Details

simplify6.5m (55.6%)

prune2.9m (24.7%)

sample1.2m (10.2%)

Algorithm
67×intervals
Results
28.5s268269×body80valid
10.1s13677×body1280valid
5.3s16980×body160valid
5.2s3760×body2560valid
4.6s9522×body640valid
3.3s2270×body10240exit
2.8s75783×pre80true
1.8s19500×body80nan
1.7s6815×body320valid
265.0ms262×body5120valid
7.0ms100×pre80false

series28.2s (4.0%)

Calls

275 calls:

1.2s
(/ (/ i n) (fma 100 (exp (* n (log1p (/ i n)))) -100))
560.0ms
(cbrt (+ (* (* (* 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))))
552.0ms
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
547.0ms
(sqrt (fma (* -4 c) a (* b b)))
529.0ms
(cbrt (+ (* (* (* 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))))

rewrite28.1s (4.0%)

Algorithm
99×rewrite-expression-head
Calls

275 calls:

2.0s
(/ (/ (/ PI 1) (/ (+ b a) (/ (- (/ 1 a) (/ 1 b)) 2))) (- b a))
1.7s
(+ (+ (* 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)))
1.6s
(+ (+ (+ (* 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)))
1.1s
(+ (* (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (- (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) 3)) (+ (* (* x1 x1) (fma 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) (- (* (sqrt 6) (sqrt 6))))) 0))
1.1s
(+ (* (* (* 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)))
Rules
127902×times-frac
75929×*-un-lft-identity
72815×add-sqr-sqrt
36993×add-cube-cbrt
14250×difference-of-squares
11913×distribute-lft-out--
7246×div-inv
6481×distribute-lft-out
3779×associate-/l*
2084×prod-diff
1081×add-exp-log
943×add-cbrt-cube
736×pow1
709×associate-/r*
558×sqrt-prod
519×add-log-exp
357×associate-/r/
317×associate-*r*
277×expm1-log1p-u
275×log1p-expm1-u prod-exp insert-posit16
272×associate-+l+
258×associate-*l*
257×div-exp
237×cbrt-unprod
218×unpow-prod-down
217×pow-prod-down
194×cbrt-undiv
190×fma-neg
184×flip-+ flip3-+
169×distribute-rgt-in distribute-lft-in
158×distribute-rgt-neg-in
153×distribute-lft-neg-in
131×associate-*r/
114×flip3-- flip--
109×sum-log fma-udef
106×fma-def
89×unswap-sqr
83×sqr-pow
78×exp-sum
65×frac-2neg clear-num frac-add
63×cbrt-prod
55×associate-/l/
52×sqrt-pow1 *-commutative
51×difference-of-sqr-1 neg-mul-1 sub-neg
47×frac-times
45×exp-prod
41×log-pow
40×pow1/2 diff-log
36×cbrt-div
34×swap-sqr
33×rem-sqrt-square
31×associate-*l/
30×1-exp
28×pow-prod-up
27×log-prod pow1/3
24×rec-exp
23×div-sub
21×pow-plus +-commutative
18×associate-+r+ pow-sqr
14×pow-flip hypot-def
13×sqrt-div inv-pow
12×pow-exp pow2 pow-to-exp
9×associate--l+ distribute-lft-neg-out
8×pow-div
7×distribute-frac-neg
5×exp-diff log-div
4×cube-prod un-div-inv
3×neg-sub0 expm1-udef associate--l- pow-unpow pow3
2×expm1-log1p frac-sub log1p-expm1 hypot-1-def rem-log-exp rem-exp-log log1p-udef
1×remove-posit16 unpow3 neg-log sqrt-unprod pow-pow rem-square-sqrt rem-cbrt-cube cube-mult associate--r-

regimes4.5s (0.6%)

Accuracy

Total 27.0b remaining (19%)

Threshold costs 2.2b (1.6%)

9.0b54.7%Compound Interest
4.4b77.3%Kahan p9 Example
3.2b0%Complex division, real part
3.1b87.9%The quadratic formula (r1)
2.4b0%Complex division, imag part

localize3.8s (0.5%)

bsearch1.6s (0.2%)

end1.0ms (0.0%)