Details

simplify3.7m

prune2.9m

sample1.5m

Algorithm
64×intervals
Results
38.7s269429×body80valid
12.6s13917×body1280valid
7.3s16851×body160valid
5.6s3921×body2560valid
5.2s9428×body640valid
3.6s1998×body10240exit
3.3s75774×pre80true
2.9s6772×body320valid
2.9s19322×body80nan
303.0ms261×body5120valid

rewrite30.1s

Algorithm
107×rewrite-expression-head
Calls

332 calls:

Slowest
3.0s
(* (/ (+ (* (* x1 x1) 3) (- (* x2 2) x1)) (+ 1 (* x1 x1))) (+ (* (* (- (/ (+ (* (* x1 x1) 3) (- (* x2 2) x1)) (+ 1 (* x1 x1))) 3) (+ 1 (* x1 x1))) (* x1 2)) (* (* x1 x1) 3)))
2.9s
(* (/ (+ (* (* x1 x1) 3) (- (* x2 2) x1)) (+ 1 (* x1 x1))) (+ (* (* (- (/ (+ (* (* x1 x1) 3) (- (* x2 2) x1)) (+ 1 (* x1 x1))) 3) (+ 1 (* x1 x1))) (* x1 2)) (* (* x1 x1) 3)))
2.7s
(* (/ (+ (* (* x1 x1) 3) (- (* x2 2) x1)) (+ 1 (* x1 x1))) (+ (* (* (- (/ (+ (* (* x1 x1) 3) (- (* x2 2) x1)) (+ 1 (* x1 x1))) 3) (+ 1 (* x1 x1))) (* x1 2)) (* (* x1 x1) 3)))
1.2s
(+ (log (* (exp (+ b (+ c d))) (exp e))) a)
973.0ms
(+ (+ (+ (* 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)))
Rules
7753×times-frac
6993×*-un-lft-identity
6911×add-sqr-sqrt
6315×frac-times
4939×flip-+ flip3-+
4262×associate-*l/
3310×associate-*r/
3014×add-cube-cbrt
2176×pow1
1908×add-exp-log
1721×add-cbrt-cube
1561×difference-of-squares
1268×distribute-lft-out--
1069×associate-*r*
904×frac-add
756×cbrt-div
743×prod-exp
742×associate-/l/
688×add-log-exp
681×distribute-lft-out
645×cbrt-unprod
581×div-inv
572×pow-prod-down
511×associate-/l*
506×associate-*l*
498×pow-prod-up
483×associate-/r/
360×div-exp
346×sqrt-prod
332×insert-posit16
310×cbrt-undiv
302×pow-plus
291×associate-/r*
244×flip3-- flip--
217×pow-sqr
190×unpow-prod-down
153×swap-sqr
146×exp-prod
129×sum-log
126×sqr-pow
124×pow2
122×unswap-sqr
110×distribute-rgt-neg-in
100×*-commutative
99×log-pow
95×sqrt-div
90×difference-of-sqr-1
88×sub-neg
86×log-prod
72×diff-log
71×distribute-rgt-in distribute-lft-in
66×frac-2neg clear-num
60×pow-flip
59×cbrt-prod
57×distribute-lft-neg-in
56×exp-sum
48×sqrt-pow1
44×pow1/2
41×+-commutative
35×rem-sqrt-square
30×div-sub
28×pow3
27×1-exp rec-exp
23×frac-sub
21×associate-+l+
19×neg-mul-1
16×associate-+r+ pow1/3
14×rem-log-exp log-div
12×pow-exp pow-to-exp rem-exp-log
10×cube-unmult
distribute-rgt-out-- associate--l+
distribute-lft1-in associate--l- distribute-frac-neg
difference-of-sqr--1 exp-to-pow
neg-sub0 exp-diff pow-unpow distribute-lft-neg-out inv-pow
un-div-inv
cube-prod neg-log sum-cubes
associate-+r- associate--r+
sub-div pow-pow e-exp-1
remove-posit16 unpow3 sqrt-unprod associate-+l- rem-square-sqrt rem-cbrt-cube cube-mult associate--r- distribute-rgt-out distribute-rgt1-in

series26.0s

Calls

332 calls:

Slowest
566.0ms
(* (/ (+ (* (* x1 x1) 3) (- (* x2 2) x1)) (+ 1 (* x1 x1))) (+ (* (* (- (/ (+ (* (* x1 x1) 3) (- (* x2 2) x1)) (+ 1 (* x1 x1))) 3) (+ 1 (* x1 x1))) (* x1 2)) (* (* x1 x1) 3)))
533.0ms
(* (/ (+ (* (* x1 x1) 3) (- (* x2 2) x1)) (+ 1 (* x1 x1))) (+ (* (* (- (/ (+ (* (* x1 x1) 3) (- (* x2 2) x1)) (+ 1 (* x1 x1))) 3) (+ 1 (* x1 x1))) (* x1 2)) (* (* x1 x1) 3)))
505.0ms
(* (/ (+ (* (* x1 x1) 3) (- (* x2 2) x1)) (+ 1 (* x1 x1))) (+ (* (* (- (/ (+ (* (* x1 x1) 3) (- (* x2 2) x1)) (+ 1 (* x1 x1))) 3) (+ 1 (* x1 x1))) (* x1 2)) (* (* x1 x1) 3)))
494.0ms
(+ (* (* (* 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)))
481.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))

regimes4.8s

Accuracy

Total 34.9b remaining (15.8%)

Threshold costs 2.3b (1.1%)

12.8b54%Compound Interest
4.7b76.6%Kahan p9 Example
4.5b84.1%The quadratic formula (r2)
4.3b84.7%The quadratic formula (r1)
2.6b0%Complex division, imag part

localize4.0s

bsearch1.4s

end1.0ms