Details

sample47.2s (37.2%)

Algorithm
73×intervals
Results
18.5s293045×body80valid
7.0s14380×body1280valid
3.1s3816×body2560valid
2.9s9566×body640valid
2.9s16789×body160valid
2.4s100604×pre80true
1.2s6863×body320valid
1.0s19293×body80nan
282.0ms200×body10240exit
226.0ms2046×body80overflowed
144.0ms235×body5120valid
9.0ms100×pre80false

prune26.0s (20.5%)

series24.4s (19.2%)

Calls

307 calls:

421.0ms
(cbrt (pow (- (* 9.0 (pow x 4.0)) (pow y 4)) 3))
410.0ms
(- (* 9.0 (pow x 4.0)) (pow y 4))
407.0ms
(+ (* 9.0 (pow x 4.0)) (- (pow y 4)))
405.0ms
(- (* 9.0 (pow x 4.0)) (pow y 4.0))
402.0ms
(cbrt (pow (- (* 9.0 (pow x 4.0)) (pow y 4.0)) 3))

rewrite14.1s (11.1%)

Algorithm
109×rewrite-expression-head
Calls

307 calls:

1.5s
(+ (+ (* (* (* 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 (* (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) x1))) (* (* (- 6.0) x1) x1))
1.2s
(+ (+ (* 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)))
597.0ms
(+ (+ (+ (* 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)))
556.0ms
(+ (+ (* 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)))
460.0ms
(* (* (* 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))
Rules
3329×add-sqr-sqrt
3288×*-un-lft-identity
3012×times-frac
2020×add-cube-cbrt
1734×add-exp-log
1532×add-cbrt-cube
942×associate-*r*
801×pow1
709×add-log-exp
692×associate-*l*
608×prod-exp
518×cbrt-unprod
489×sqrt-prod
415×distribute-lft-out
394×difference-of-squares
375×div-exp
326×cbrt-undiv
317×unpow-prod-down
292×flip-+ flip3-+
276×associate-*r/
254×associate-/l*
239×frac-times
237×associate-/r/
232×associate-/r*
226×distribute-lft-out--
223×cbrt-prod
221×flip3-- flip--
211×unswap-sqr
206×div-inv
196×pow-prod-down
165×sum-log
149×associate-*l/
143×sqr-pow
136×cube-prod
121×swap-sqr
116×sqrt-div
106×sub-neg
100×frac-sub
92×*-commutative
85×distribute-rgt-in distribute-lft-in
80×exp-neg log-prod
73×associate-/l/
72×diff-log
71×neg-sub0
67×sqrt-pow1
63×frac-add
62×exp-diff
56×distribute-rgt-neg-in
53×clear-num frac-2neg
50×pow-exp
47×pow1/2 unpow2
46×cbrt-div
45×+-commutative
39×pow-to-exp
35×pow-prod-up
34×associate-+l+
33×associate-+r+
30×distribute-lft-neg-in rem-sqrt-square
26×un-div-inv log-pow
25×1-exp rec-exp
23×pow-sqr
22×pow-plus
19×pow-unpow div-sub
18×pow2
17×unpow3 cube-mult
16×log-div
14×cube-div rem-cube-cbrt
13×associate--l+
12×pow-pow
11×pow1/3
10×distribute-lft-neg-out neg-mul-1
neg-log associate--l-
pow-flip
rem-log-exp
inv-pow sum-cubes
associate-+r- distribute-frac-neg exp-prod rem-cbrt-cube associate--r+
unsub-neg exp-sum
distribute-lft1-in distribute-rgt-out-- associate-+l-
sqrt-undiv rem-exp-log sqrt-unprod pow3 cube-unmult sub-div rem-square-sqrt distribute-rgt-out exp-to-pow

simplify9.6s (7.6%)

Algorithm
179×egg-herbie

regimes3.0s (2.3%)

Accuracy

Total 26.3b remaining (6.2%)

Threshold costs 2.7b (0.6%)

6.1b66.1%Compound Interest
4.5b79%Kahan p9 Example
3.6b86%The quadratic formula (r2)
3.2b0%Complex division, imag part
2.9b0%Complex division, real part

localize1.4s (1.1%)

bsearch1.1s (0.9%)

end1.0ms (0.0%)