Details

simplify6.8m (61.0%)

sample1.3m (12.0%)

Algorithm
73×intervals
Results
26.0s285416×body80valid
10.0s25113×body160valid
9.9s13589×body1280valid
4.6s3866×body2560valid
4.5s2153×body10240exit
3.9s9505×body640valid
2.7s100646×pre80true
1.7s6916×body320valid
1.7s19387×body80nan
220.0ms235×body5120valid
6.0ms100×pre80false

prune1.1m (10.3%)

series50.5s (7.6%)

Calls

328 calls:

6.5s
(* (* (sqrt a) (sqrt (+ (+ b c) d))) (sqrt (* a (+ (+ b c) d))))
925.0ms
(- (* 9.0 (pow x 4.0)) (pow y 4.0))
742.0ms
(+ (+ (* (* x x) (- (- (* 11.0 (* (* x y) (* x y))) (pow y 6.0)) (+ 2.0 (* (pow y 4.0) 121.0)))) (* (pow y 6.0) 333.75)) (+ (* (pow y 8.0) 5.5) (/ x (* 2.0 y))))
704.0ms
(- (* 9.0 (pow x 4.0)) (* (* y y) (* y y)))
694.0ms
(- (* 9.0 (pow x 4.0)) (* (* y y) (* y y)))

rewrite46.3s (7.0%)

Algorithm
110×rewrite-expression-head
Calls

328 calls:

9.4s
(+ (+ (* (* (* 2.0 x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)) (/ (+ (* (* 8.0 x2) (* x1 x1)) (- (* 12.0 (* (* x1 x1) (* x1 x1))) (* (* 4.0 x1) (* x1 x1)))) (+ (* x1 x1) 1.0))) (* (- 6.0) (* x1 x1)))
4.0s
(+ (+ (* (* (* 2.0 x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)) (* (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (* x1 x1))) (* (- 6.0) (* x1 x1)))
3.9s
(+ (+ (* (* (* 2.0 x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)) (/ (* (* 4.0 (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1)) (* x1 x1)) (+ (* x1 x1) 1.0))) (* (- 6.0) (* x1 x1)))
2.0s
(+ (+ (* (* x x) (- (- (* 11.0 (* (* x y) (* x y))) (pow y 6.0)) (+ 2.0 (* (pow y 4.0) 121.0)))) (* (pow y 6.0) 333.75)) (+ (* (pow y 8.0) 5.5) (/ x (* 2.0 y))))
1.3s
(+ (+ (* 333.75 (pow 33096.0 6.0)) (* (* 77617.0 77617.0) (+ (+ (+ (* (* 11.0 (* 77617.0 77617.0)) (* 33096.0 33096.0)) (- (pow 33096.0 6.0))) (* -121.0 (pow 33096.0 4.0))) -2.0))) (* 5.5 (pow 33096.0 8.0)))
Rules
4162×times-frac
4017×*-un-lft-identity
3695×add-sqr-sqrt
2530×add-cube-cbrt
1868×add-exp-log
1739×add-cbrt-cube
1213×pow1
910×associate-*r*
772×add-log-exp
681×prod-exp
666×associate-*l*
635×cbrt-unprod
513×distribute-lft-out
466×frac-times
427×associate-*r/
422×pow-prod-down
379×associate-/r*
376×div-exp
371×difference-of-squares
369×sqrt-prod
339×flip3-- flip--
338×flip-+ flip3-+
330×cbrt-undiv
304×sqrt-div
285×associate-/l*
271×associate-*l/
253×div-inv
249×distribute-lft-out--
234×associate-/r/
170×swap-sqr
168×sum-log
147×unswap-sqr
127×cbrt-div
112×sub-neg
109×sqrt-pow1
104×frac-sub
101×unpow-prod-down
99×*-commutative
94×diff-log
77×pow-prod-up
65×frac-2neg clear-num
64×sqr-pow
62×pow1/2
61×distribute-rgt-in distribute-lft-in
57×associate-/l/
49×frac-add
45×pow-plus log-pow
44×log-prod +-commutative pow-sqr
43×distribute-rgt-neg-in
33×distribute-lft-neg-in
32×cbrt-prod
29×exp-prod
25×pow2
23×rem-sqrt-square
21×associate-+l+ associate-+r+ div-sub
19×1-exp rec-exp associate--r+
18×pow3
16×associate--l+
15×log-div
14×pow-exp pow-to-exp
13×distribute-lft-neg-out associate--l- pow1/3
11×neg-mul-1
rem-log-exp distribute-rgt-out--
pow-flip inv-pow
associate-+r- sqrt-unprod
neg-sub0 exp-to-pow sum-cubes
exp-sum distribute-frac-neg neg-log un-div-inv rem-cbrt-cube unsub-neg
pow-unpow sub-div rem-exp-log associate-+l- rem-square-sqrt associate--r-
exp-diff
distribute-lft1-in cube-unmult pow-pow lft-mult-inverse

regimes7.9s (1.2%)

Accuracy

Total 37.0b remaining (8.4%)

Threshold costs 3.0b (0.7%)

10.7b53.5%Compound Interest
4.8b83.3%The quadratic formula (r1)
4.5b78.5%Kahan p9 Example
3.7b87.1%The quadratic formula (r2)
3.1b0%Complex division, imag part

localize4.7s (0.7%)

bsearch1.5s (0.2%)

end1.0ms (0.0%)