Details

simplify6.2m (65.4%)

prune1.2m (12.9%)

sample1.2m (12.7%)

Algorithm
67×intervals
Results
26.7s269715×body80valid
11.6s13754×body1280valid
5.9s16919×body160valid
4.9s9464×body640valid
4.0s3871×body2560valid
3.8s2157×body10240exit
3.3s75847×pre80true
2.0s6830×body320valid
1.4s19388×body80nan
207.0ms224×body5120valid
7.0ms100×pre80false

series27.9s (4.9%)

Calls

287 calls:

1.1s
(/ (/ i n) (fma 100 (exp (* n (log1p (/ i n)))) -100))
566.0ms
(+ (* (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (fma (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (/ 1 (+ (* x1 x1) 1)) -3)) (+ (* (fma 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) (- (* (sqrt 6) (sqrt 6)))) (* x1 x1)) 0))
556.0ms
(+ (* (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (fma (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (/ 1 (+ (* x1 x1) 1)) -3)) (+ (* (* (cbrt (fma 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) (- (* (sqrt 6) (sqrt 6))))) (cbrt (fma 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) (- (* (sqrt 6) (sqrt 6)))))) (* (cbrt (fma 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) (- (* (sqrt 6) (sqrt 6))))) (* x1 x1))) 0))
535.0ms
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
492.0ms
(+ (* (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (fma (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (/ 1 (+ (* x1 x1) 1)) -3)) (* (* x1 x1) (- (* 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) 6)))

rewrite14.5s (2.5%)

Algorithm
99×rewrite-expression-head
Calls

287 calls:

951.0ms
(+ (+ (* 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)))
951.0ms
(+ (+ (+ (* 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)))
766.0ms
(+ (* (* (* 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)))
645.0ms
(- (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) 3)
510.0ms
(+ (+ (+ (+ e d) c) b) a)
Rules
9613×times-frac
8255×*-un-lft-identity
7549×add-sqr-sqrt
4786×add-cube-cbrt
2199×prod-diff
1334×add-exp-log
1182×add-cbrt-cube
998×difference-of-squares
961×distribute-lft-out--
875×pow1
826×distribute-lft-out
660×sqrt-prod
639×div-inv
591×associate-*l*
571×associate-*r*
547×add-log-exp
490×associate-/l*
461×prod-exp
407×cbrt-unprod
341×associate-/r/
291×associate-+l+ expm1-log1p-u
288×log1p-expm1-u
287×insert-posit16
270×pow-prod-down div-exp
250×associate-/r*
226×distribute-rgt-neg-in
222×distribute-lft-neg-in
202×cbrt-undiv
170×flip-+ flip3-+
163×fma-neg
150×sqrt-div
142×flip3-- flip--
121×unswap-sqr
115×swap-sqr fma-udef
113×sum-log
110×distribute-rgt-in distribute-lft-in
102×fma-def
88×associate-*r/
80×exp-sum
75×associate-*l/
74×neg-mul-1
72×*-commutative
68×cbrt-prod
63×frac-times
56×pow-prod-up sub-neg
54×frac-2neg clear-num
51×difference-of-sqr-1
45×exp-prod
44×unpow-prod-down diff-log
42×associate-/l/
40×sqrt-pow1
39×pow1/2
36×pow-plus
33×pow1/3
32×1-exp rec-exp rem-sqrt-square
30×frac-add
28×log-prod
27×associate-+r+
26×pow-sqr
25×+-commutative
22×div-sub
21×cbrt-div
20×log-pow
19×pow2 sqr-pow
15×hypot-def
14×frac-sub
12×pow-flip associate--r+ inv-pow
11×pow-exp pow-to-exp
rem-exp-log
associate--l+ pow3
distribute-frac-neg distribute-lft-neg-out
pow-div un-div-inv
log1p-expm1 sub-div associate--l- log1p-udef
neg-sub0 exp-diff log-div
expm1-udef pow-unpow rem-cbrt-cube
remove-posit16 rem-log-exp distribute-rgt-out-- associate-+l- associate--r-
expm1-log1p sqrt-undiv cube-unmult neg-log sqrt-unprod pow-pow rem-square-sqrt distribute-rgt-out

regimes4.1s (0.7%)

Accuracy

Total 29.2b remaining (19%)

Threshold costs 2.1b (1.3%)

10.4b47.8%Compound Interest
4.8b83%The quadratic formula (r2)
4.6b83.5%The quadratic formula (r1)
3.6b0%Complex division, imag part
2.4b0%Complex division, real part

localize3.6s (0.6%)

bsearch1.0s (0.2%)

end1.0ms (0.0%)