Details

simplify38.7m (56.7%)

prune9.5m (13.9%)

sample9.0m (13.2%)

Algorithm
539×intervals
Results
3.4m2650395×body80valid
1.0m537826×body80nan
35.9s46444×body1280valid
24.5s44586×body640valid
9.4s25567×body320valid
7.1s5711×body2560valid
3.8s13639×body160valid
1.5s1543×body10240exit
170.0ms655×body640nan
153.0ms479×body1280nan
109.0ms417×body320nan
90.0ms34×body5120valid
59.0ms239×body160nan

series6.0m (8.7%)

Calls

2481 calls:

5.9s
(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
5.6s
(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
4.0s
(+ (* (* a b) (* (* a b) (* a b))) (* (+ (* x y) (* z t)) (* (+ (* x y) (* z t)) (+ (* x y) (* z t)))))
2.9s
(* (/ 1 (+ (sqrt 2.0) (sqrt (+ x y)))) (- (/ x (- (sqrt 2.0) (sqrt (+ x y)))) (/ y (- (sqrt 2.0) (sqrt (+ x y))))))
1.7s
(* (/ (cbrt (- z t)) (cbrt (cbrt (- a t)))) (* (/ (cbrt (- z t)) (cbrt (- a t))) (/ y (cbrt (- a t)))))

rewrite2.2m (3.3%)

Algorithm
878×rewrite-expression-head
Calls

2481 calls:

6.3s
(+ (+ (+ (+ (+ (* (log (cbrt y)) (* 3 x)) z) t) a) (* (- b 0.5) (log c))) (* y i))
2.5s
(+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i))
2.5s
(* (cbrt (+ x (+ z (+ (+ y x) (+ y x))))) (cbrt (+ x (+ z (+ (+ y x) (+ y x))))))
2.2s
(* (cbrt (+ x (+ z (+ (+ y x) (+ y x))))) (cbrt (+ x (+ z (+ (+ y x) (+ y x))))))
2.2s
(* (cbrt (+ x (+ z (+ (+ y x) (+ y x))))) (cbrt (+ x (+ z (+ (+ y x) (+ y x))))))
Rules
36008×times-frac
34809×*-un-lft-identity
32195×add-sqr-sqrt
22059×add-cube-cbrt
12747×cbrt-div
12334×associate-*r/
12140×add-exp-log
9286×add-cbrt-cube
7048×pow1
6367×frac-times
6172×associate-*r*
6060×cbrt-prod
5172×associate-*l*
4429×frac-sub
3896×add-log-exp
3763×prod-exp
3697×flip3-- flip--
3607×distribute-lft-out--
3477×difference-of-squares
3395×distribute-lft-out
3281×associate-/r*
3051×cbrt-unprod
2828×div-exp
2667×tanh-def
2571×associate-*l/
2562×sqrt-prod
2438×associate-/l*
2382×associate-/r/
2096×pow-prod-down
1959×div-inv
1953×cbrt-undiv
1671×flip-+ flip3-+
1380×log-prod
1252×unswap-sqr
1074×distribute-rgt-in distribute-lft-in
991×swap-sqr
823×pow1/3
811×*-commutative
683×sub-neg
589×sqrt-div
541×associate-/l/
532×frac-2neg clear-num
504×sum-log
384×pow-prod-up
361×log-pow
333×1-exp
328×exp-prod
326×associate--l+
319×sqrt-pow1
311×rec-exp
307×diff-log
283×associate-+r+
278×pow-sqr
276×frac-add
274×+-commutative
219×pow1/2
182×pow-plus
179×associate-+l+
158×exp-sum
143×div-sub
134×pow2
131×cube-unmult
85×rem-log-exp log-div
84×pow3
78×rem-sqrt-square
69×pow-flip
65×associate--r+
64×inv-pow
62×pow-exp
60×distribute-rgt-out
53×difference-cubes
48×distribute-rgt-out--
44×un-div-inv
41×distribute-rgt-neg-in
40×pow-unpow sum-cubes cosh-def associate-+l-
38×associate-+r-
37×distribute-lft-neg-in
35×unpow-prod-down
33×pow-pow
32×distribute-lft-neg-out
30×cos-mult
22×sub-div rem-exp-log
20×distribute-rgt-neg-out pow-to-exp
19×sqrt-unprod
18×unpow1/3 unsub-neg
17×sqr-pow
16×sinh-def associate--r-
15×neg-mul-1
14×rem-cbrt-cube count-2
13×sqr-cos
12×associate--l- rem-square-sqrt
11×distribute-lft1-in distribute-rgt1-in
9×exp-diff
7×exp-to-pow
6×unpow-prod-up
5×sin-2 diff-cos
4×neg-sub0
3×sqrt-undiv cos-diff
2×pow-sub exp-neg tan-quot cos-sum exp-lft-cube e-exp-1
1×sin-sum distribute-frac-neg sin-cos-mult sin-mult sum-cos sqr-neg

regimes2.2m (3.2%)

Accuracy

Total 190.3b remaining (35.1%)

Threshold costs 24.8b (4.6%)

12.9b58.4%Diagrams.TwoD.Arc:arcBetween from diagrams-lib-1.3.0.3
11.2b-33%Linear.Matrix:det44 from linear-1.19.1.3
9.6b58.6%Data.Octree.Internal:octantDistance from Octree-0.5.4.2
9.4b39.3%AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1
7.1b63.4%Data.Array.Repa.Algorithms.Pixel:doubleRmsOfRGB8 from repa-algorithms-3.4.0.1

localize30.0s (0.7%)

bsearch13.0s (0.3%)

end6.0ms (0.0%)