Details

simplify13.6m (69.2%)

prune2.3m (11.9%)

sample1.5m (7.7%)

Algorithm
72×intervals
Results
31.6s276753×body80valid
11.2s13550×body1280valid
11.0s25188×body160valid
6.0s9451×body640valid
4.6s3894×body2560valid
3.7s100571×pre80true
3.4s2170×body10240exit
3.0s19551×body80nan
2.0s6828×body320valid
208.0ms264×body5120valid
4.0ms100×pre80false

rewrite53.4s (4.5%)

Algorithm
102×rewrite-expression-head
Calls

288 calls:

3.5s
(* (sqrt (* (* (exp d) (exp e)) (* (exp a) (* (exp c) (exp b))))) (sqrt (* (* (exp d) (exp e)) (* (exp a) (* (exp c) (exp b))))))
2.7s
(+ (+ (* 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)))
2.5s
(/ (log (exp (- (pow (+ 1.0 (/ i n)) n) 1.0))) (/ i n))
2.4s
(+ (* (* (* 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)) (+ (* (fma 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) (- (* (sqrt 6.0) (sqrt 6.0)))) (* x1 x1)) (* (* x1 x1) (fma 6.0 -1 6.0))))
2.2s
(+ (* (* (* 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)) (+ (* (fma 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) (- (* (sqrt 6.0) (sqrt 6.0)))) (* x1 x1)) (* (* x1 x1) (fma 6.0 -1 6.0))))
Rules
4173×*-un-lft-identity
4130×add-sqr-sqrt
3337×times-frac
3131×add-cube-cbrt
1875×prod-diff
1733×pow1
1420×add-exp-log
1278×add-cbrt-cube
888×pow-prod-down
571×add-log-exp
528×associate-+l+
489×sqrt-prod
474×prod-exp
455×associate-*r*
432×difference-of-squares
412×cbrt-unprod
357×distribute-rgt-in distribute-lft-in
356×sqrt-pow1
333×div-exp
314×associate-*l*
291×log1p-expm1-u
288×expm1-log1p-u insert-posit16
285×cbrt-undiv distribute-lft-out--
275×associate-/l*
257×div-inv
235×distribute-lft-out
226×fma-neg
220×associate-/r*
218×exp-prod
201×unpow-prod-down log-pow
200×associate-/r/
172×flip-+ flip3-+
165×exp-sum
148×flip3-- flip--
140×pow-prod-up
131×cbrt-prod
125×log-prod
116×associate-*r/
106×swap-sqr
104×sum-log
101×sqr-pow
92×frac-times
81×sub-neg
78×distribute-rgt-neg-in pow-sqr
76×unswap-sqr
73×distribute-lft-neg-in
65×fma-def
64×associate-/l/
62×*-commutative
56×associate-*l/
54×frac-2neg clear-num
53×diff-log
48×fma-udef
45×cbrt-div
44×pow1/2 frac-add
37×sqrt-div
33×pow-plus
26×div-sub
25×neg-mul-1
24×+-commutative
22×pow1/3 1-exp rec-exp
20×associate-+r+ pow2 rem-sqrt-square
16×log-div
14×rem-log-exp
12×pow-exp pow-to-exp
11×exp-to-pow rem-exp-log
pow-unpow pow-flip
exp-diff associate--l- inv-pow
distribute-lft-neg-out pow3 distribute-frac-neg hypot-def
neg-sub0
expm1-log1p expm1-udef log1p-expm1 neg-log pow-pow distribute-rgt-out log1p-udef
+-inverses associate--l+ distribute-rgt-out-- associate-+l- rem-cbrt-cube
associate-+r- sqrt-unprod un-div-inv rem-square-sqrt unsub-neg

series48.2s (4.1%)

Calls

288 calls:

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)) (+ (* (fma 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) (- (* (sqrt 6.0) (sqrt 6.0)))) (* x1 x1)) (* (* x1 x1) (fma 6.0 -1 6.0))))
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) (fma 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) (- (* (cbrt 6.0) (* (cbrt 6.0) (cbrt 6.0)))))) (* (* x1 x1) (fma 6.0 -1 6.0))))
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)) (+ (* (fma 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) (- (* (sqrt 6.0) (sqrt 6.0)))) (* x1 x1)) (* (* x1 x1) (fma 6.0 -1 6.0))))
1.0s
(- (* 9.0 (pow x 4.0)) (pow y 4.0))
1.0s
(- (* 9.0 (pow x 4.0)) (pow y 4.0))

localize14.7s (1.2%)

regimes14.4s (1.2%)

Accuracy

Total 34.4b remaining (13.5%)

Threshold costs 3.1b (1.2%)

10.6b50.7%Compound Interest
8.3b32.8%Complex division, real part
4.5b77.5%Kahan p9 Example
3.5b-10.9%Complex division, imag part
3.0b90%The quadratic formula (r2)

bsearch2.1s (0.2%)

end1.0ms (0.0%)