Details

sample4.4m (35.9%)

Algorithm
56×intervals
16×halfpoints
Results
51.0s66591×body1280valid
32.0s17465×body2560valid
19.9s42320×body640valid
11.7s13110×body10240exit
8.6s93621×body80valid
6.1s20970×body320valid
4.9s63689×body80nan
2.4s10714×body160valid
2.0s47471×pre80true
610.0ms658×body1280nan
401.0ms647×body640nan
326.0ms454×body5120valid
173.0ms407×body320nan
35.0ms178×body160nan

simplify4.2m (34.6%)

prune1.4m (11.7%)

rewrite58.4s (7.9%)

Algorithm
122×rewrite-expression-head
Calls

405 calls:

14.8s
(cbrt (* (* (* (* (* eps (* eps (* eps 1/6))) b) b) (* (* (* eps (* eps (* eps 1/6))) b) b)) (* (* (* eps (* eps (* eps 1/6))) b) b)))
14.2s
(cbrt (* (* (* (* (* eps (* eps (* eps 1/6))) b) b) (* (* (* eps (* eps (* eps 1/6))) b) b)) (* (* (* eps (* eps (* eps 1/6))) b) b)))
2.7s
(+ (+ (/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0))) (- (/ 2.0 x))) (/ 1.0 (- x 1.0)))
1.5s
(- (+ (+ (/ 0.5 n) (- 1.0 (/ 0.16666666666666669 (* n n)))) (* (log n) 1.0)) 1.0)
1.3s
(+ (* (* (- (exp x) 2.0) (* (- (exp x) 2.0) (- (exp x) 2.0))) (* (* (* (exp x) (exp x)) (exp x)) (+ (* (* (exp x) (exp x)) (exp x)) (* 2.0 (* 2.0 2.0))))) (+ (* (* (exp x) (exp x)) (exp x)) (* 2.0 (* 2.0 2.0))))
Rules
23602×sqrt-prod
20216×*-un-lft-identity
19614×times-frac
9875×add-sqr-sqrt
8139×add-cube-cbrt
6211×distribute-lft-out
1271×add-exp-log
1195×add-cbrt-cube
1116×pow1
960×associate-/l*
749×difference-of-squares
748×add-log-exp
721×sqrt-div
587×distribute-lft-out--
577×associate-/r/
502×frac-times
456×flip-+ flip3-+
425×associate-/r*
404×flip3-- flip--
371×div-inv
366×associate-*r/
352×prod-exp
337×cbrt-unprod
334×associate-*l*
324×associate-*l/
320×pow-prod-down
288×tan-quot
287×associate-*r*
243×cbrt-prod
221×div-exp
214×frac-add
189×exp-prod
188×cbrt-undiv
159×log-prod
139×cbrt-div
130×unpow-prod-down
126×log-pow
124×diff-log
117×sub-neg
114×unswap-sqr
91×pow1/3
85×pow-prod-up
80×associate-/l/
77×frac-2neg clear-num
76×*-commutative
72×sqr-pow
65×pow-sqr
61×swap-sqr
60×distribute-rgt-neg-in
59×sum-log
54×exp-sum
52×pow-unpow
50×sqrt-pow1
44×pow1/2
40×pow-plus
35×distribute-lft-neg-in
34×distribute-rgt-in distribute-lft-in
33×rem-sqrt-square log-div
29×frac-sub pow2
27×div-sub
25×+-commutative
24×difference-cubes
19×pow3
18×exp-diff
17×associate--l+
15×associate-+l+ rem-log-exp
14×1-exp rec-exp complex-mul-def
13×neg-mul-1 associate--r+
12×neg-sub0 exp-to-pow
11×associate-+l-
10×associate--l- associate-+r+ neg-log
cube-unmult exp-lft-cube
pow-exp associate-+r- pow-to-exp distribute-rgt-out--
sub-div
distribute-neg-frac
rem-exp-log
unsub-neg sqrt-unprod pow-pow
pow-flip *.c-commutative inv-pow +.c-commutative rem-cbrt-cube
associate-*l*.c sin-sum distribute-frac-neg sin-mult exp-neg cos-sum tan-sum complex-add-def
quot-tan diff-atan frac-2neg.c distribute-neg-out distribute-rgt-neg-out sub0-neg un-div-inv diff-sin rem-square-sqrt associate-+l+.c diff-cos associate--r-

series56.6s (7.7%)

Calls

405 calls:

1.7s
(sqrt (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (* (/ (+ (sqrt (exp x)) (sqrt 1.0)) (+ (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))) (/ (- (sqrt (exp x)) (sqrt 1.0)) (- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))))))
1.4s
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
892.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
813.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
791.0ms
(log (* (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))) (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))))

localize6.2s (0.8%)

regimes6.0s (0.8%)

Accuracy

Total 41.5b remaining (21.4%)

Threshold costs 5.8b (3%)

13.5b36.6%expax (section 3.5)
4.7b86%quad2p (problem 3.2.1, positive)
4.7b86%quadp (p42, positive)
4.0b85.8%quad2m (problem 3.2.1, negative)
3.9b86.3%quadm (p42, negative)

bsearch3.6s (0.5%)

end1.0ms (0.0%)