Details

simplify8.5m (67.2%)

prune1.5m (11.7%)

sample1.2m (9.7%)

Algorithm
73×intervals
Results
25.7s286164×body80valid
9.6s25112×body160valid
8.6s13925×body1280valid
4.6s9164×body640valid
4.1s3804×body2560valid
3.4s2143×body10240exit
3.0s100577×pre80true
1.8s19328×body80nan
1.7s7014×body320valid
184.0ms213×body5120valid
3.0ms100×pre80false

series45.1s (5.9%)

Calls

287 calls:

3.2s
(cbrt (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))))
3.0s
(cbrt (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))))
2.9s
(cbrt (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))))
945.0ms
(+ (* (* (* 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))))
725.0ms
(cbrt (* (* (- (* (pow x 4.0) 9.0) (pow y 4.0)) (- (* (pow x 4.0) 9.0) (pow y 4.0))) (- (* (pow x 4.0) 9.0) (pow y 4.0))))

rewrite30.6s (4.0%)

Algorithm
103×rewrite-expression-head
Calls

287 calls:

4.3s
(+ (+ (* (* (* 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)))
3.1s
(+ (+ (+ (* 333.75 (pow y 6.0)) (* (* x x) (- (- (- (* (* (* (* 11.0 x) x) y) y) (pow y 6.0)) (* 121.0 (pow y 4.0))) 2.0))) (* 5.5 (pow y 8.0))) (/ x (* 2.0 y)))
3.0s
(+ (+ (* 333.75 (pow y 6.0)) (* (* x x) (- (- (- (* (* (* (* 11.0 x) x) y) y) (pow y 6.0)) (* 121.0 (pow y 4.0))) 2.0))) (* 5.5 (pow y 8.0)))
2.4s
(+ (+ (* (* (* 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)))
953.0ms
(+ (* (* (* 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))))
Rules
6380×times-frac
6219×*-un-lft-identity
5948×add-sqr-sqrt
4800×add-cube-cbrt
3082×prod-diff
1327×add-exp-log
1259×add-cbrt-cube
972×distribute-rgt-in distribute-lft-in
971×pow1
695×associate-*r*
604×sqrt-prod
562×add-log-exp
539×div-inv
516×associate-*l*
496×associate-+l+
457×prod-exp
442×cbrt-unprod
422×distribute-lft-out
416×difference-of-squares
316×pow-prod-down
315×distribute-lft-out--
289×log1p-expm1-u
287×expm1-log1p-u
280×associate-/l*
261×cbrt-prod
243×associate-/r*
240×div-exp
220×frac-times
212×flip3-- flip--
211×cbrt-undiv associate-*r/
208×fma-neg
206×flip-+ flip3-+
186×associate-/r/
152×unpow-prod-down
146×associate-*l/
145×distribute-rgt-neg-in
141×distribute-lft-neg-in
122×sum-log
115×unswap-sqr
104×swap-sqr
98×frac-sub
92×fma-def
90×sub-neg
84×exp-neg
77×sqrt-pow1
76×*-commutative
75×sqr-pow
72×sqrt-div
69×neg-sub0
63×exp-diff pow1/2
62×associate-/l/
57×cbrt-div
55×frac-2neg clear-num
54×pow-prod-up
47×neg-mul-1
46×diff-log
45×rem-sqrt-square
40×log-pow
37×pow1/3 frac-add
34×log-prod pow-sqr
33×fma-udef
31×pow-plus
26×log-div
25×+-commutative
22×un-div-inv
21×div-sub
19×associate-+r+
16×pow2
14×associate--l-
13×1-exp rec-exp
distribute-lft-neg-out distribute-frac-neg hypot-def
rem-log-exp exp-prod
pow-flip associate--r+ inv-pow
cube-prod pow-exp pow3 pow-to-exp
pow-unpow sqrt-unprod rem-square-sqrt
expm1-log1p expm1-udef neg-log unsub-neg associate--r-
exp-sum associate--l+ unpow3 sub-div pow-pow distribute-rgt-out-- associate-+l- cube-mult rem-cbrt-cube distribute-rgt-out

regimes5.3s (0.7%)

Accuracy

Total 36.0b remaining (14%)

Threshold costs 2.9b (1.1%)

10.8b52.6%Compound Interest
8.5b28.8%Complex division, real part
4.5b84.2%The quadratic formula (r1)
4.3b84.8%The quadratic formula (r2)
3.2b0%Complex division, imag part

localize3.7s (0.5%)

bsearch1.3s (0.2%)

end1.0ms (0.0%)