Details

sample4.5m

Algorithm
56×intervals
14×halfpoints
Results
1.1m66872×body1280valid
39.0s17140×body2560valid
24.7s42745×body640valid
13.9s12897×body10240exit
11.8s93579×body80valid
8.7s20405×body320valid
7.7s62508×body80nan
3.5s11077×body160valid
2.6s47424×pre80true
770.0ms645×body1280nan
577.0ms468×body5120valid
538.0ms703×body640nan
230.0ms396×body320nan
63.0ms218×body160nan

prune3.5m

simplify3.3m

series36.0s

Calls

334 calls:

Slowest
952.0ms
(expm1 (expm1 (log1p (log1p (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))))
838.0ms
(log (exp (fma (* (cbrt (pow (+ x 1) (/ 1 n))) (cbrt (pow (+ x 1) (/ 1 n)))) (cbrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ 1 n)) 1)))))
808.0ms
(fma (* (cbrt (pow (+ x 1) (/ 1 n))) (cbrt (pow (+ x 1) (/ 1 n)))) (cbrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ 1 n)) 1)))
661.0ms
(/ (* (expm1 (* (+ a b) eps)) (/ (/ eps (* (cbrt (expm1 (* eps b))) (cbrt (expm1 (* eps b))))) (cbrt (expm1 (* eps b))))) (expm1 (* eps a)))
621.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

rewrite9.2s

Algorithm
110×rewrite-expression-head
Calls

334 calls:

Slowest
532.0ms
(/ (- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1)))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))
327.0ms
(/ (* x (fma (* (* (* x x) 1/45) (* (* x x) 1/45)) (* (* x x) 1/45) 1/27)) (+ (* 1/3 1/3) (- (* (* 1/45 (* x x)) (* 1/45 (* x x))) (* 1/3 (* 1/45 (* x x))))))
220.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
203.0ms
(* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x)))
202.0ms
(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
Rules
12251×*-un-lft-identity
11948×times-frac
11067×add-sqr-sqrt
8745×add-cube-cbrt
6896×prod-diff
1886×pow1
1377×sqrt-prod
1150×difference-of-squares
1019×add-exp-log
911×add-cbrt-cube
909×div-inv
853×distribute-lft-out--
788×distribute-lft-out
771×unpow-prod-down
541×fma-neg
537×associate-/r/
533×add-log-exp
519×pow-prod-up
504×log-prod
497×associate--l+
488×associate-+l+
474×distribute-rgt-in distribute-lft-in
377×pow-prod-down
349×exp-sum
334×log1p-expm1-u associate-/r*
329×expm1-log1p-u
326×insert-posit16
317×associate-/l*
296×flip3-- flip--
276×associate-*l*
263×sqr-pow
258×associate-*r*
248×prod-exp
224×cbrt-unprod
216×pow-sqr
210×distribute-rgt-neg-in
209×frac-sub
202×flip-+ flip3-+
195×div-exp
192×pow-plus
174×log-pow
169×cbrt-prod
168×distribute-lft-neg-in
151×frac-times
149×cbrt-undiv
128×pow2
100×associate-/l/
99×exp-prod
97×diff-log
96×fma-def
94×associate-*l/
93×sqrt-pow1
91×sub-neg
86×swap-sqr
84×sqrt-div unswap-sqr
82×associate-*r/
69×pow1/2
65×frac-2neg clear-num
58×pow-unpow
56×neg-mul-1
51×*-commutative
41×cbrt-div
36×associate-+r+
33×un-div-inv
32×pow-flip
31×pow1/3 difference-of-sqr-1
29×associate--r+
28×sum-log tan-quot 1-exp rec-exp log-div
25×rem-sqrt-square
23×inv-pow div-sub fma-udef
19×rem-log-exp
17×+-commutative pow-pow
16×log1p-udef
13×associate--l- frac-add
11×expm1-log1p expm1-udef pow-exp
10×neg-sub0
pow-to-exp
exp-diff neg-log log1p-def
log1p-expm1
cube-unmult associate-+l-
sin-mult
sin-sum pow3 sqrt-unprod sqr-sin distribute-rgt-out--
associate-+r- +.c-commutative tan-sum frac-2neg-c exp-neg hypot-def cos-sum associate--r- e-exp-1
quot-tan diff-atan sin-cos-mult sub-div rem-exp-log rem-square-sqrt diff-sin rem-cbrt-cube unpow1/3 diff-cos expm1-def

localize4.0s

regimes3.9s

Accuracy

Total 27.1b remaining (21.5%)

Threshold costs 4.4b (3.4%)

5.0b81.9%quadp (p42, positive)
4.9b81.9%quad2p (problem 3.2.1, positive)
4.2b84.7%quadm (p42, negative)
4.0b-19.3%expq3 (problem 3.4.2)
3.5b87.5%quad2m (problem 3.2.1, negative)

bsearch3.0s

end1.0ms