Details

simplify5.2m (42.0%)

prune4.7m (37.9%)

sample1.6m (12.8%)

Algorithm
67×intervals
Results
38.9s269715×body80valid
12.4s13754×body1280valid
8.1s16919×body160valid
5.8s9464×body640valid
5.6s3871×body2560valid
5.3s2157×body10240exit
4.0s75847×pre80true
2.9s6830×body320valid
2.3s19388×body80nan
243.0ms224×body5120valid
11.0ms100×pre80false

series27.3s (3.7%)

Calls

286 calls:

1.1s
(/ (/ i n) (fma (exp (* n (log1p (/ i n)))) 100 -100))
597.0ms
(+ (* (* (* 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))
495.0ms
(/ (fma (pow (+ 1 (/ i n)) n) 100 -100) (/ i n))
484.0ms
(/ (fma (exp (* n (log1p (/ i n)))) 100 -100) (/ i n))
471.0ms
(+ (* (* (* 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)))

rewrite17.2s (2.3%)

Algorithm
99×rewrite-expression-head
Calls

286 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)))
782.0ms
(+ (+ (* 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)))
771.0ms
(+ (* (* (* 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)))
654.0ms
(- (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) 3)
487.0ms
(+ (+ (+ (+ e d) c) b) a)
Rules
140525×times-frac
70576×*-un-lft-identity
69940×add-sqr-sqrt
66811×add-cube-cbrt
31674×prod-diff
12082×sqrt-prod
7977×distribute-rgt-neg-in
7950×distribute-lft-neg-in
3564×div-inv
2650×neg-mul-1
1361×add-exp-log
1201×add-cbrt-cube
1179×distribute-lft-out--
1146×difference-of-squares
805×distribute-lft-out
754×pow1
704×cbrt-prod
674×associate-/r/
670×associate-/l*
652×associate-*l*
579×add-log-exp
498×associate-*r*
419×fma-neg
408×prod-exp
358×cbrt-unprod
355×associate-/r*
340×div-exp
291×expm1-log1p-u
287×log1p-expm1-u
286×insert-posit16
265×cbrt-undiv
196×pow-prod-down
185×flip-+ flip3-+
148×associate-+l+
141×sum-log
131×fma-def
119×distribute-rgt-in distribute-lft-in
115×unswap-sqr
110×swap-sqr
102×flip3-- flip--
90×associate-*r/
84×frac-times
78×associate-*l/
66×*-commutative
64×frac-2neg clear-num
59×fma-udef
53×cbrt-div
48×pow-prod-up sub-neg
44×unpow-prod-down
41×associate--r+
40×associate-/l/
39×diff-log
38×exp-prod
36×sqrt-pow1
35×pow1/2
33×associate-+r+
31×pow1/3 1-exp rec-exp pow-plus
30×exp-sum sqrt-div +-commutative
28×rem-sqrt-square
27×frac-add
26×pow-sqr
25×div-sub
24×log-prod
19×sqr-pow
17×pow2
14×hypot-def
12×log-pow
11×pow-exp pow-to-exp
10×frac-sub associate--l+
9×pow-flip rem-exp-log
8×neg-sub0 pow3 inv-pow
7×distribute-frac-neg distribute-lft-neg-out
6×log1p-expm1 un-div-inv log1p-udef
5×associate--l- distribute-rgt-out--
4×expm1-udef exp-diff neg-log associate-+l- rem-cbrt-cube log-div
3×pow-unpow sub-div
2×expm1-log1p remove-posit16
1×sqrt-undiv sqrt-unprod pow-pow rem-log-exp rem-square-sqrt associate--r-

regimes5.4s (0.7%)

Accuracy

Total 30.7b remaining (19.5%)

Threshold costs 2.4b (1.5%)

10.4b47.8%Compound Interest
4.8b83%The quadratic formula (r2)
4.6b83.5%The quadratic formula (r1)
3.6b0%Complex division, imag part
2.4b0%Complex division, real part

localize3.4s (0.5%)

bsearch1.2s (0.2%)

end1.0ms (0.0%)