Details

simplify5.7m (55.1%)

prune2.2m (20.9%)

sample1.5m (14.5%)

Algorithm
67×intervals
Results
36.8s270095×body80valid
11.6s13610×body1280valid
8.6s16900×body160valid
5.9s3865×body2560valid
5.3s9461×body640valid
4.3s2230×body10240exit
3.7s75830×pre80true
2.9s19682×body80nan
2.8s6714×body320valid
304.0ms240×body5120valid
10.0ms100×pre80false

series31.4s (5.1%)

Calls

310 calls:

909.0ms
(cbrt (- (* x2 2) (- x1 (* (* x1 x1) 3))))
844.0ms
(cbrt (- (* x2 2) (- x1 (* (* x1 x1) 3))))
803.0ms
(* (- (* x2 2) (- x1 (* (* x1 x1) 3))) (* (/ 1 (+ 1 (* x1 x1))) (+ (* (* x1 x1) 3) (* (* 2 (+ 1 (* x1 x1))) (* (- (/ (- (* x2 2) (- x1 (* (* x1 x1) 3))) (+ 1 (* x1 x1))) 3) x1)))))
759.0ms
(* (/ (- (* 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))))
511.0ms
(cbrt (+ (- 2 (* x x)) (* (* x (* x x)) 2/3)))

rewrite16.3s (2.6%)

Algorithm
100×rewrite-expression-head
Calls

310 calls:

985.0ms
(+ (+ (+ (* 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)))
918.0ms
(+ (+ (* 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)))
507.0ms
(+ (* (* (* 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)))
463.0ms
(* (- (* x y) z) (+ (* x y) z))
422.0ms
(- (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) 3)
Rules
8252×times-frac
6539×*-un-lft-identity
6537×add-sqr-sqrt
3266×add-cube-cbrt
1594×add-exp-log
1393×add-cbrt-cube
1244×pow1
1102×difference-of-squares
1096×distribute-lft-out--
851×associate-*r*
768×sqrt-prod
729×add-log-exp
559×associate-/l*
548×distribute-lft-out
465×div-inv
464×prod-exp
462×associate-*l*
431×div-exp
386×cbrt-unprod
354×associate-/r*
339×cbrt-undiv
309×flip-+ flip3-+
290×pow-prod-down
263×associate-/r/
217×frac-times pow-prod-up
201×flip3-- flip--
200×unpow-prod-down
180×associate-*l/
176×sum-log
175×associate-*r/
133×sqr-pow
126×unswap-sqr
109×log-prod
107×pow-sqr
98×difference-of-sqr-1
93×sqrt-div
92×frac-sub
90×cbrt-div
89×pow-plus
87×cbrt-prod
86×associate-/l/
81×sub-neg
75×frac-2neg clear-num *-commutative
74×exp-neg diff-log
71×exp-prod
66×pow2
62×neg-sub0
59×exp-diff
55×swap-sqr
47×+-commutative
46×distribute-rgt-in log-pow distribute-lft-in
43×sqrt-pow1 pow1/2
41×distribute-rgt-neg-in
40×pow-flip
39×exp-sum
36×1-exp rec-exp
32×distribute-lft-neg-in
25×associate-+l+
24×div-sub frac-add
22×associate--l+ rem-sqrt-square
20×associate-+r+ un-div-inv
17×pow1/3
16×pow-unpow
14×log-div
13×rem-exp-log
12×pow-exp distribute-rgt-out-- associate--r+ neg-mul-1 pow-to-exp
11×associate--l- inv-pow
8×difference-of-sqr--1 pow-div
7×neg-log sqrt-unprod rem-log-exp
6×pow-pow
5×cube-unmult associate-+l-
4×distribute-lft-neg-out associate-+r- distribute-frac-neg sub-div
2×pow3 associate--r-
1×distribute-lft1-in exp-to-pow remove-double-div rem-square-sqrt rem-cbrt-cube unsub-neg

regimes6.1s (1.0%)

Accuracy

Total 35.2b remaining (13.4%)

Threshold costs 3.5b (1.3%)

11.0b51.2%Compound Interest
4.3b77.6%Kahan p9 Example
4.3b84.8%The quadratic formula (r2)
4.1b85.4%The quadratic formula (r1)
2.8b0%Complex division, real part

localize3.7s (0.6%)

bsearch1.5s (0.2%)

end1.0ms (0.0%)