Details

simplify7.2m (43.8%)

sample3.4m (20.6%)

Algorithm
60×intervals
Results
1.5m335535×body80valid
34.1s209954×body80nan
27.5s21622×body1280valid
11.6s10986×body640valid
5.8s5344×body2560valid
3.1s4963×body320valid
1.0s2487×body160valid
910.0ms16512×pre80true
207.0ms236×body5120valid

prune3.3m (20.3%)

series1.2m (7.6%)

Calls

358 calls:

11.3s
(+ (- (- (* c b) (* (* 27.0 j) k)) (* 4.0 (* x i))) (* (- (* (* x 18.0) (* y z)) (* a 4.0)) t))
10.3s
(+ (- (- (* c b) (* 27.0 (* j k))) (* 4.0 (* x i))) (* (- (* (* x 18.0) (* y z)) (* a 4.0)) t))
1.6s
(/ (- (* (* (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (cos a)) (+ 1 (* (tan y) (tan z)))) (* (* (cos y) (cos z)) (* (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (sin a)))) (* (* (- 1 (* (tan y) (tan z))) (cos a)) (* (* (cos y) (cos z)) (+ 1 (* (tan y) (tan z))))))
1.0s
(/ 1 (/ (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i) (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t)))
842.0ms
(sqrt (+ (+ (* x y) (* z t)) (* a b)))

rewrite31.0s (3.1%)

Algorithm
104×rewrite-expression-head
Calls

358 calls:

4.3s
(* (* x (* (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))) (/ 1 y))
4.1s
(* (* x (* (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))) (/ 1 y))
4.0s
(* (* x (* (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))) (/ 1 y))
3.9s
(* (* x (* (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))) (/ 1 y))
1.1s
(/ (* x (* (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (sqrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))) y)
Rules
3596×add-sqr-sqrt
3461×*-un-lft-identity
3286×times-frac
2364×add-cube-cbrt
1899×add-exp-log
1521×add-cbrt-cube
1355×pow1
800×associate-*l*
720×prod-exp
716×cbrt-prod
691×frac-times
604×associate-*r*
569×cbrt-unprod
568×add-log-exp
465×flip3-- flip--
458×associate-*r/
457×associate-*l/
455×pow-prod-down
449×flip-+ flip3-+
407×cbrt-div
373×difference-of-squares
345×div-exp
344×associate-/l*
318×associate-/r*
304×sqrt-prod
285×distribute-lft-out--
275×distribute-lft-out
236×cbrt-undiv
231×associate-/r/
230×distribute-rgt-neg-in
223×div-inv
217×distribute-lft-neg-in
210×sqrt-div
187×associate-/l/
178×distribute-rgt-in distribute-lft-in
176×unswap-sqr
174×frac-sub
169×log-prod
166×exp-prod
147×sub-neg
144×*-commutative
99×swap-sqr
68×pow-prod-up
67×diff-log
66×tan-quot frac-2neg clear-num neg-mul-1
65×1-exp
64×cos-mult
62×associate-+r+
58×sqrt-pow1
57×pow1/2
55×sum-log rec-exp pow1/3
50×sin-mult
49×pow-sqr
46×exp-diff
45×pow-flip
44×log-pow
42×difference-of-sqr-1
40×associate-+l+
39×pow-plus
37×unpow-prod-down
33×rem-sqrt-square
30×pow-unpow exp-sum
28×frac-add
27×associate--l+
24×rem-exp-log
20×pow2 +-commutative associate--r+
19×div-sub
17×inv-pow
14×associate-+l-
13×pow-exp log-div
12×sqr-pow sub-div
10×neg-sub0 cube-prod pow-div un-div-inv
9×pow-to-exp
7×neg-log
6×pow3 cube-div
5×associate--l- pow-pow
4×distribute-neg-frac distribute-frac-neg e-exp-1 cos-2
3×sqrt-unprod rem-log-exp rem-cbrt-cube
2×associate-+r- distribute-rgt-out-- tan-sum exp-neg rem-square-sqrt cos-sum distribute-neg-in
1×cube-unmult unpow3 exp-to-pow cube-mult associate--r-

regimes28.0s (2.8%)

Accuracy

Total 37.3b remaining (25.3%)

Threshold costs 4.9b (3.3%)

12.2b-17.1%Linear.Matrix:det44 from linear-1.19.1.3
6.2b27.9%Linear.Matrix:det33 from linear-1.19.1.3
4.1b85.4%The quadratic formula (r1)
2.4b0%cos(2*x)/(cos^2(x)*sin^2(x))
2.2b0%Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2

bsearch10.8s (1.1%)

localize6.5s (0.7%)

end1.0ms (0.0%)