Details

prune3.8m (43.7%)

simplify2.5m (28.4%)

sample1.5m (17.9%)

Algorithm
67×intervals
Results
38.7s269560×body80valid
12.6s13921×body1280valid
7.3s16735×body160valid
6.8s9326×body640valid
5.4s3888×body2560valid
4.6s2316×body10240exit
3.5s75820×pre80true
2.5s6890×body320valid
1.9s19765×body80nan
218.0ms218×body5120valid
10.0ms100×pre80false

series28.7s (5.5%)

Calls

280 calls:

614.0ms
(cbrt x)
537.0ms
(+ (* (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (fma (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (/ 1 (+ (* x1 x1) 1)) -3)) (+ (* (fma 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) (- (* (sqrt 6) (sqrt 6)))) (* x1 x1)) 0))
535.0ms
(/ (/ (/ (/ PI 2) (+ a b)) (- b a)) a)
512.0ms
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
500.0ms
(+ (* (* (* 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)))

rewrite13.3s (2.6%)

Algorithm
101×rewrite-expression-head
Calls

280 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)))
908.0ms
(+ (+ (+ (* 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))) (/ 77617 (* 2 33096)))
786.0ms
(+ (* (* (* 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)))
661.0ms
(- (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) 3)
480.0ms
(+ (+ (+ (+ e d) c) b) a)
Rules
20691×times-frac
15013×*-un-lft-identity
12411×add-sqr-sqrt
9885×add-cube-cbrt
2173×prod-diff
1579×associate-/l*
1477×distribute-lft-out
1293×add-exp-log
1286×sqrt-prod
1176×difference-of-squares
1115×add-cbrt-cube
1065×distribute-lft-out--
884×pow1
840×div-inv
547×add-log-exp
490×associate-/r/
488×associate-/r*
436×associate-*l*
407×associate-*r*
366×div-exp
365×associate-+l+
311×prod-exp
283×cbrt-unprod
282×expm1-log1p-u
280×log1p-expm1-u insert-posit16
279×flip-+ flip3-+
267×pow-prod-down
263×cbrt-undiv
238×distribute-rgt-neg-in
191×fma-neg
190×cbrt-prod
165×distribute-lft-neg-in
136×distribute-rgt-in distribute-lft-in
123×swap-sqr
116×flip3-- flip--
112×sum-log
106×fma-def unpow-prod-down
93×unswap-sqr
87×associate-*r/
82×associate-/l/
73×frac-2neg clear-num
61×sub-neg
59×*-commutative
58×pow-prod-up
55×neg-mul-1
47×sqrt-div diff-log
45×1-exp rec-exp
43×associate-*l/
42×frac-times sqr-pow pow-sqr
40×pow1/3
34×pow-plus fma-udef
30×sqrt-pow1 associate-+r+ pow1/2
28×log-prod frac-add
25×exp-sum
24×+-commutative
23×rem-sqrt-square
20×div-sub
17×pow2 exp-prod
16×pow-flip
14×inv-pow
13×pow-exp pow-to-exp
12×distribute-rgt-out--
11×associate--l+ log-pow
10×distribute-frac-neg
9×pow-unpow
8×cbrt-div pow-div
7×neg-sub0 distribute-lft-neg-out
6×sum-cubes hypot-def cube-mult log-div
5×associate--l-
4×exp-diff frac-sub neg-log pow-pow rem-exp-log
2×log1p-expm1 sub-div associate--r+ rem-log-exp exp-to-pow un-div-inv log1p-udef
1×expm1-udef remove-posit16 cube-unmult pow3 sqrt-unprod remove-double-div associate-+l- log1p-def unpow1/3 rem-square-sqrt distribute-rgt-out

regimes4.0s (0.8%)

Accuracy

Total 49.2b remaining (33%)

Threshold costs 2.2b (1.5%)

15.8b38.1%Compound Interest
8.3b28.9%Complex division, imag part
7.2b32.7%Complex division, real part
4.9b82.2%The quadratic formula (r1)
4.8b75.9%Kahan p9 Example

localize3.8s (0.7%)

bsearch2.1s (0.4%)

end1.0ms (0.0%)