%)

sample4.5m (37.0%)

Algorithm
56×intervals
16×halfpoints
Results
52.0s66599×body1280valid
31.6s17327×body2560valid
19.8s41902×body640valid
9.7s12868×body10240exit
8.2s93800×body80valid
7.7s21104×body320valid
5.7s64266×body80nan
2.7s10710×body160valid
1.6s47408×pre80true
597.0ms654×body1280nan
491.0ms674×body640nan
465.0ms510×body5120valid
126.0ms374×body320nan
41.0ms207×body160nan

prune56.9s (7.9%)

series50.2s (6.9%)

Calls

378 calls:

646.0ms
(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
623.0ms
(/ 1.0 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
609.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
562.0ms
(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))
561.0ms
(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))

rewrite26.1s (3.6%)

Algorithm
124×rewrite-expression-head
Calls

378 calls:

3.1s
(- (+ (- (+ (/ 0.5 n) 1.0) (/ 0.16666666666666669 (* n n))) (* (log n) 1.0)) 1.0)
607.0ms
(/ (/ (/ 1.0 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
521.0ms
(+ (- (+ (/ 0.5 n) 1.0) (/ 0.16666666666666669 (* n n))) (* (log n) 1.0))
476.0ms
(/ (- (* (exp (+ x x)) (exp (+ x x))) (* (* 1.0 1.0) (* 1.0 1.0))) (* (+ (exp x) 1.0) (+ (exp (+ x x)) (* 1.0 1.0))))
398.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
Rules
24009×sqrt-prod
20231×*-un-lft-identity
19838×times-frac
10126×add-sqr-sqrt
8387×add-cube-cbrt
6213×distribute-lft-out
1457×add-exp-log
1176×add-cbrt-cube
1020×associate-/l*
934×associate-*r*
735×pow1
707×sqrt-div
646×add-log-exp
644×associate-*l*
567×unpow-prod-down
564×difference-of-squares
544×associate-/r/
477×distribute-lft-out--
453×associate-/r*
413×div-inv
398×prod-exp
383×flip-+ flip3-+
347×cbrt-prod
307×div-exp
284×unswap-sqr
273×cbrt-unprod
231×cbrt-undiv
227×flip3-- flip--
225×sqr-pow
218×associate-*l/
152×pow-unpow
147×pow-prod-down
142×cube-prod
138×associate-*r/
114×cbrt-div log-prod
111×associate-/l/
108×unpow2
97×distribute-rgt-neg-in
96×diff-log
93×frac-times
92×*-commutative
90×sub-neg
84×frac-2neg clear-num
74×pow-exp
72×pow-to-exp
68×frac-add
66×distribute-lft-neg-in
64×log-pow
56×pow1/3
55×sum-log
53×swap-sqr
45×distribute-rgt-in distribute-lft-in
39×tan-quot
36×neg-mul-1 frac-sub
30×log-div +-commutative div-sub
28×sqrt-pow1
26×pow1/2
24×associate--l+
22×unpow3 cube-mult
20×rem-sqrt-square
16×rec-exp 1-exp
15×exp-prod neg-sub0
14×pow-pow exp-sum associate--r+
13×associate-+l+ complex-mul-def
12×associate--l- pow-prod-up pow-sqr
10×associate-+l- rem-log-exp
8×neg-log
7×cube-div sin-mult cos-mult
6×exp-diff un-div-inv pow-flip pow-plus distribute-frac-neg
5×sin-cos-mult pow2
4×rem-cube-cbrt inv-pow *.c-commutative sqrt-undiv
3×cos-sum associate-+r+ sqrt-unprod +.c-commutative sin-sum
2×difference-cubes rem-exp-log pow3 associate--r- exp-neg sub-div complex-add-def tan-sum rem-cbrt-cube
1×sub0-neg associate-+r- associate-+l+.c distribute-lft-neg-out diff-atan diff-cos associate-*l*.c frac-2neg.c exp-to-pow diff-sin

regimes3.5s (0.5%)

Accuracy

Total 27.2b remaining (20.7%)

Threshold costs 5.9b (4.5%)

6.1b76.7%quadp (p42, positive)
5.5b77.2%quad2m (problem 3.2.1, negative)
5.5b77.2%quadm (p42, negative)
1.7b92.8%quad2p (problem 3.2.1, positive)
1.4b83.7%2nthrt (problem 3.4.6)

localize3.2s (0.4%)

bsearch1.9s (0.3%)

end1.0ms (0.0%)