Details

simplify7.8m (63.2%)

prune2.1m (16.7%)

sample1.5m (12.4%)

Algorithm
67×intervals
Results
36.7s269448×body80valid
12.0s13771×body1280valid
8.4s16830×body160valid
6.4s9477×body640valid
5.6s3895×body2560valid
4.8s2170×body10240exit
3.5s75932×pre80true
3.0s6903×body320valid
2.8s19333×body80nan
325.0ms232×body5120valid
7.0ms100×pre80false

series27.4s (3.7%)

Calls

305 calls:

823.0ms
(* (/ (- (* x2 2) (- x1 (* (* x1 x1) 3))) (+ 1 (* x1 x1))) (+ (* (* x1 x1) 3) (* (* 2 (+ 1 (* x1 x1))) (* (- (/ (- (* x2 2) (- x1 (* (* x1 x1) 3))) (+ 1 (* x1 x1))) 3) x1))))
764.0ms
(* (/ (- (* x2 2) (- x1 (* (* x1 x1) 3))) (+ 1 (* x1 x1))) (+ (* (* x1 x1) 3) (* (* 2 (+ 1 (* x1 x1))) (* (- (/ (- (* x2 2) (- x1 (* (* x1 x1) 3))) (+ 1 (* x1 x1))) 3) x1))))
479.0ms
(+ (* (* (* 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 (* x1 x1))))
465.0ms
(/ (sqrt (/ (- 1 v) (* (- 3 (* 2 v)) 0.125))) w)
433.0ms
(+ (* (* (* 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)))

rewrite20.0s (2.7%)

Algorithm
102×rewrite-expression-head
Calls

305 calls:

1.7s
(/ (+ (* (* (* x x) (* x x)) (* x x)) (* (* (* (* x x) (* x x)) (* (* x x) (* x x))) x)) (* (* x x) (+ (- (* x x) (* x (* x x))) (* (* x x) (* x x)))))
1.3s
(+ (* (* (* 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 (* 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)))
887.0ms
(+ (+ (+ (* 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)))
671.0ms
(- (+ (exp (+ (- x) (* x eps))) (/ (exp (+ (- x) (* x eps))) eps)) (- (/ (exp (- (- x) (* x eps))) eps) (exp (- (- x) (* x eps)))))
Rules
6975×times-frac
5799×add-sqr-sqrt
5666×*-un-lft-identity
2888×add-cube-cbrt
1491×add-exp-log
1354×add-cbrt-cube
1211×pow1
985×difference-of-squares
933×distribute-lft-out--
761×associate-*r*
687×add-log-exp
613×sqrt-prod
517×associate-/l*
512×associate-*l*
477×prod-exp
454×distribute-lft-out
416×cbrt-unprod
403×div-inv
334×div-exp
322×pow-prod-down
305×insert-posit16
289×associate-/r*
277×cbrt-undiv
220×associate-/r/
219×unpow-prod-down
214×flip-+ flip3-+
166×pow-prod-up
149×sqr-pow
142×flip3-- flip--
138×sum-log
133×associate-*r/
124×unswap-sqr
103×associate-*l/
96×sqrt-div
92×pow-sqr
90×difference-of-sqr-1
89×*-commutative
88×distribute-rgt-neg-in
85×diff-log
82×cbrt-prod
81×sub-neg
80×distribute-lft-neg-in
79×pow-plus
69×frac-times
67×frac-2neg clear-num
65×associate-/l/
62×sqrt-pow1
59×exp-prod
58×swap-sqr
55×pow2
46×distribute-rgt-in distribute-lft-in
42×pow1/2
41×frac-sub
39×frac-add
37×+-commutative
34×rem-sqrt-square
31×log-pow
28×log-prod neg-mul-1
25×cbrt-div
24×associate-+l+ div-sub rem-exp-log
23×pow1/3 1-exp rec-exp
21×exp-diff
18×associate-+r+ exp-sum
17×neg-sub0
16×log-div
13×pow-exp
12×pow-to-exp
11×associate--l+ distribute-lft-neg-out associate-+l-
10×associate--l- distribute-frac-neg
pow-unpow neg-log
associate--r+ distribute-rgt-out--
pow-flip inv-pow rem-log-exp
un-div-inv distribute-neg-frac
remove-posit16 cube-unmult pow-pow distribute-rgt-out
distribute-lft1-in distribute-rgt-neg-out pow3 sqrt-unprod sub-div associate--r-
unpow-prod-up associate-+r- rem-square-sqrt unsub-neg e-exp-1 pow-sub

regimes4.8s (0.6%)

Accuracy

Total 31.9b remaining (14.7%)

Threshold costs 2.7b (1.2%)

11.9b55.9%Compound Interest
5.2b81.1%The quadratic formula (r2)
4.6b77.8%Kahan p9 Example
4.3b84.7%The quadratic formula (r1)
1.9b0%Complex division, real part

localize3.6s (0.5%)

bsearch1.5s (0.2%)

end1.0ms (0.0%)