Details

simplify5.7m (60.0%)

sample1.3m (13.5%)

Algorithm
73×intervals
Results
28.8s293166×body80valid
10.0s13730×body1280valid
6.0s16763×body160valid
4.1s9648×body640valid
3.3s3825×body2560valid
3.3s100591×pre80true
2.4s2085×body10240exit
2.0s6894×body320valid
1.3s19379×body80nan
192.0ms239×body5120valid
4.0ms100×pre80false

series1.1m (11.4%)

Calls

309 calls:

16.7s
(/ (/ (/ (- (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))
905.0ms
(fma (- (* (* (* (* 11.0 x) x) y) y) (+ (pow y 6.0) (fma (pow y 4.0) 121.0 2.0))) (* x x) (fma 5.5 (pow y 8.0) (/ x (* 2.0 y))))
710.0ms
(expm1 (log1p (* (pow y 6.0) 333.75)))

prune55.5s (9.8%)

rewrite21.4s (3.8%)

Algorithm
109×rewrite-expression-head
Calls

309 calls:

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)))
1.6s
(+ (+ (* 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
(+ (* (* (* 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)))
933.0ms
(- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)
714.0ms
(/ (/ (/ (- (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))
Rules
10040×times-frac
8333×*-un-lft-identity
7993×add-sqr-sqrt
6708×add-cube-cbrt
3474×prod-diff
1513×add-exp-log
1273×add-cbrt-cube
700×div-inv
675×sqrt-prod
655×unpow-prod-down difference-of-squares
654×distribute-rgt-in distribute-lft-in
626×add-log-exp
617×distribute-lft-out
519×pow1
480×associate-*r*
454×cube-prod
453×associate-/l*
439×associate-*l* prod-exp
399×div-exp
350×fma-neg
338×cbrt-undiv
320×cbrt-unprod
311×log1p-expm1-u expm1-log1p-u
310×associate-/r*
289×sqr-pow
225×distribute-lft-out--
208×flip-+ flip3-+
203×associate-/r/
160×frac-times
147×flip-- flip3--
139×associate-+l+
134×associate-*r/
133×sum-log
119×associate-*l/
116×unswap-sqr
112×cbrt-prod fma-def
101×frac-sub
95×distribute-rgt-neg-in
87×distribute-lft-neg-in
81×pow-prod-down
80×exp-neg
77×unpow3 cube-mult
76×clear-num frac-2neg
73×sub-neg
68×neg-sub0
64×associate-/l/
60×exp-diff
56×diff-log
54×*-commutative
49×fma-udef
45×pow-unpow
42×1-exp
39×pow-exp
33×pow-to-exp
31×+-commutative
29×rec-exp neg-mul-1
28×frac-add
26×log-prod
23×associate-+r+
22×un-div-inv
21×swap-sqr
20×div-sub
19×sqrt-div
17×pow-pow
16×log-pow
15×pow1/2 sqrt-pow1
12×rem-sqrt-square unpow2
11×pow1/3
10×difference-cubes
9×rem-cube-cbrt
8×distribute-frac-neg log-div
7×cbrt-div
6×inv-pow distribute-lft-neg-out pow-flip expm1-udef exp-prod
5×expm1-log1p hypot-udef neg-log associate-+l- rem-log-exp
4×pow-prod-up pow2 pow-sqr pow-plus rem-cbrt-cube
3×cube-div log1p-udef associate--l- log1p-expm1 sub-div associate--l+
2×exp-sum distribute-rgt-out-- associate--r+
1×rem-exp-log unsub-neg distribute-rgt-out associate-+r-

regimes4.5s (0.8%)

Accuracy

Total 35.9b remaining (14.4%)

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
3.1b89.2%The quadratic formula (r1)
1.3b0%Rosa's DopplerBench

localize2.7s (0.5%)

bsearch1.8s (0.3%)

end1.0ms (0.0%)