Details

prune3.9m

simplify1.8m

sample1.5m

Algorithm
64×intervals
Results
36.6s269899×body80valid
12.0s13808×body1280valid
7.5s16884×body160valid
5.8s9579×body640valid
4.7s3812×body2560valid
3.5s75662×pre80true
2.9s2056×body10240exit
2.8s19413×body80nan
2.4s6679×body320valid
711.0ms234×body5120valid

series25.1s

Calls

282 calls:

Slowest
816.0ms
(+ (* (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (fma (/ (* (cbrt (- (+ (* (* 3 x1) x1) (* 2 x2)) x1)) (cbrt (- (+ (* (* 3 x1) x1) (* 2 x2)) x1))) (sqrt (+ (* x1 x1) 1))) (/ (cbrt (- (+ (* (* 3 x1) x1) (* 2 x2)) x1)) (sqrt (+ (* x1 x1) 1))) -3)) (* (* x1 x1) (- (* 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) 6)))
664.0ms
(+ (* (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (fma (/ 1 (sqrt (+ (* x1 x1) 1))) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (sqrt (+ (* x1 x1) 1))) -3)) (* (* x1 x1) (- (* 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) 6)))
551.0ms
(* (* (* 3 x1) x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)))
513.0ms
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
489.0ms
(/ x (fma x x 1))

rewrite14.9s

Algorithm
96×rewrite-expression-head
Calls

282 calls:

Slowest
1.1s
(+ (+ (+ (* 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)))
998.0ms
(+ (+ (* 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)))
815.0ms
(+ (* (* (* 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)))
654.0ms
(- (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) 3)
327.0ms
(+ (+ (+ (+ e d) c) b) a)
Rules
14265×times-frac
14090×*-un-lft-identity
13148×add-sqr-sqrt
9973×add-cube-cbrt
9183×prod-diff
3938×exp-sum
2444×distribute-rgt-in distribute-lft-in
1977×associate--r+
1287×add-exp-log
1280×difference-of-squares
1176×add-cbrt-cube
1054×distribute-lft-out
1035×distribute-lft-out-- div-inv
1018×pow1
934×associate-*r*
720×sqrt-prod
532×add-log-exp
450×associate-/r* associate-*l*
440×associate-/l*
435×prod-exp
419×sub-neg
403×cbrt-unprod
341×pow-prod-down
307×associate-/r/
284×expm1-log1p-u
282×log1p-expm1-u insert-posit16
249×div-exp
214×distribute-rgt-neg-in
201×fma-neg
198×flip-+ flip3-+
187×cbrt-undiv
143×associate-+l+
128×associate-+r+
122×unpow-prod-down associate-*r/
117×distribute-lft-neg-in
114×flip3-- flip--
103×fma-def
99×unswap-sqr
98×sum-log
82×*-commutative
76×pow-prod-up
67×frac-times
65×sqrt-div
61×associate-*l/
58×exp-prod
56×frac-2neg clear-num associate-/l/
52×fma-udef
51×sqr-pow diff-log
46×cbrt-prod
41×pow-plus
39×neg-mul-1
38×pow-sqr
37×rem-sqrt-square
36×sqrt-pow1 pow1/2
31×swap-sqr
28×1-exp rec-exp
27×log-prod
24×frac-add
23×frac-sub log-pow
22×+-commutative
21×pow-flip
20×pow2
19×cbrt-div
16×pow1/3 div-sub
11×pow-exp pow-to-exp
10×associate--l+ inv-pow rem-exp-log hypot-def
7×distribute-lft-neg-out
5×neg-sub0 associate--l- pow3
4×exp-diff distribute-frac-neg neg-log log-div
3×pow-unpow cube-unmult
2×expm1-udef log1p-expm1 rem-log-exp log1p-udef
1×expm1-log1p remove-posit16 associate-+r- sqrt-undiv sqrt-unprod pow-pow un-div-inv rem-square-sqrt rem-cbrt-cube associate--r-

regimes3.9s

Accuracy

Total 45.5b remaining (31%)

Threshold costs 1.9b (1.3%)

14.1b45.9%Compound Interest
7.2b33.6%Complex division, real part
6.8b37.6%Complex division, imag part
4.9b82.4%The quadratic formula (r1)
4.7b76.6%Kahan p9 Example

localize3.4s

bsearch2.3s

end1.0ms