Details

simplify5.0m (51.9%)

prune2.0m (20.9%)

sample1.6m (16.1%)

Algorithm
67×intervals
Results
37.3s268462×body80valid
12.9s13769×body1280valid
8.5s16845×body160valid
6.6s3825×body2560valid
6.3s9384×body640valid
4.8s2213×body10240exit
3.4s75853×pre80true
2.5s6913×body320valid
2.2s19523×body80nan
270.0ms218×body5120valid
11.0ms100×pre80false

series27.2s (4.7%)

Calls

317 calls:

768.0ms
(* (* a (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d))))
504.0ms
(- (/ 1 (/ a (sqrt (- (* b b) (* (* c a) 4))))) (/ b a))
491.0ms
(sqrt (sqrt (+ (+ b c) d)))
484.0ms
(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))))
456.0ms
(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))))

rewrite26.0s (4.5%)

Algorithm
104×rewrite-expression-head
Calls

317 calls:

1.4s
(/ (+ (/ (/ (/ PI (+ a b)) 2) a) (- (/ (/ (/ 1 (/ (+ a b) PI)) 2) b))) (- b a))
1.1s
(+ (* (* (* 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)))) (* (* x1 x1) -6)))
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)))
876.0ms
(cbrt (* (* (* (* y y) (* y y)) (* (* y y) (* y y))) (* (* y y) (* y y))))
792.0ms
(+ (+ (* 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
45821×times-frac
24678×*-un-lft-identity
22990×add-sqr-sqrt
16342×add-cube-cbrt
4516×sqrt-prod
3529×add-exp-log
2614×add-cbrt-cube
2546×difference-of-squares
2495×distribute-lft-out--
1838×div-inv
1759×distribute-lft-out
1542×pow1
1454×div-exp
1171×prod-exp
970×associate-/r/
948×cbrt-unprod
798×cbrt-undiv
736×flip-+ flip3-+
693×add-log-exp
633×associate-*r*
604×distribute-rgt-neg-in
569×associate-/l*
459×associate-/r*
449×associate-*l*
446×frac-times
395×sqrt-div
353×pow-prod-down
329×associate-*r/
317×insert-posit16
289×pow-prod-up
263×flip3-- flip--
251×associate-*l/
202×1-exp
168×cbrt-div
164×pow-sqr
155×sum-log
148×frac-sub
139×cbrt-prod
137×pow-plus
136×unpow-prod-down
122×swap-sqr
116×rec-exp
113×unswap-sqr
109×sqr-pow
101×pow2
90×sub-neg
89×difference-of-sqr-1 *-commutative
80×associate-/l/
73×exp-neg
70×frac-add
66×diff-log
65×frac-2neg clear-num
61×neg-sub0
60×exp-prod
59×exp-diff
51×distribute-rgt-in distribute-lft-in
49×distribute-lft-neg-in
44×sqrt-pow1
39×+-commutative pow1/2
34×rem-sqrt-square
30×div-sub
27×associate-+l+
26×log-prod
23×pow1/3
21×un-div-inv
17×pow-flip exp-sum neg-mul-1 log-pow
16×associate-+r+
11×pow-exp pow-to-exp
9×distribute-lft1-in inv-pow
8×associate--l+
7×distribute-rgt-out-- cube-unmult
6×associate--l- exp-to-pow rem-exp-log log-div
5×associate-+r- pow3
4×neg-log rem-log-exp
3×pow-unpow distribute-frac-neg sub-div unsub-neg
2×remove-posit16 associate--r+ distribute-lft-neg-out distribute-neg-frac rem-cbrt-cube
1×pow-pow associate-+l- distribute-rgt-out

regimes5.8s (1.0%)

Accuracy

Total 30.8b remaining (11.9%)

Threshold costs 2.5b (1%)

10.2b55.3%Compound Interest
5.3b73%Kahan p9 Example
4.2b84.9%The quadratic formula (r1)
2.8b0%Complex division, real part
2.5b0%Complex division, imag part

localize4.1s (0.7%)

bsearch1.6s (0.3%)

end1.0ms (0.0%)