Details

simplify4.5m (56.2%)

sample1.6m (19.7%)

Algorithm
67×intervals
Results
37.6s269715×body80valid
12.8s13754×body1280valid
7.7s16919×body160valid
6.3s3871×body2560valid
5.8s9464×body640valid
4.2s2157×body10240exit
4.1s75847×pre80true
3.1s6830×body320valid
2.4s19388×body80nan
353.0ms224×body5120valid
9.0ms100×pre80false

prune1.1m (13.5%)

series24.7s (5.2%)

Calls

291 calls:

722.0ms
(cbrt (* (* 0.12900613773279798 x) x))
483.0ms
(+ (* (* (* 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)))
443.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
416.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
399.0ms
(- (/ (pow (+ 1 (/ i n)) n) (/ i n)) (/ 1 (/ i n)))

rewrite15.1s (3.2%)

Algorithm
102×rewrite-expression-head
Calls

291 calls:

828.0ms
(+ (+ (* 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)))
797.0ms
(+ (+ (+ (* 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)))
660.0ms
(+ (* (* (* 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)))
494.0ms
(- (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) 3)
452.0ms
(+ (+ (+ (+ e d) c) b) a)
Rules
9533×times-frac
6253×*-un-lft-identity
5681×add-sqr-sqrt
4304×add-cube-cbrt
2036×add-exp-log
1493×add-cbrt-cube
842×pow1
752×div-exp
651×add-log-exp
645×associate-/l*
631×distribute-lft-out
629×associate-*r*
586×difference-of-squares
580×sqrt-prod
549×prod-exp
521×associate-/r*
484×associate-*l*
461×cbrt-undiv
383×cbrt-unprod
367×div-inv
348×associate-/r/
291×insert-posit16
286×flip-+ flip3-+
261×distribute-lft-out--
198×unpow-prod-down
180×pow-prod-down
156×sum-log
136×unswap-sqr
128×sqr-pow
114×pow-prod-up
113×flip3-- flip--
96×associate-*r/
89×difference-of-sqr-1
83×sqrt-div
78×sub-neg
77×associate-/l/
70×*-commutative
69×1-exp rec-exp
63×frac-2neg clear-num
56×diff-log
55×associate-*l/
53×log-prod distribute-rgt-neg-in
50×swap-sqr
48×distribute-rgt-in distribute-lft-in
47×sqrt-pow1 pow1/2
46×+-commutative
45×frac-times
44×pow-sqr
41×pow-plus cbrt-prod
37×exp-prod
36×distribute-lft-neg-in
31×pow2
30×cbrt-div
26×exp-sum log-pow frac-add
25×pow1/3 rem-sqrt-square
22×div-sub
21×associate-+l+
18×log-div
17×pow-flip
15×associate-+r+
14×pow-exp pow-to-exp
12×associate--l+ neg-mul-1
9×rem-log-exp
8×inv-pow
7×neg-sub0 distribute-frac-neg distribute-lft-neg-out 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 distribute-rgt-out
2×distribute-lft1-in associate-+r- sub-div associate--r+ pow-pow exp-to-pow
1×sqrt-undiv pow3 sqrt-unprod difference-of-sqr--1

regimes5.5s (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%)

bsearch1.5s (0.3%)

end1.0ms (0.0%)