Details

prune4.1m (39.6%)

simplify3.5m (33.8%)

sample1.5m (14.8%)

Algorithm
64×intervals
Results
37.2s268890×body80valid
13.2s13981×body1280valid
7.0s17012×body160valid
5.9s9329×body640valid
5.8s3959×body2560valid
3.8s75672×pre80true
3.8s1953×body10240exit
2.8s6683×body320valid
2.0s18921×body80nan
296.0ms229×body5120valid

series28.6s (4.6%)

Calls

283 calls:

Slowest
625.0ms
(+ (* (* (* 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)))
549.0ms
(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))))
536.0ms
(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))))
512.0ms
(/ 1 (/ (- 1 v) (* (- 3 (* 2 v)) 0.125)))
446.0ms
(/ (* (expm1 (* n (log1p (/ i n)))) 100) (/ i n))

bsearch17.4s (2.8%)

rewrite15.2s (2.5%)

Algorithm
99×rewrite-expression-head
Calls

283 calls:

Slowest
1.0s
(+ (+ (+ (* 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)))
909.0ms
(+ (+ (* 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)))
854.0ms
(+ (* (* (* 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)))
619.0ms
(cbrt (* (* (/ 1 (/ (fma y y (* x x)) (* (- x y) (+ y x)))) (/ 1 (/ (fma y y (* x x)) (* (- x y) (+ y x))))) (/ 1 (/ (fma y y (* x x)) (* (- x y) (+ y x))))))
587.0ms
(- (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) 3)
Rules
18083×times-frac
11933×add-sqr-sqrt
11767×*-un-lft-identity
10196×add-cube-cbrt
5006×prod-diff
1446×unpow-prod-down
1328×add-exp-log
1130×add-cbrt-cube
1111×sqrt-prod
889×div-inv
775×pow1
677×associate-*r*
674×difference-of-squares
559×sqr-pow
554×add-log-exp
466×associate-/r*
457×associate-/l*
422×associate-*l*
389×distribute-lft-out
370×prod-exp
328×div-exp
317×distribute-lft-out--
308×cbrt-unprod
291×log1p-expm1-u
285×expm1-log1p-u
283×insert-posit16
263×associate-/r/
262×cbrt-prod
249×cbrt-undiv
219×fma-neg
206×flip-- flip3--
199×pow-prod-down
196×associate-*r/
190×distribute-rgt-neg-in
181×flip-+ flip3-+
177×distribute-lft-neg-in
172×frac-times
156×distribute-rgt-in distribute-lft-in
150×associate-*l/
149×unswap-sqr
142×associate-+l+
117×sum-log
115×swap-sqr
99×difference-of-sqr-1
88×frac-sub
76×exp-neg
71×fma-def
70×frac-2neg clear-num
64×cbrt-div
63×neg-sub0 *-commutative
61×associate-/l/
59×neg-mul-1
58×sub-neg
57×exp-diff
56×frac-add
54×fma-udef
50×pow-prod-up
48×diff-log
43×sqrt-pow1
41×pow1/2
37×1-exp rec-exp
36×sqrt-div
34×pow-sqr
30×rem-sqrt-square
29×associate-+r+
27×pow-plus
25×un-div-inv
24×div-sub
22×pow-exp pow-to-exp
21×+-commutative
19×pow1/3
17×pow2
15×exp-sum
14×distribute-lft-neg-out
13×pow-flip inv-pow
12×expm1-udef
hypot-def
expm1-log1p
distribute-frac-neg
pow-div
associate--l-
cube-prod log-prod log1p-expm1 pow3 neg-log log1p-udef
pow-unpow hypot-udef expm1-def
cube-unmult sqrt-unprod rem-square-sqrt log-pow log-div
difference-cubes unpow3 pow-pow rem-log-exp log1p-def rem-cbrt-cube cube-mult distribute-rgt-out

regimes7.1s (1.2%)

Accuracy

Total 42.3b remaining (31.5%)

Threshold costs 3.3b (2.5%)

9.2b12.5%Compound Interest
7.6b32.8%Complex division, real part
6.7b36.5%Complex division, imag part
5.0b82.5%The quadratic formula (r2)
4.8b75.1%Kahan p9 Example

localize4.4s (0.7%)

end1.0ms (0.0%)