Details

sample1.3m (31.3%)

Algorithm
73×intervals
Results
25.9s294796×body80valid
9.7s13851×body1280valid
5.6s16767×body160valid
4.8s9523×body640valid
4.6s3885×body2560valid
3.1s2230×body10240exit
3.0s100646×pre80true
1.7s19317×body80nan
1.6s6744×body320valid
166.0ms227×body5120valid
6.0ms100×pre80false

prune57.3s (23.9%)

rewrite42.3s (17.6%)

Algorithm
112×rewrite-expression-head
Calls

309 calls:

4.3s
(+ (+ (* 333.75 (pow y 6.0)) (* (* x x) (- (- (- (* (* (* (* 11.0 x) x) y) y) (pow y 6.0)) (* 121.0 (pow y 4.0))) 2.0))) (* 5.5 (pow y 8.0)))
1.7s
(+ (+ (* 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)))
1.6s
(+ (+ (+ (* 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))) (/ 77617.0 (* 2.0 33096.0)))
1.5s
(* (- (/ 1.0 (+ (pow 1.0 3) (pow x 3))) (/ x (+ (pow 1.0 3) (pow x 3)))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))
994.0ms
(+ (* (* (* 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)) (* (* x1 x1) (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0)))
Rules
5698×times-frac
5179×*-un-lft-identity
4613×add-sqr-sqrt
2820×add-cube-cbrt
1816×cbrt-div
1740×add-exp-log
1662×associate-*r/
1487×add-cbrt-cube
1139×flip-- flip3--
1079×frac-times
1074×associate-*r*
839×unpow-prod-down
731×add-log-exp
717×frac-add
711×distribute-lft-out
690×pow1
687×difference-of-squares
596×associate-/r*
568×associate-*l/
553×prod-exp
547×associate-*l*
471×cbrt-unprod
464×div-exp
437×distribute-lft-out--
359×cbrt-undiv
345×cbrt-prod
307×cube-prod
290×sqrt-prod
285×sqr-pow
276×swap-sqr div-inv
239×flip-+ flip3-+
219×associate-/l*
193×associate-/r/
167×pow-prod-down
165×unswap-sqr
152×sum-log
112×sub-neg
97×diff-log
92×associate-/l/
91×unpow2
68×*-commutative
65×distribute-rgt-in distribute-lft-in
62×distribute-rgt-neg-in
61×clear-num frac-2neg
58×sqrt-div
51×pow-to-exp pow-exp
45×+-commutative
42×associate--l+
40×pow-unpow
38×unpow3 cube-mult
36×associate-+l+
33×distribute-lft-neg-in pow1/3
32×associate-+r+ log-prod
27×frac-sub 1-exp
24×distribute-lft-neg-out
23×rec-exp
22×pow-prod-up sum-cubes sqrt-pow1
20×cube-div pow1/2 div-sub
18×rem-sqrt-square associate--l- pow-plus
17×pow-pow
12×pow-sqr pow2 log-div
11×neg-sub0 neg-mul-1
log-pow neg-log associate--r+
sub-div
pow-flip exp-prod rem-cbrt-cube
inv-pow distribute-rgt-out-- unsub-neg
distribute-frac-neg exp-sum
un-div-inv associate-+r- difference-of-sqr-1 associate--r- exp-to-pow rem-log-exp
exp-diff rem-exp-log distribute-lft1-in distribute-rgt-out associate-+l-
rem-cube-cbrt difference-cubes sqrt-pow2 pow3 cube-unmult

series42.2s (17.6%)

Calls

309 calls:

1.0s
(- (* 9.0 (pow x 4.0)) (pow y 4))
965.0ms
(cbrt (+ (* (* (* 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)) (* (* (* x1 x1) (* (cbrt (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0)) (cbrt (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0)))) (cbrt (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0)))))
868.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ (cbrt i) n))
782.0ms
(+ (* 9.0 (pow x 4.0)) (- (pow y 4)))
730.0ms
(cbrt (+ (* (* (* 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)) (* (* (* x1 x1) (* (cbrt (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0)) (cbrt (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0)))) (cbrt (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0)))))

simplify14.2s (5.9%)

regimes4.6s (1.9%)

Accuracy

Total 40.1b remaining (9%)

Threshold costs 4.1b (0.9%)

10.3b58.9%Compound Interest
6.9b-2101.3%Rosa's TurbineBenchmark
4.8b75.7%Kahan p9 Example
4.5b84.1%The quadratic formula (r2)
3.0b-2.1%Complex division, real part

localize2.9s (1.2%)

bsearch1.4s (0.6%)

end1.0ms (0.0%)