Details

series11.0m (54.3%)

Calls

321 calls:

3.2s
(- (- (+ (- (* (* (* x 18.0) (* y z)) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* j (* 27.0 k)))
1.8s
(* (cbrt (fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t))) (cbrt (fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t))))
1.4s
(fma x (- (* y z) (* t a)) (fma b (- (* i a) (* c z)) (+ (* (* j c) t) (- (* y (* i j))))))
914.0ms
(+ x (/ (- (fma (fma (tan z) (tan y) -1) (sin a) (* (+ (tan y) (tan z)) (cos a)))) (* (cos a) (fma (tan z) (tan y) -1))))
892.0ms
(/ (fma (fma (fma (fma x y z) y 27464.7644705) y 230661.510616) y t) (* (cbrt (fma (fma (fma (+ y a) y b) y c) y i)) (cbrt (fma (fma (fma (+ y a) y b) y c) y i))))

simplify5.3m (26.3%)

sample2.2m (10.7%)

Algorithm
59×intervals
Results
34.5s263830×body80valid
25.0s208236×body80nan
21.3s21184×body1280valid
7.9s11301×body640valid
4.7s5339×body2560valid
2.7s5091×body320valid
1.1s2420×body160valid
819.0ms16512×pre80true
92.0ms224×body5120valid

prune55.0s (4.5%)

rewrite34.5s (2.9%)

Algorithm
99×rewrite-expression-head
Calls

325 calls:

19.5s
(- (- (+ (- (* (* (* x 18.0) (* y z)) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* j (* 27.0 k)))
350.0ms
(+ (- (* (* x 18.0) (* (* y z) t)) (* (* a 4.0) t)) (* b c))
321.0ms
(* (* (* (* x 18.0) y) z) t)
286.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
270.0ms
(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
Rules
7615×times-frac
5850×*-un-lft-identity
5762×add-sqr-sqrt
4877×add-cube-cbrt
2810×add-exp-log
1641×prod-exp
1587×cbrt-prod
1352×prod-diff
1208×add-cbrt-cube
841×unpow-prod-down
768×pow1
729×distribute-rgt-neg-in
724×distribute-lft-neg-in
685×cube-prod
591×associate-*r*
455×add-log-exp
450×associate-*l*
444×div-inv
424×cbrt-unprod
422×div-exp
392×distribute-rgt-in distribute-lft-in
357×associate-/l*
351×associate--l+
349×pow-exp
345×pow-to-exp
326×log1p-expm1-u
325×expm1-log1p-u
298×associate-/r*
283×difference-of-squares
279×distribute-lft-out--
264×sqrt-prod
243×distribute-lft-out
203×neg-mul-1
200×pow-prod-down
189×cbrt-undiv
181×fma-neg
175×flip3-- flip--
158×unswap-sqr
135×sqr-pow
130×exp-prod
110×log-pow
108×frac-times
103×cbrt-div associate-*l/
102×associate-/r/
97×associate-*r/
96×*-commutative
84×sqrt-div
80×log-prod
70×fma-def
68×flip-+ unpow-prod-up flip3-+
63×unpow3 cube-mult sub-neg
62×clear-num frac-2neg
56×pow1/3
51×diff-log
42×associate-/l/ sqrt-pow1
41×fma-udef
40×pow-unpow tan-quot
38×associate-+l+ 1-exp associate-+r+ rec-exp
35×distribute-neg-frac
28×pow1/2
25×rem-sqrt-square
24×sum-log
21×swap-sqr
20×sin-mult
18×exp-sum log-div
17×pow-pow
16×unpow2
15×+-commutative frac-sub
14×cos-mult
13×pow-prod-up neg-sub0
12×pow-sub associate-+l-
11×sub-div
10×un-div-inv div-sub
9×exp-neg
8×exp-diff associate-+r- pow-plus
7×rem-exp-log inv-pow pow-sqr pow-flip
6×cube-div distribute-frac-neg
5×associate--l- distribute-lft-neg-out
4×rem-cube-cbrt pow2 neg-log
3×rem-log-exp
2×cos-sum frac-add tan-sum distribute-rgt-out-- rem-cbrt-cube cube-neg
1×expm1-udef e-exp-1 log1p-udef pow3 log1p-expm1 expm1-log1p unsub-neg log-rec acos-asin sqrt-unprod exp-to-pow

regimes9.6s (0.8%)

Accuracy

Total 30.1b remaining (23.5%)

Threshold costs 4.3b (3.3%)

6.6b15.3%Linear.Matrix:det33 from linear-1.19.1.3
4.5b84.3%The quadratic formula (r1)
2.2b0%cos(2*x)/(cos^2(x)*sin^2(x))
2.0b0%Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2
1.9b68%Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1

localize3.7s (0.3%)

bsearch2.4s (0.2%)

end1.0ms (0.0%)