Details

sample4.4m (39.8%)

Algorithm
56×intervals
16×halfpoints
Results
50.8s66823×body1280valid
29.0s16913×body2560valid
21.2s42623×body640valid
10.9s12526×body10240exit
9.1s93843×body80valid
6.1s20586×body320valid
5.7s63900×body80nan
2.2s10767×body160valid
1.5s47359×pre80true
788.0ms458×body5120valid
495.0ms649×body1280nan
409.0ms683×body640nan
156.0ms348×body320nan
36.0ms192×body160nan

simplify3.6m (32.3%)

prune1.1m (9.9%)

rewrite55.5s (8.3%)

Algorithm
124×rewrite-expression-head
Calls

407 calls:

9.8s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (pow (- (- (+ (+ (/ (* 1 (* (pow (* a eps) 3) (exp (* eps b)))) 6) (* (/ 1 2) (* (pow a 2) (* (pow eps 2) (exp (* eps b)))))) (* a (* eps (exp (* eps b))))) (+ (* (/ 1.0 2.0) (* (pow a 2) (pow eps 2))) (* 1.0 (* a eps)))) (/ (* 6004799503160661.0 (pow (* a eps) 3)) 3.602879701896397e+16)) 1))
5.9s
(- (- (+ (+ (/ (* 1 (* (pow (* a eps) 3) (exp (* eps b)))) 6) (* (/ 1 2) (* (pow a 2) (* (pow eps 2) (exp (* eps b)))))) (* a (* eps (exp (* eps b))))) (+ (* (/ 1.0 2.0) (* (pow a 2) (pow eps 2))) (* 1.0 (* a eps)))) (/ (* 6004799503160661.0 (pow (* a eps) 3)) 3.602879701896397e+16))
2.6s
(/ (+ (/ (pow x 5) 60) (+ (+ (/ (pow x 3) 3) x) x)) (sqrt 2.0))
2.3s
(/ (+ (/ (pow x 5) 60) (+ (+ (/ (pow x 3) 3) x) x)) (sqrt 2.0))
2.1s
(* (/ (+ (/ (pow x 5) 60) (+ (+ (/ (pow x 3) 3) x) x)) (sqrt 2.0)) (sin y))
Rules
8832×times-frac
7433×*-un-lft-identity
7222×add-sqr-sqrt
4627×add-cube-cbrt
2077×add-exp-log
1377×unpow-prod-down
1176×sqrt-prod
1150×add-cbrt-cube
827×difference-of-squares
826×associate-/l*
784×pow1
768×distribute-lft-out
753×add-log-exp
727×associate-*l*
724×distribute-lft-out--
680×div-exp
630×associate-*r*
571×prod-exp
546×associate-/r*
518×sqr-pow
507×associate-*l/
417×cbrt-div
414×unswap-sqr
403×unpow2
325×div-inv
324×log-prod
305×flip-+ flip3-+
300×frac-add
272×flip-- flip3--
258×cbrt-undiv
248×cbrt-prod
235×associate-/r/
234×pow-exp
232×cube-prod
231×pow-to-exp
216×frac-times
210×cbrt-unprod
181×log-pow
144×swap-sqr
133×sub-neg
132×associate-*r/
126×diff-log
120×associate-/l/
102×1-exp
99×pow-unpow
96×rec-exp
94×frac-2neg clear-num
92×pow-prod-down
83×associate-+l+
75×*-commutative
72×sum-log
67×frac-sub
66×sqrt-pow1
64×pow1/3
59×sqrt-div
52×pow1/2 exp-prod
49×distribute-rgt-in distribute-lft-in
44×unpow3
39×cube-mult
37×distribute-rgt-neg-in
36×log-div
35×+-commutative
32×rem-sqrt-square
28×associate--l+
24×complex-mul-def div-sub
23×rem-log-exp
22×pow-prod-up exp-sum tan-quot
19×associate--r+ pow-flip
18×pow-pow pow-sqr
17×neg-sub0
15×sum-cubes cos-mult
13×associate--l- inv-pow associate-+l-
12×un-div-inv neg-log
distribute-rgt-out-- pow2 pow-plus
cube-div
exp-diff associate-+r+ sin-mult
rem-cube-cbrt sqrt-unprod *.c-commutative
difference-of-sqr-1
associate-+r- sub-div +.c-commutative complex-add-def
associate--r- sqrt-undiv exp-to-pow
rem-exp-log associate-+l+.c exp-neg rem-square-sqrt associate-*l*.c cos-sum sqr-cos tan-sum rem-cbrt-cube sin-sum
sin-cos-mult diff-atan diff-cos distribute-rgt-out frac-2neg.c diff-sin log-rec

series54.5s (8.1%)

Calls

407 calls:

1.4s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (pow (- (- (+ (+ (/ (* 1 (* (pow (* a eps) 3) (exp (* eps b)))) 6) (* (/ 1 2) (* (pow a 2) (* (pow eps 2) (exp (* eps b)))))) (* a (* eps (exp (* eps b))))) (+ (* (/ 1.0 2.0) (* (pow a 2) (pow eps 2))) (* 1.0 (* a eps)))) (/ (* 6004799503160661.0 (pow (* a eps) 3)) 3.602879701896397e+16)) 1))
1.4s
(- (* (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))
1.3s
(- (* (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (cbrt (pow (pow x (/ 1.0 n)) 3)))
686.0ms
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
598.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))

regimes4.8s (0.7%)

Accuracy

Total 22.9b remaining (11.4%)

Threshold costs 7.5b (3.8%)

3.4b88.5%quadm (p42, negative)
3.3b0%expq3 (problem 3.4.2)
3.1b89.1%quadp (p42, positive)
1.8b82.6%2cos (problem 3.3.5)
1.5b83.5%2nthrt (problem 3.4.6)

localize4.2s (0.6%)

bsearch2.2s (0.3%)

end1.0ms (0.0%)