Details

series10.9m (54.1%)

Calls

320 calls:

3.4s
(- (- (+ (- (* (* (* x 18.0) (* y z)) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* j (* 27.0 k)))
1.6s
(* (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))))
981.0ms
(+ x (/ (- (fma (fma (tan z) (tan y) -1) (sin a) (* (+ (tan y) (tan z)) (cos a)))) (* (cos a) (fma (tan z) (tan y) -1))))
858.0ms
(/ (- (fma (fma (tan z) (tan y) -1) (sin a) (* (+ (tan y) (tan z)) (cos a)))) (* (cos a) (fma (tan z) (tan y) -1)))
854.0ms
(/ (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))))

simplify5.4m (26.9%)

sample2.1m (10.3%)

Algorithm
59×intervals
Results
37.1s263830×body80valid
26.5s208236×body80nan
19.8s21184×body1280valid
9.3s11301×body640valid
5.2s5339×body2560valid
2.9s5091×body320valid
823.0ms16512×pre80true
780.0ms2420×body160valid
654.0ms224×body5120valid

prune54.4s (4.5%)

rewrite34.5s (2.9%)

Algorithm
98×rewrite-expression-head
Calls

324 calls:

19.2s
(- (- (+ (- (* (* (* x 18.0) (* y z)) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* j (* 27.0 k)))
345.0ms
(+ (- (* (* x 18.0) (* (* y z) t)) (* (* a 4.0) t)) (* b c))
310.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))
270.0ms
(* (/ (+ 0 (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2)) (/ 1 a))
253.0ms
(* (cbrt (- (+ t 1.0) z)) (cbrt (- (+ t 1.0) z)))
Rules
7702×times-frac
5903×*-un-lft-identity
5832×add-sqr-sqrt
4930×add-cube-cbrt
2820×add-exp-log
1646×prod-exp
1573×cbrt-prod
1355×prod-diff
1218×add-cbrt-cube
830×unpow-prod-down
771×pow1
758×distribute-rgt-neg-in
753×distribute-lft-neg-in
677×cube-prod
621×associate-*r*
489×associate-*l*
456×add-log-exp
447×div-inv
429×cbrt-unprod
424×div-exp
392×distribute-rgt-in distribute-lft-in
369×associate-/l*
351×associate--l+
346×pow-exp
343×pow-to-exp
325×log1p-expm1-u
324×expm1-log1p-u
298×associate-/r*
285×difference-of-squares
279×distribute-lft-out--
264×sqrt-prod
243×distribute-lft-out
215×neg-mul-1
203×pow-prod-down
191×cbrt-undiv
181×fma-neg
175×flip3-- flip--
164×unswap-sqr
133×exp-prod
132×sqr-pow
110×log-pow
108×frac-times
106×associate-*l/
103×cbrt-div
102×associate-/r/
99×*-commutative
97×associate-*r/
84×sqrt-div
80×log-prod
70×fma-def
68×flip-+ flip3-+
67×unpow-prod-up
64×sub-neg
62×clear-num frac-2neg
61×unpow3 cube-mult
55×pow1/3
52×diff-log
42×associate-/l/ sqrt-pow1
40×tan-quot
38×associate-+l+ 1-exp associate-+r+ rec-exp
35×distribute-neg-frac
34×pow-unpow fma-udef
28×pow1/2
25×rem-sqrt-square
24×sum-log
21×swap-sqr
20×sin-mult
18×log-div
17×exp-sum
16×unpow2 neg-sub0
15×+-commutative frac-sub
14×cos-mult
13×pow-prod-up
12×pow-sub associate-+l- div-sub pow-pow
11×sub-div
10×un-div-inv exp-neg
9×exp-diff distribute-frac-neg
8×rem-exp-log associate-+r- pow-plus
7×inv-pow pow-sqr pow-flip
6×cube-div neg-log
5×associate--l- distribute-lft-neg-out distribute-neg-in
4×pow2
3×rem-cube-cbrt rem-log-exp
2×frac-add tan-sum distribute-rgt-out-- cos-sum cube-neg
1×expm1-udef log1p-udef sqrt-unprod pow3 log1p-expm1 expm1-log1p unsub-neg log-rec acos-asin distribute-rgt-neg-out exp-to-pow rem-cbrt-cube

regimes9.8s (0.8%)

Accuracy

Total 30.0b remaining (23.4%)

Threshold costs 4.2b (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%)

bsearch2.3s (0.2%)

end1.0ms (0.0%)