Details

simplify8.0m (52.0%)

prune4.7m (30.5%)

sample1.6m (10.5%)

Algorithm
67×intervals
Results
39.3s270095×body80valid
12.4s13610×body1280valid
8.7s16900×body160valid
6.8s9461×body640valid
5.2s3865×body2560valid
4.9s2230×body10240exit
3.7s75830×pre80true
2.7s6714×body320valid
2.7s19682×body80nan
331.0ms240×body5120valid
5.0ms100×pre80false

series36.5s (3.9%)

Calls

284 calls:

7.7s
(/ (/ (fma (exp (+ (* (log1p (/ i n)) n) (* (log1p (/ i n)) (+ n n)))) 1000000 -1000000) (fma (exp (* (log1p (/ i n)) n)) (* (exp (* (log1p (/ i n)) n)) 10000) (+ (* (exp (* (log1p (/ i n)) n)) 10000) 10000))) (/ i n))
810.0ms
(+ (+ (* (+ (* (* (/ 1 (sqrt (+ (* x1 x1) 1))) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (sqrt (+ (* x1 x1) 1)))) (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)))) (fma (* -6 x1) (/ (fma 3 (* x1 x1) (- (* 2 x2) x1)) (fma x1 x1 1)) (+ (* (fma 4 (/ (fma 3 (* x1 x1) (- (* 2 x2) x1)) (fma x1 x1 1)) -6) (* x1 x1)) 0))) (+ (* x1 x1) 1)) (* (* (* 3 x1) x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)))) (* (* x1 x1) x1))
622.0ms
(+ (* (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (fma (/ 1 (sqrt (+ (* x1 x1) 1))) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (sqrt (+ (* x1 x1) 1))) (- (* 3 1)))) (fma (* (* 0 2) x1) (/ (fma (* x1 3) x1 (- (* 2 x2) x1)) (fma x1 x1 1)) (* (* x1 x1) (fma 4 (/ (fma (* x1 3) x1 (- (* 2 x2) x1)) (fma x1 x1 1)) -6))))
545.0ms
(/ (- (sqrt (fma b b (* -4 (* a c)))) b) a)
506.0ms
(+ (* (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (- (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) 3)) (+ (* (fma 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) (- (* (sqrt 6) (sqrt 6)))) (* x1 x1)) (* 0 (* x1 x1))))

rewrite18.9s (2.0%)

Algorithm
97×rewrite-expression-head
Calls

284 calls:

3.8s
(+ (+ (* (+ (* (* (/ 1 (sqrt (+ (* x1 x1) 1))) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (sqrt (+ (* x1 x1) 1)))) (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)))) (fma (* -6 x1) (/ (fma 3 (* x1 x1) (- (* 2 x2) x1)) (fma x1 x1 1)) (+ (* (fma 4 (/ (fma 3 (* x1 x1) (- (* 2 x2) x1)) (fma x1 x1 1)) -6) (* x1 x1)) 0))) (+ (* x1 x1) 1)) (* (* (* 3 x1) x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)))) (* (* x1 x1) x1))
1.6s
(* (/ (/ 0.125 (sqrt (sqrt (/ (- 1 v) (fma -2 v 3))))) (sqrt (/ 1 (* (cbrt (fma -2 v 3)) (cbrt (fma -2 v 3)))))) (/ (/ (* w r) (sqrt (sqrt (/ (- 1 v) (fma -2 v 3))))) (sqrt (/ (- 1 v) (cbrt (fma -2 v 3))))))
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)))
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)))
769.0ms
(+ (* (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (- (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) 3)) (+ (* (fma 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) (- (* (sqrt 6) (sqrt 6)))) (* x1 x1)) (* 0 (* x1 x1))))
Rules
20896×times-frac
13090×*-un-lft-identity
12909×add-sqr-sqrt
9792×add-cube-cbrt
8355×sqrt-prod
3708×prod-diff
2003×associate-+l+
1892×associate-*r*
1480×difference-of-squares
1356×add-exp-log
1349×associate-*l*
1217×add-cbrt-cube
980×div-inv
979×pow1
784×distribute-lft-out--
686×cbrt-prod
551×distribute-lft-out
530×add-log-exp
405×prod-exp
391×associate-/r*
368×associate-/r/
362×associate-/l*
340×cbrt-unprod
328×div-exp
288×log1p-expm1-u
287×expm1-log1p-u
271×cbrt-undiv
266×flip-+ flip3-+
253×pow-prod-down
209×distribute-rgt-in distribute-lft-in
204×unswap-sqr
187×sqrt-div
181×frac-times
160×fma-neg
152×associate-*r/
147×associate-*l/
135×pow-prod-up
132×flip-- flip3--
113×sum-log distribute-rgt-neg-in
106×distribute-lft-neg-in
98×fma-def
83×frac-sub
78×log-prod
74×exp-neg
73×*-commutative
68×frac-2neg clear-num unpow-prod-down
63×pow-plus
61×pow-sqr
60×neg-sub0
57×exp-diff
55×exp-prod fma-udef
54×sub-neg
53×associate-/l/
50×frac-add
48×sqrt-pow1
44×pow1/2
42×swap-sqr
38×pow2 neg-mul-1
36×exp-sum
35×pow-flip diff-log
31×1-exp rec-exp
27×sqr-pow
25×log-pow rem-sqrt-square
23×+-commutative
20×un-div-inv
18×div-sub
17×associate-+r+
12×rem-exp-log
11×hypot-def
10×pow1/3
distribute-rgt-out--
sqrt-unprod inv-pow
expm1-log1p expm1-udef distribute-rgt-neg-out
pow3 neg-log associate--l-
distribute-lft-neg-out distribute-frac-neg rem-log-exp distribute-rgt-out log-div
pow-unpow log1p-expm1 pow-exp pow-to-exp log1p-udef
cbrt-div difference-of-sqr-1 sub-div associate--r+ pow-div hypot-udef log1p-def unsub-neg expm1-def
distribute-rgt1-in distribute-lft1-in pow-pow associate-+l- rem-square-sqrt rem-cbrt-cube count-2

regimes4.9s (0.5%)

Accuracy

Total 38.1b remaining (27.9%)

Threshold costs 2.0b (1.5%)

13.3b41.7%Compound Interest
7.0b34.8%Complex division, real part
6.4b36.3%Complex division, imag part
4.3b84.8%The quadratic formula (r2)
4.1b85.3%The quadratic formula (r1)

localize3.7s (0.4%)

bsearch1.7s (0.2%)

end1.0ms (0.0%)