Details

simplify4.4m (58.8%)

sample1.2m (16.2%)

Algorithm
67×intervals
Results
28.0s269715×body80valid
11.2s13754×body1280valid
5.8s16919×body160valid
4.9s3871×body2560valid
4.6s9464×body640valid
2.9s75847×pre80true
2.6s2157×body10240exit
2.4s19388×body80nan
2.3s6830×body320valid
167.0ms224×body5120valid
7.0ms100×pre80false

prune1.0m (13.9%)

series24.2s (5.4%)

Calls

293 calls:

462.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
432.0ms
(+ (* (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (- (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) 3)) (* (* x1 x1) (- (* 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) 6)))
394.0ms
(* (cbrt (* (* 0.12900613773279798 x) x)) (cbrt (* (* 0.12900613773279798 x) x)))
389.0ms
(cbrt (* (* 0.12900613773279798 x) x))
370.0ms
(- (/ (pow (+ 1 (/ i n)) n) (/ i n)) (/ 1 (/ i n)))

rewrite16.1s (3.6%)

Algorithm
102×rewrite-expression-head
Calls

293 calls:

986.0ms
(+ (+ (+ (* 333.75 (pow 33096 6)) (* (* 77617 77617) (+ (+ (+ (* (* 11 (* 77617 77617)) (* 33096 33096)) (- (pow 33096 6))) (* -121 (pow 33096 4))) -2))) (* 5.5 (pow 33096 8))) (/ 77617 (* 2 33096)))
985.0ms
(+ (+ (* 333.75 (pow 33096 6)) (* (* 77617 77617) (+ (+ (+ (* (* 11 (* 77617 77617)) (* 33096 33096)) (- (pow 33096 6))) (* -121 (pow 33096 4))) -2))) (* 5.5 (pow 33096 8)))
611.0ms
(+ (* (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (- (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) 3)) (* (* x1 x1) (- (* 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) 6)))
530.0ms
(- (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) 3)
423.0ms
(+ (* (* a (sqrt (+ b c))) (sqrt (+ b c))) (* a d))
Rules
9549×times-frac
6380×*-un-lft-identity
5647×add-sqr-sqrt
4300×add-cube-cbrt
2088×add-exp-log
1547×add-cbrt-cube
871×pow1
766×div-exp
664×distribute-lft-out
653×add-log-exp
652×associate-*r* associate-/l*
600×difference-of-squares
573×prod-exp
497×associate-/r*
482×associate-*l*
476×cbrt-undiv
407×cbrt-unprod
388×sqrt-prod
365×div-inv
349×associate-/r/
293×insert-posit16
289×flip-+ flip3-+
280×distribute-lft-out--
198×unpow-prod-down
184×pow-prod-down
154×sum-log
128×sqr-pow
121×pow-prod-up
119×unswap-sqr
117×associate-*r/
116×flip3-- flip--
104×swap-sqr
94×sqrt-div
89×difference-of-sqr-1
80×sub-neg
74×associate-/l/
72×*-commutative
68×1-exp rec-exp associate-*l/
64×frac-times
61×frac-2neg clear-num
58×diff-log
53×log-prod distribute-rgt-neg-in
49×distribute-rgt-in distribute-lft-in
48×pow-plus
47×sqrt-pow1 pow-sqr
46×pow1/2
44×cbrt-div +-commutative
43×cbrt-prod
37×exp-prod
36×distribute-lft-neg-in
34×pow2
27×pow1/3 rem-sqrt-square
26×exp-sum log-pow frac-add
22×div-sub
21×associate-+l+
18×log-div
15×associate-+r+
14×pow-flip pow-exp pow-to-exp
12×associate--l+ neg-mul-1
9×rem-log-exp
7×neg-sub0 distribute-frac-neg distribute-lft-neg-out inv-pow rem-exp-log
6×pow-unpow distribute-rgt-out--
5×remove-posit16 associate--l- neg-log associate-+l-
4×exp-diff un-div-inv
3×frac-sub cube-unmult pow3
2×distribute-lft1-in associate-+r- sub-div associate--r+ pow-pow exp-to-pow distribute-rgt-out
1×sqrt-undiv difference-of-sqr--1 rem-cbrt-cube

regimes4.9s (1.1%)

Accuracy

Total 35.9b remaining (13.8%)

Threshold costs 3.0b (1.1%)

11.7b56.6%Compound Interest
5.2b72.8%Kahan p9 Example
4.8b83%The quadratic formula (r2)
4.6b83.5%The quadratic formula (r1)
2.9b0%Complex division, imag part

localize3.8s (0.8%)

bsearch1.3s (0.3%)

end1.0ms (0.0%)