Details

simplify6.8m (61.5%)

prune1.6m (14.9%)

sample1.2m (11.3%)

Algorithm
73×intervals
Results
26.9s286164×body80valid
10.2s25112×body160valid
9.1s13925×body1280valid
4.0s9164×body640valid
3.8s3804×body2560valid
2.8s2143×body10240exit
2.6s100577×pre80true
2.4s19328×body80nan
1.6s7014×body320valid
151.0ms213×body5120valid
6.0ms100×pre80false

series45.4s (6.9%)

Calls

305 calls:

3.1s
(cbrt (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)))
2.8s
(cbrt (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)))
2.8s
(cbrt (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)))
952.0ms
(+ (* (* (* 2.0 x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)) (+ (* (* x1 x1) (fma 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) (- (* (sqrt 6.0) (sqrt 6.0))))) (* (fma 6.0 -1 6.0) (* x1 x1))))
655.0ms
(- (* 9.0 (pow x 4.0)) (pow y 4.0))

rewrite24.8s (3.8%)

Algorithm
107×rewrite-expression-head
Calls

305 calls:

1.9s
(- (+ (exp (* x (- eps 1.0))) (/ (exp (* x (- eps 1.0))) eps)) (/ (exp (- (* x (+ 1.0 eps)))) eps))
1.7s
(+ (* (* (* 2.0 x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)) (+ (* (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (* x1 x1)) (* (- 6.0) (* x1 x1))))
1.2s
(+ (+ (* 333.75 (pow 33096.0 6.0)) (* (* 77617.0 77617.0) (+ (+ (+ (* (* 11.0 (* 77617.0 77617.0)) (* 33096.0 33096.0)) (- (pow 33096.0 6.0))) (* -121.0 (pow 33096.0 4.0))) -2.0))) (* 5.5 (pow 33096.0 8.0)))
1.1s
(- (/ (* (+ (* 333.75 (pow 33096.0 6.0)) (* (* 77617.0 77617.0) (+ (+ (+ (* (* 11.0 (* 77617.0 77617.0)) (* 33096.0 33096.0)) (- (pow 33096.0 6.0))) (* -121.0 (pow 33096.0 4.0))) -2.0))) (+ (* 333.75 (pow 33096.0 6.0)) (* (* 77617.0 77617.0) (+ (+ (+ (* (* 11.0 (* 77617.0 77617.0)) (* 33096.0 33096.0)) (- (pow 33096.0 6.0))) (* -121.0 (pow 33096.0 4.0))) -2.0)))) (- (+ (* 333.75 (pow 33096.0 6.0)) (* (* 77617.0 77617.0) (+ (+ (+ (* (* 11.0 (* 77617.0 77617.0)) (* 33096.0 33096.0)) (- (pow 33096.0 6.0))) (* -121.0 (pow 33096.0 4.0))) -2.0))) (* 5.5 (pow 33096.0 8.0)))) (- (/ (* (* 5.5 (pow 33096.0 8.0)) (* 5.5 (pow 33096.0 8.0))) (- (+ (* 333.75 (pow 33096.0 6.0)) (* (* 77617.0 77617.0) (+ (+ (+ (* (* 11.0 (* 77617.0 77617.0)) (* 33096.0 33096.0)) (- (pow 33096.0 6.0))) (* -121.0 (pow 33096.0 4.0))) -2.0))) (* 5.5 (pow 33096.0 8.0)))) (/ 77617.0 (* 2.0 33096.0))))
1.0s
(+ (* (* (* 2.0 x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (fma (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (/ 1 (+ (* x1 x1) 1.0)) (- 3.0))) (+ (* (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (* x1 x1)) (* (- 6.0) (* x1 x1))))
Rules
7562×times-frac
7123×*-un-lft-identity
6708×add-sqr-sqrt
5191×add-cube-cbrt
2969×prod-diff
1562×add-exp-log
1307×add-cbrt-cube
937×pow1
845×associate-*r*
828×distribute-rgt-in distribute-lft-in
626×associate-+l+
602×div-inv
576×add-log-exp
574×sqrt-prod
569×difference-of-squares
518×prod-exp
516×distribute-lft-out
479×distribute-lft-out--
446×associate-*l*
386×cbrt-unprod
364×div-exp
345×associate-/l*
341×associate-/r*
305×expm1-log1p-u log1p-expm1-u
285×cbrt-undiv
273×pow-prod-down
265×associate-/r/
258×cbrt-prod
242×flip3-- flip--
212×frac-times
206×flip-+ flip3-+
202×associate-*r/
196×fma-neg
173×unpow-prod-down
162×sqrt-pow1
146×distribute-rgt-neg-in
142×distribute-lft-neg-in
137×swap-sqr
136×unswap-sqr
131×associate-*l/
121×exp-sum
117×sum-log
106×frac-sub
100×fma-def
93×cbrt-div
86×sqr-pow
82×sqrt-div
81×exp-neg
76×*-commutative sub-neg
74×pow1/2
72×pow-prod-up
67×neg-sub0 frac-2neg clear-num
66×associate-/l/
65×associate--r+
61×exp-diff
57×pow1/3
48×frac-add
47×diff-log
46×pow-sqr
45×neg-mul-1
43×rem-sqrt-square
40×log-prod
37×fma-udef
33×pow-plus
32×distribute-neg-in
26×pow-exp pow-to-exp
25×+-commutative div-sub
23×associate-+r+
21×1-exp rec-exp un-div-inv
19×pow2
18×log-pow
associate--l+ hypot-def
distribute-lft-neg-out
distribute-frac-neg exp-prod
associate--l- log-div
pow-flip associate-+r- pow3
cube-prod inv-pow rem-log-exp distribute-neg-frac
pow-unpow sqrt-unprod rem-square-sqrt unsub-neg
neg-log sub-div associate-+l- rem-cbrt-cube distribute-rgt-out
unpow3 pow-pow distribute-rgt-out-- cube-mult associate--r-

regimes5.7s (0.9%)

Accuracy

Total 35.4b remaining (13.8%)

Threshold costs 3.0b (1.2%)

10.8b52.6%Compound Interest
8.5b28.8%Complex division, real part
4.5b84.4%The quadratic formula (r1)
4.3b84.9%The quadratic formula (r2)
3.2b0%Complex division, imag part

localize4.4s (0.7%)

bsearch1.2s (0.2%)

end1.0ms (0.0%)