Details

simplify3.6m

prune1.9m

sample1.6m

Algorithm
64×intervals
Results
37.6s270072×body80valid
12.8s13427×body1280valid
8.2s16888×body160valid
6.2s3866×body2560valid
5.8s9534×body640valid
4.1s2043×body10240exit
3.3s75626×pre80true
2.6s6935×body320valid
2.2s19446×body80nan
366.0ms241×body5120valid

series24.4s

Calls

312 calls:

Slowest
577.0ms
(* (+ (* (* x1 x1) 3) (- (* x2 2) x1)) (* (/ 1 (+ 1 (* x1 x1))) (+ (* x1 (* (* 2 (+ 1 (* x1 x1))) (- (/ (+ (* (* x1 x1) 3) (- (* x2 2) x1)) (+ 1 (* x1 x1))) 3))) (* (* x1 x1) 3))))
559.0ms
(* (/ (+ (* (* x1 x1) 3) (- (* x2 2) x1)) (+ 1 (* x1 x1))) (+ (* x1 (* (* 2 (+ 1 (* x1 x1))) (- (/ (+ (* (* x1 x1) 3) (- (* x2 2) x1)) (+ 1 (* x1 x1))) 3))) (* (* x1 x1) 3)))
556.0ms
(* (/ (+ (* (* x1 x1) 3) (- (* x2 2) x1)) (+ 1 (* x1 x1))) (+ (* x1 (* (* 2 (+ 1 (* x1 x1))) (- (/ (+ (* (* x1 x1) 3) (- (* x2 2) x1)) (+ 1 (* x1 x1))) 3))) (* (* x1 x1) 3)))
538.0ms
(* (/ (- t1) (+ t1 u)) v)
445.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

rewrite20.9s

Algorithm
103×rewrite-expression-head
Calls

312 calls:

Slowest
1.8s
(* (/ (+ (* (* x1 x1) 3) (- (* x2 2) x1)) (+ 1 (* x1 x1))) (+ (* x1 (* (* 2 (+ 1 (* x1 x1))) (- (/ (+ (* (* x1 x1) 3) (- (* x2 2) x1)) (+ 1 (* x1 x1))) 3))) (* (* x1 x1) 3)))
1.8s
(* (/ (+ (* (* x1 x1) 3) (- (* x2 2) x1)) (+ 1 (* x1 x1))) (+ (* x1 (* (* 2 (+ 1 (* x1 x1))) (- (/ (+ (* (* x1 x1) 3) (- (* x2 2) x1)) (+ 1 (* x1 x1))) 3))) (* (* x1 x1) 3)))
1.7s
(* (+ (* (* x1 x1) 3) (- (* x2 2) x1)) (* (/ 1 (+ 1 (* x1 x1))) (+ (* x1 (* (* 2 (+ 1 (* x1 x1))) (- (/ (+ (* (* x1 x1) 3) (- (* x2 2) x1)) (+ 1 (* x1 x1))) 3))) (* (* x1 x1) 3))))
879.0ms
(+ (+ (+ (* 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)))
841.0ms
(+ (+ (* 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)))
Rules
3700×times-frac
3670×*-un-lft-identity
3473×add-sqr-sqrt
2189×add-cube-cbrt
1498×add-exp-log
1368×add-cbrt-cube
953×pow1
773×associate-*r*
717×sqrt-prod
716×add-log-exp
495×difference-of-squares
478×associate-*l*
472×prod-exp
424×distribute-lft-out cbrt-unprod
385×cbrt-prod
373×associate-/r*
339×div-exp
312×insert-posit16
301×cbrt-undiv
284×associate-/l*
263×flip-+ flip3-+
261×pow-prod-down
245×distribute-lft-out--
229×div-inv
193×associate-/r/
190×unpow-prod-down
180×sum-log
144×unswap-sqr
133×flip3-- flip--
127×associate-*r/
126×sqr-pow
121×sqrt-div
119×swap-sqr
99×associate-*l/
97×frac-times
89×difference-of-sqr-1
88×*-commutative
72×sub-neg
65×distribute-rgt-neg-in associate-/l/
62×frac-2neg clear-num diff-log
61×sqrt-pow1
57×exp-prod
56×log-prod cbrt-div pow-prod-up log-pow
54×distribute-lft-neg-in
51×+-commutative
45×exp-sum
41×pow1/2
40×distribute-rgt-in distribute-lft-in pow-sqr
32×frac-add
31×pow-plus
30×rem-sqrt-square
24×associate-+r+
20×frac-sub
19×pow1/3 log-div
18×associate-+l+ 1-exp rec-exp pow2 neg-mul-1
17×div-sub
14×distribute-rgt-out--
12×pow-exp pow-to-exp rem-log-exp
neg-sub0 associate--r+
exp-diff associate--l- associate--l+
pow-unpow pow-flip distribute-frac-neg inv-pow
neg-log distribute-lft-neg-out distribute-rgt-out
cube-prod
remove-posit16 associate-+r- pow3 sub-div rem-exp-log associate-+l-
pow-pow un-div-inv exp-to-pow associate--r-
distribute-lft1-in sqrt-undiv cube-unmult unpow3 sqrt-unprod rem-square-sqrt rem-cbrt-cube cube-mult distribute-rgt1-in

bsearch17.0s

regimes6.9s

Accuracy

Total 37.1b remaining (16.6%)

Threshold costs 2.5b (1.1%)

12.8b52.9%Compound Interest
4.9b81.9%The quadratic formula (r1)
4.5b76.6%Kahan p9 Example
4.4b84.3%The quadratic formula (r2)
2.8b0%Complex division, real part

localize4.1s

end1.0ms