Details

simplify2.4m (37.4%)

sample1.6m (25.2%)

Algorithm
67×intervals
Results
40.8s269560×body80valid
11.7s13921×body1280valid
7.7s16735×body160valid
5.9s9326×body640valid
5.4s3888×body2560valid
4.4s2316×body10240exit
4.0s75820×pre80true
3.4s6890×body320valid
2.3s19765×body80nan
314.0ms218×body5120valid
10.0ms100×pre80false

prune1.5m (24.2%)

series25.7s (6.7%)

Calls

279 calls:

588.0ms
(+ (* (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (fma (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (/ 1 (+ (* x1 x1) 1)) -3)) (+ (* (* x1 x1) (fma 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) (- (* (sqrt 6) (sqrt 6))))) 0))
517.0ms
(+ (* (* (* 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)))
495.0ms
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
479.0ms
(+ (* (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (fma (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (/ 1 (+ (* x1 x1) 1)) -3)) (* (* x1 x1) (- (* 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) 6)))
368.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))

rewrite14.5s (3.8%)

Algorithm
101×rewrite-expression-head
Calls

279 calls:

1.0s
(+ (+ (+ (* 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)))
985.0ms
(+ (+ (* 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)))
850.0ms
(- (+ (exp (* (- eps 1) x)) (+ (/ (exp (* (- eps 1) x)) eps) (/ 1 (exp (fma eps x x))))) (/ 1 (* eps (exp (fma eps x x)))))
721.0ms
(+ (* (* (* 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)))
706.0ms
(- (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) 3)
Rules
20721×times-frac
15134×*-un-lft-identity
12459×add-sqr-sqrt
9929×add-cube-cbrt
2251×prod-diff
1582×associate-/l*
1526×distribute-lft-out
1304×sqrt-prod
1293×add-exp-log
1181×difference-of-squares
1118×add-cbrt-cube
1075×distribute-lft-out--
879×pow1
861×div-inv
557×add-log-exp
492×associate-/r*
490×associate-/r/
437×associate-*l*
406×associate-*r*
371×associate-+l+
368×div-exp
311×prod-exp
283×cbrt-unprod
281×expm1-log1p-u flip-+ flip3-+
279×log1p-expm1-u insert-posit16
266×pow-prod-down
264×cbrt-undiv
238×distribute-rgt-neg-in
197×fma-neg
165×distribute-lft-neg-in cbrt-prod
162×distribute-rgt-in distribute-lft-in
119×flip3-- flip--
117×sum-log swap-sqr
108×fma-def
106×unpow-prod-down
90×unswap-sqr
88×associate-*r/
82×associate-/l/
74×frac-2neg clear-num
64×sub-neg
59×*-commutative
56×pow-prod-up
55×neg-mul-1
50×diff-log
47×sqrt-div
46×1-exp rec-exp
44×associate-*l/
42×frac-times sqr-pow
40×pow-sqr
39×fma-udef
33×pow-plus
32×associate-+r+
31×pow1/3
30×sqrt-pow1 pow1/2
28×log-prod frac-add
27×exp-sum
26×+-commutative
23×rem-sqrt-square
20×pow-flip div-sub
19×exp-prod
16×pow2
15×inv-pow
13×pow-exp pow-to-exp
12×associate--l+ distribute-rgt-out--
11×log-pow
10×distribute-frac-neg
9×pow-unpow
8×cbrt-div pow-div
7×neg-sub0 distribute-lft-neg-out
6×frac-sub sum-cubes hypot-def cube-mult log-div
5×associate--l-
4×exp-diff neg-log pow-pow
3×rem-exp-log
2×log1p-expm1 difference-of-sqr-1 sub-div associate--r+ un-div-inv rem-log-exp log1p-udef
1×expm1-udef remove-posit16 cube-unmult pow3 sqrt-unprod exp-to-pow remove-double-div associate-+l- log1p-def unpow1/3 rem-square-sqrt

regimes3.8s (1.0%)

Accuracy

Total 49.2b remaining (33.1%)

Threshold costs 2.1b (1.4%)

15.8b38.1%Compound Interest
8.3b28.9%Complex division, imag part
7.2b32.7%Complex division, real part
5.0b80.9%The quadratic formula (r1)
4.8b75.9%Kahan p9 Example

localize3.8s (1.0%)

bsearch2.2s (0.6%)

end0.0ms (0.0%)