Details

simplify5.5m (43.4%)

sample3.0m (23.4%)

Algorithm
60×intervals
Results
1.2m336284×body80valid
24.7s207529×body80nan
20.0s21276×body1280valid
8.7s11136×body640valid
5.4s5272×body2560valid
3.3s5091×body320valid
1.3s2515×body160valid
888.0ms16512×pre80true
142.0ms217×body5120valid

prune2.2m (17.1%)

series1.1m (8.9%)

Calls

347 calls:

2.2s
(/ (* (cbrt (+ (* (fma (fma (fma x y z) y 27464.7644705) y 230661.510616) y) t)) (cbrt (+ (* (fma (fma (fma x y z) y 27464.7644705) y 230661.510616) y) t))) (/ (fma (fma (fma (+ y a) y b) y c) y i) (cbrt (fma (fma (fma (fma x y z) y 27464.7644705) y 230661.510616) y t))))
1.3s
(* (sqrt (+ (sqrt x) (sqrt 1.0))) (* (sqrt (- (sqrt x) (sqrt 1.0))) (sqrt x)))
909.0ms
(fma (- (cbrt x)) (* (cbrt x) (cbrt x)) (* (cbrt x) (* (cbrt x) (cbrt x))))
812.0ms
(fma (- (cbrt x)) (* (cbrt x) (cbrt x)) (* (cbrt x) (* (cbrt x) (cbrt x))))
810.0ms
(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x))

regimes22.4s (3.0%)

Accuracy

Total 47.8b remaining (29.6%)

Threshold costs 1.9b (1.2%)

12.2b-14.6%Linear.Matrix:det44 from linear-1.19.1.3
11.5b-6.5%Linear.Matrix:det33 from linear-1.19.1.3
4.4b87.3%The quadratic formula (r1)
3.9b28.1%Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1
2.2b0%cos(2*x)/(cos^2(x)*sin^2(x))

rewrite22.0s (2.9%)

Algorithm
104×rewrite-expression-head
Calls

347 calls:

873.0ms
(* (* x (sqrt (/ (pow z y) (/ (exp b) (pow a (- t 1.0)))))) (/ (sqrt (/ (pow z y) (/ (exp b) (pow a (- t 1.0))))) y))
868.0ms
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x)))
827.0ms
(* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x))
804.0ms
(* x (/ (/ (pow z y) (/ (exp b) (pow a (- t 1.0)))) y))
510.0ms
(* (* x (sqrt (pow z y))) (/ (sqrt (/ (pow z y) (/ (exp b) (pow a (- t 1.0))))) y))
Rules
24156×times-frac
14689×*-un-lft-identity
14602×add-sqr-sqrt
13332×add-cube-cbrt
5066×prod-diff
4349×associate-*r*
3769×unpow-prod-down
3689×unpow-prod-up
3435×sqrt-prod
3234×add-exp-log
2536×cbrt-prod
2120×prod-exp
1183×add-cbrt-cube
1155×sqr-pow
858×distribute-rgt-neg-in
855×pow1
794×distribute-lft-neg-in
770×distribute-rgt-in distribute-lft-in
704×associate--l+
693×associate-*l*
685×associate-/r*
671×div-inv
521×pow-exp
520×pow-to-exp
485×add-log-exp
474×cube-prod
470×div-exp
418×sub-neg
393×distribute-lft-out--
383×cbrt-unprod
355×difference-of-squares
347×log1p-expm1-u expm1-log1p-u
334×associate-/l*
304×distribute-lft-out
231×neg-mul-1
230×flip3-- flip--
228×fma-neg
213×pow-prod-down
200×cbrt-undiv
196×associate-/r/
185×unswap-sqr
181×swap-sqr
134×associate-*r/
113×associate-+r+
108×fma-def
106×cbrt-div log-pow *-commutative
102×pow-sub log-prod
95×frac-times
94×associate-*l/
83×pow1/3
75×associate-+l+ sqrt-div
64×clear-num frac-2neg
54×flip-+ flip3-+
50×unpow3 cube-mult
47×diff-log
40×sum-log
37×associate-/l/
34×pow1/2 sqrt-pow1
33×tan-quot
31×fma-udef
30×pow-unpow
26×rem-sqrt-square
22×associate-+l- log-div
19×frac-sub
18×+-commutative exp-sum pow-pow
17×frac-add exp-prod
14×associate-+r- 1-exp rec-exp sin-mult
12×neg-sub0 cos-mult
9×sub-div neg-log div-sub
8×pow-sqr pow-prod-up
7×unpow2
5×rem-exp-log distribute-rgt-out--
4×pow-plus associate--l- inv-pow pow2 pow-flip hypot-def sqrt-unprod distribute-neg-frac
3×rem-cube-cbrt distribute-frac-neg rem-cbrt-cube
2×exp-diff cos-sum distribute-rgt-out tan-sum rem-log-exp
1×distribute-lft1-in pow3 unpow1/2 acos-asin distribute-rgt-neg-out cube-neg

bsearch6.2s (0.8%)

localize4.3s (0.6%)

end0.0ms (0.0%)