Details

simplify3.3m

prune3.2m

sample1.6m

Algorithm
64×intervals
Results
39.5s269429×body80valid
12.9s13917×body1280valid
7.4s16851×body160valid
6.8s9428×body640valid
5.6s3921×body2560valid
4.4s75774×pre80true
4.1s1998×body10240exit
3.3s6772×body320valid
2.6s19322×body80nan
341.0ms261×body5120valid

series24.7s

Calls

270 calls:

Slowest
922.0ms
(/ (/ i n) (fma 100 (exp (* n (log1p (/ i n)))) -100))
470.0ms
(* (fma (/ 1 (sqrt (fma x1 x1 1))) (/ (fma 3 (* x1 x1) (- (* x2 2) x1)) (sqrt (fma x1 x1 1))) -3) (* (* x1 2) (/ (fma 3 (* x1 x1) (- (* x2 2) x1)) (fma x1 x1 1))))
469.0ms
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
417.0ms
(+ (* (* (* 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)))
398.0ms
(fma (fma (/ (fma 3 (* x1 x1) (- (* x2 2) x1)) (fma x1 x1 1)) 4 -6) (* x1 x1) (* (fma (/ 1 (sqrt (fma x1 x1 1))) (/ (fma 3 (* x1 x1) (- (* x2 2) x1)) (sqrt (fma x1 x1 1))) -3) (* (* x1 2) (/ (fma 3 (* x1 x1) (- (* x2 2) x1)) (fma x1 x1 1)))))

rewrite13.3s

Algorithm
94×rewrite-expression-head
Calls

270 calls:

Slowest
999.0ms
(+ (+ (+ (* 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)))
936.0ms
(+ (+ (* 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)))
772.0ms
(+ (log (exp (+ e (+ b (+ d c))))) a)
703.0ms
(+ (* (* (* 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)))
690.0ms
(+ (log (* (exp e) (* (exp b) (* (exp d) (exp c))))) a)
Rules
10353×times-frac
10123×add-sqr-sqrt
9572×*-un-lft-identity
7046×add-cube-cbrt
5948×prod-diff
3405×exp-sum
2140×associate-+l+
1800×distribute-rgt-in distribute-lft-in
1290×add-exp-log
1186×add-cbrt-cube
1137×difference-of-squares
958×associate-*r*
889×sqrt-prod
881×pow1
773×distribute-lft-out--
548×add-log-exp
505×div-inv
460×associate-/r*
439×distribute-lft-out
387×associate-/l*
374×prod-exp
355×sub-neg
348×cbrt-unprod
338×associate-*l*
331×div-exp
272×expm1-log1p-u
271×cbrt-undiv
270×log1p-expm1-u insert-posit16
265×pow-prod-down
205×associate-/r/
179×fma-neg
169×flip-+ flip3-+
160×fma-def
158×distribute-rgt-neg-in
144×distribute-lft-neg-in
125×sum-log
115×exp-prod
85×associate-*r/
83×flip3-- flip--
79×log-pow
77×unswap-sqr
66×frac-times pow-prod-up
64×frac-2neg clear-num *-commutative
56×cbrt-prod
48×neg-mul-1
46×fma-udef
45×associate-*l/
43×diff-log
41×associate-/l/
34×pow-plus
33×pow-sqr
30×sqrt-pow1 cbrt-div frac-add
29×+-commutative rem-sqrt-square
28×pow1/2
26×1-exp rec-exp
23×swap-sqr
22×associate-+r+
20×pow1/3
18×div-sub
17×pow2
13×hypot-def
12×unpow-prod-down
11×sqrt-div
8×neg-sub0 log-prod pow-flip distribute-frac-neg inv-pow
6×distribute-lft-neg-out
5×exp-diff frac-sub sqr-pow neg-log associate--l- rem-exp-log
4×pow3 associate-+l-
3×pow-exp pow-unpow cube-unmult pow-to-exp
2×log1p-expm1 sub-div log1p-udef
1×expm1-udef remove-posit16 associate-+r- associate--l+ pow-pow un-div-inv hypot-udef rem-cbrt-cube rem-log-exp log-div

regimes5.3s

Accuracy

Total 39.9b remaining (28%)

Threshold costs 2.0b (1.4%)

9.6b52.2%Compound Interest
9.6b16.7%Complex division, real part
4.9b75.7%Kahan p9 Example
4.4b84.1%The quadratic formula (r2)
4.3b84.5%The quadratic formula (r1)

localize2.9s

bsearch1.3s

end2.0ms