Details

simplify5.6m (59.5%)

sample1.3m (13.4%)

Algorithm
73×intervals
Results
28.4s293166×body80valid
8.9s13730×body1280valid
6.1s16763×body160valid
4.9s9648×body640valid
3.5s3825×body2560valid
3.1s2085×body10240exit
2.9s100591×pre80true
1.8s6894×body320valid
1.5s19379×body80nan
277.0ms239×body5120valid
4.0ms100×pre80false

series1.1m (11.5%)

Calls

309 calls:

16.1s
(/ (/ (/ (- (pow (+ 1.0 (/ i n)) (* 2 (* 2 n))) (* 1.0 (pow 1.0 3))) (fma 1.0 1.0 (pow (+ 1.0 (/ i n)) (* 2 n)))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))
2.7s
(/ (/ (- (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0)) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))
2.1s
(+ (pow y 6.0) (fma (pow y 4.0) 121.0 2.0))
1.0s
(* (pow y 6.0) 333.75)
902.0ms
(expm1 (log1p (* (pow y 6.0) 333.75)))

prune56.2s (9.9%)

rewrite22.6s (4.0%)

Algorithm
109×rewrite-expression-head
Calls

309 calls:

1.8s
(+ (+ (* 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)))
1.7s
(+ (+ (+ (* 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)))
1.2s
(+ (* (* (* 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) (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0)))
1.0s
(- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)
770.0ms
(+ (+ (+ (+ e d) c) b) a)
Rules
10162×times-frac
8437×*-un-lft-identity
8201×add-sqr-sqrt
6818×add-cube-cbrt
3546×prod-diff
1464×add-exp-log
1256×add-cbrt-cube
769×sqrt-prod
705×div-inv
685×difference-of-squares
655×unpow-prod-down
654×distribute-rgt-in distribute-lft-in
617×add-log-exp
599×distribute-lft-out
528×associate-*r*
520×pow1
466×associate-/l*
458×associate-*l*
454×cube-prod
397×prod-exp
394×div-exp
372×fma-neg
335×cbrt-undiv
311×log1p-expm1-u expm1-log1p-u
310×cbrt-unprod associate-/r*
289×sqr-pow
239×distribute-lft-out--
208×associate-/r/
195×flip-+ flip3-+
160×frac-times
157×flip-- flip3--
139×associate-+l+
131×unswap-sqr
130×associate-*r/
124×sum-log
119×associate-*l/
112×cbrt-prod
97×frac-sub
82×fma-def
81×pow-prod-down distribute-rgt-neg-in
80×exp-neg
78×distribute-lft-neg-in
77×unpow3 cube-mult sub-neg
75×clear-num frac-2neg
64×associate-/l/ neg-sub0
60×diff-log exp-diff
56×*-commutative
49×fma-udef
45×pow-unpow
39×pow-exp
33×pow-to-exp
31×1-exp
28×frac-add +-commutative
27×rec-exp
26×neg-mul-1 log-prod
23×associate-+r+
22×un-div-inv
21×swap-sqr div-sub
17×sqrt-div pow-pow
16×log-pow
14×sqrt-pow1 pow1/2
12×unpow2
11×rem-sqrt-square pow1/3
10×difference-cubes associate--l+
9×rem-cube-cbrt
8×distribute-frac-neg log-div
7×cbrt-div inv-pow pow-flip
6×distribute-lft-neg-out expm1-udef exp-prod
5×expm1-log1p hypot-udef rem-log-exp
4×associate--l- pow-prod-up pow2 pow-sqr pow-plus rem-cbrt-cube
3×cube-div log1p-udef log1p-expm1 sub-div
2×neg-log exp-sum distribute-rgt-out--
1×rem-exp-log unsub-neg distribute-rgt-out associate-+r- associate-+l- associate--r+

regimes4.7s (0.8%)

Accuracy

Total 37.4b remaining (14.9%)

Threshold costs 3.9b (1.6%)

11.9b48.5%Compound Interest
7.4b35.2%Complex division, imag part
7.0b35.7%Complex division, real part
4.6b84.1%The quadratic formula (r1)
1.3b0%Rosa's DopplerBench

localize3.0s (0.5%)

bsearch1.7s (0.3%)

end1.0ms (0.0%)