Details

simplify4.0m (53.6%)

sample1.5m (20.3%)

Algorithm
67×intervals
Results
35.9s269715×body80valid
13.0s13754×body1280valid
8.4s16919×body160valid
5.7s9464×body640valid
5.4s3871×body2560valid
5.2s2157×body10240exit
3.6s75847×pre80true
2.5s19388×body80nan
2.4s6830×body320valid
735.0ms224×body5120valid
11.0ms100×pre80false

prune58.0s (12.8%)

series26.4s (5.8%)

Calls

296 calls:

734.0ms
(* (* (+ (+ b c) (+ a d)) (+ (+ b c) (+ a d))) (+ (+ b c) (+ a d)))
483.0ms
(* (/ 1 (fabs (cbrt (+ (* c c) (* d d))))) (/ (+ (* a c) (* b d)) (sqrt (cbrt (+ (* c c) (* d d))))))
399.0ms
(- (/ (pow (+ 1 (/ i n)) n) (/ i n)) (/ 1 (/ i n)))
390.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
386.0ms
(* (/ 1 (sqrt 2)) (/ (/ (+ (/ (/ PI (sqrt 2)) a) (/ (- (/ PI (sqrt 2))) b)) (- b a)) (+ a b)))

rewrite23.7s (5.2%)

Algorithm
102×rewrite-expression-head
Calls

296 calls:

3.6s
(/ (cbrt (+ (* (- 2 (* x x)) (* (- 2 (* x x)) (- 2 (* x x)))) (* (* (* (* x x) (* x x)) (* x (* (* x x) (* x x)))) 8/27))) (cbrt (+ (* (* (* (* x x) x) 2/3) (* (* (* x x) x) 2/3)) (- (* (- 2 (* x x)) (- 2 (* x x))) (* (* (* (* x x) x) 2/3) (- 2 (* x x)))))))
1.4s
(+ (* (- 2 (* x x)) (* (- 2 (* x x)) (- 2 (* x x)))) (* (* (* (* x x) (* x x)) (* x (* (* x x) (* x x)))) 8/27))
939.0ms
(+ (+ (+ (* 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)))
858.0ms
(+ (+ (* 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)))
543.0ms
(+ (* (* (* 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)))
Rules
10971×times-frac
9800×*-un-lft-identity
6467×add-sqr-sqrt
4223×add-cube-cbrt
2028×distribute-lft-out
1680×flip-+ flip3-+
1574×add-exp-log
1452×add-cbrt-cube
1440×associate-*r*
1276×pow1
1228×distribute-rgt-neg-in
1200×frac-add
1191×frac-times
1101×sqrt-prod
851×difference-of-squares
617×add-log-exp
575×distribute-lft-out--
550×prod-exp
508×associate-/l*
484×associate-*l*
478×cbrt-unprod
430×cbrt-div
368×div-exp
355×pow-prod-down
354×div-inv
321×associate-/r*
312×cbrt-undiv
296×insert-posit16
295×pow-prod-up
257×associate-*l/
237×exp-prod
235×associate-*r/
186×unpow-prod-down associate-/r/
166×flip3-- flip--
137×sum-log
131×unswap-sqr
127×pow-sqr
124×sqr-pow
117×cbrt-prod
112×swap-sqr sqrt-div
95×pow-plus
89×difference-of-sqr-1
88×associate-/l/ distribute-lft-neg-in
86×*-commutative
73×sub-neg
63×pow2
59×sqrt-pow1
58×frac-2neg clear-num
56×distribute-rgt-in distribute-lft-in
54×diff-log
53×log-prod pow1/2
42×pow-flip
41×+-commutative
36×pow1/3
35×div-sub
29×log-pow
28×1-exp rec-exp
25×associate-+r+ rem-sqrt-square
22×associate-+l+
18×log-div
16×neg-mul-1
14×distribute-frac-neg
11×pow-exp pow-to-exp
10×exp-sum rem-exp-log
neg-sub0 rem-log-exp
cube-unmult pow3
frac-sub associate--l+ distribute-lft-neg-out inv-pow
associate-+r- pow-unpow distribute-rgt-out--
associate--r+
exp-diff associate-+l- rem-cbrt-cube
associate--l- neg-log unsub-neg distribute-rgt-out
distribute-lft1-in sub-div pow-pow
remove-posit16 sqrt-undiv un-div-inv distribute-neg-frac associate--r-

regimes4.5s (1.0%)

Accuracy

Total 35.7b remaining (16.1%)

Threshold costs 2.9b (1.3%)

11.7b56.6%Compound Interest
5.2b72.8%Kahan p9 Example
4.8b82.9%The quadratic formula (r2)
4.6b83.4%The quadratic formula (r1)
2.9b0%Complex division, imag part

localize3.6s (0.8%)

bsearch1.4s (0.3%)

end1.0ms (0.0%)