Details

simplify10.2m (63.3%)

prune3.1m (19.4%)

sample1.6m (9.9%)

Algorithm
67×intervals
Results
37.8s269855×body80valid
13.0s13855×body1280valid
8.4s16827×body160valid
6.4s9452×body640valid
6.1s3814×body2560valid
4.6s2281×body10240exit
4.0s75826×pre80true
2.7s6822×body320valid
2.6s19440×body80nan
277.0ms250×body5120valid
10.0ms100×pre80false

series34.4s (3.6%)

Calls

311 calls:

7.1s
(/ (/ (- (* (* (pow (+ (/ i n) 1) n) (pow (+ (/ i n) 1) n)) (pow (+ (/ i n) 1) n)) 1) (+ (+ (pow (+ (/ i n) 1) n) 1) (* (pow (+ (/ i n) 1) n) (pow (+ (/ i n) 1) n)))) (/ i n))
1.3s
(+ (* 3 (/ (+ (* x2 -2) (- (* (* x1 x1) 3) x1)) (+ 1 (* x1 x1)))) (* (+ 1 (* x1 x1)) (+ (* (/ (+ (* (* x1 x1) 3) (- (* x2 2) x1)) (+ 1 (* x1 x1))) (+ (* x1 (* (- (/ (+ (* (* x1 x1) 3) (- (* x2 2) x1)) (+ 1 (* x1 x1))) 3) 2)) (* (* x1 x1) 4))) (+ (* -6 (* x1 x1)) x1))))
867.0ms
(+ (* (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (- (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) 3)) (* (* (cbrt (* (* x1 x1) (- (* 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) 6))) (cbrt (* (* x1 x1) (- (* 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) 6)))) (cbrt (* (* x1 x1) (- (* 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) 6)))))
494.0ms
(log (+ 1 (* (* x x) x)))
478.0ms
(log (+ 1 (* x (* x x))))

rewrite25.7s (2.7%)

Algorithm
104×rewrite-expression-head
Calls

311 calls:

2.4s
(* (/ (+ (* (* x1 x1) 3) (- (* x2 2) x1)) (+ 1 (* x1 x1))) (+ (* x1 (* (- (/ (+ (* (* x1 x1) 3) (- (* x2 2) x1)) (+ 1 (* x1 x1))) 3) 2)) (* (* x1 x1) 4)))
2.2s
(+ (* 3 (/ (+ (* x2 -2) (- (* (* x1 x1) 3) x1)) (+ 1 (* x1 x1)))) (* (+ 1 (* x1 x1)) (+ (* (/ (+ (* (* x1 x1) 3) (- (* x2 2) x1)) (+ 1 (* x1 x1))) (+ (* x1 (* (- (/ (+ (* (* x1 x1) 3) (- (* x2 2) x1)) (+ 1 (* x1 x1))) 3) 2)) (* (* x1 x1) 4))) (+ (* -6 (* x1 x1)) x1))))
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)))
963.0ms
(/ (/ (- (* (* (pow (+ (/ i n) 1) n) (pow (+ (/ i n) 1) n)) (pow (+ (/ i n) 1) n)) 1) (+ (+ (pow (+ (/ i n) 1) n) 1) (* (pow (+ (/ i n) 1) n) (pow (+ (/ i n) 1) n)))) (/ i n))
938.0ms
(+ (+ (* 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
14533×add-exp-log
14231×add-cbrt-cube
10113×times-frac
8000×prod-exp
7929×*-un-lft-identity
7870×cbrt-unprod
7252×add-sqr-sqrt
4569×div-exp
4451×cbrt-undiv
3927×add-cube-cbrt
2106×pow1
1285×difference-of-squares
1194×associate-*r*
1019×distribute-lft-out
863×associate-*r/
859×distribute-lft-out--
691×add-log-exp
641×div-inv
615×frac-times
585×associate-/l*
549×pow-prod-up
492×pow-prod-down
446×associate-*l*
399×associate-*l/
385×associate-/r*
377×sqrt-prod
365×flip3-- flip--
336×distribute-rgt-neg-in
323×cbrt-div
317×flip-+ flip3-+
311×insert-posit16
291×associate-/r/
259×distribute-lft-neg-in
240×pow-sqr
225×pow-plus
219×frac-add
202×unpow-prod-down
153×sum-log
152×pow2
143×unswap-sqr
133×frac-sub
129×sqr-pow
111×sqrt-div
93×swap-sqr
89×difference-of-sqr-1 cbrt-prod
87×neg-mul-1
86×*-commutative
79×sub-neg
73×exp-neg
71×diff-log
69×associate-/l/
67×log-prod
63×frac-2neg clear-num
62×exp-prod
61×neg-sub0
59×exp-diff
47×pow-flip
45×log-pow
44×1-exp rec-exp
40×sqrt-pow1 pow1/2
39×+-commutative
36×div-sub
35×distribute-rgt-in distribute-lft-in
32×rem-sqrt-square
24×associate-+r+
22×associate-+l+ log-div
20×exp-sum
19×un-div-inv
18×pow1/3
17×rem-exp-log
16×sub-div
15×pow-exp pow-unpow pow-to-exp
14×associate--l+
12×inv-pow
11×associate--l- rem-log-exp
distribute-rgt-out-- associate--r+
pow-div
pow3
associate-+r- cube-unmult
distribute-lft-neg-out neg-log pow-pow exp-to-pow
cube-prod remove-posit16 associate--r-
distribute-frac-neg associate-+l-
unsub-neg
distribute-lft1-in sub0-neg unpow3 sqrt-unprod distribute-neg-frac sum-cubes rem-square-sqrt cube-mult rem-cbrt-cube distribute-rgt-out

regimes5.4s (0.6%)

Accuracy

Total 37.2b remaining (16.7%)

Threshold costs 2.8b (1.3%)

16.8b39.2%Compound Interest
5.0b74.5%Kahan p9 Example
4.4b84.3%The quadratic formula (r1)
2.8b-4.7%Complex division, real part
2.5b0%Complex division, imag part

localize4.4s (0.5%)

bsearch1.9s (0.2%)

end1.0ms (0.0%)