Details

simplify7.9m (60.3%)

prune2.7m (20.6%)

sample1.5m (11.4%)

Algorithm
67×intervals
Results
35.9s269541×body80valid
13.6s13870×body1280valid
7.9s16814×body160valid
5.5s9291×body640valid
4.8s3849×body2560valid
4.1s75773×pre80true
3.9s2233×body10240exit
3.4s6892×body320valid
2.4s19430×body80nan
364.0ms237×body5120valid
10.0ms100×pre80false

series28.8s (3.6%)

Calls

315 calls:

802.0ms
(* (/ (- (* x2 2) (- x1 (* (* x1 x1) 3))) (+ 1 (* x1 x1))) (+ (* (* x1 x1) 3) (* (* 2 (+ 1 (* x1 x1))) (* (- (/ (- (* x2 2) (- x1 (* (* x1 x1) 3))) (+ 1 (* x1 x1))) 3) x1))))
550.0ms
(* (cbrt a) (cbrt a))
542.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ 1 n))
493.0ms
(/ (sqrt (/ (- 1 v) (* (- 3 (* 2 v)) 0.125))) w)
459.0ms
(+ (* x y) z)

rewrite20.4s (2.6%)

Algorithm
106×rewrite-expression-head
Calls

315 calls:

1.6s
(cbrt (/ (* (* (* (+ (* a (* a a)) (* b (* b b))) (+ (* a (* a a)) (* b (* b b)))) (* (+ b a) (- a b))) (* (* (+ (* a (* a a)) (* b (* b b))) (+ (* a (* a a)) (* b (* b b)))) (* (+ b a) (- a b)))) (* (* (+ (* b (- b a)) (* a a)) (* (+ (* b (- b a)) (* a a)) (- a b))) (* (+ (* b (- b a)) (* a a)) (* (+ (* b (- b a)) (* a a)) (- a b))))))
1.1s
(+ (+ (+ (* 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)))
920.0ms
(+ (+ (* 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)))
691.0ms
(- (+ (exp (+ (- x) (* x eps))) (/ (exp (+ (- x) (* x eps))) eps)) (- (/ (exp (- (- x) (* x eps))) eps) (exp (- (- x) (* x eps)))))
568.0ms
(+ (* (* (* 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)))
Rules
8968×frac-times
5172×flip-+ flip3-+
3814×times-frac
3762×add-sqr-sqrt
3747×*-un-lft-identity
2839×associate-*r/
2356×associate-*l/
2191×pow1
2134×add-cube-cbrt
1729×add-exp-log
1586×add-cbrt-cube
1149×flip3-- flip--
949×associate-/r/
906×cbrt-prod
885×associate-*r*
750×cbrt-div
747×add-log-exp
734×difference-of-squares
599×prod-exp
575×pow-prod-up
570×associate-*l*
539×cbrt-unprod
523×pow-prod-down
403×sqrt-prod
383×distribute-lft-out
377×div-exp
351×associate-/l*
349×distribute-lft-out--
334×cbrt-undiv
315×insert-posit16
275×pow-plus
271×div-inv
257×associate-/r*
256×pow-sqr
216×unpow-prod-down
192×sqr-pow
175×difference-of-sqr-1
169×sum-log pow2
135×unswap-sqr
102×sub-neg exp-prod
99×distribute-rgt-neg-in
94×swap-sqr
90×*-commutative distribute-lft-neg-in
88×sqrt-div
87×diff-log
73×distribute-rgt-in associate-/l/ distribute-lft-in
67×log-pow
62×frac-2neg clear-num
55×log-prod
50×pow-flip
42×+-commutative
40×frac-sub
31×frac-add
30×neg-mul-1
28×div-sub
27×associate-+l+
25×sqrt-pow1 exp-sum rem-sqrt-square
24×pow1/2
21×1-exp rec-exp
17×cube-unmult pow1/3
16×log-div
15×associate--l-
14×associate--l+
12×neg-sub0 exp-diff associate--r+ rem-exp-log
11×associate-+r+
10×pow-exp pow3 pow-to-exp
9×rem-log-exp
8×pow-div inv-pow sum-cubes
7×distribute-frac-neg associate-+l-
6×pow-unpow neg-log
5×remove-posit16 distribute-rgt-out-- sub-div difference-of-sqr--1
4×distribute-lft-neg-out un-div-inv exp-to-pow
3×associate--r-
2×pow-pow distribute-rgt-out
1×distribute-lft1-in associate-+r- rem-cbrt-cube exp-lft-cube unsub-neg distribute-rgt1-in

regimes5.9s (0.8%)

Accuracy

Total 35.5b remaining (15.7%)

Threshold costs 2.4b (1%)

12.1b46.9%Compound Interest
5.7b79.7%The quadratic formula (r2)
4.7b75.9%Kahan p9 Example
4.4b84.7%The quadratic formula (r1)
2.6b0%Complex division, real part

localize3.9s (0.5%)

bsearch1.5s (0.2%)

end1.0ms (0.0%)