Details

simplify8.7m

Calls

4912 calls:

Slowest
1.2s
(+ (pow (* (+ (* (* y y) (+ (* x y) z)) 230661.510616) y) 3) (pow t 3))
1.1s
(cbrt (* (* (- (* (* x y) (* x y)) (* (* z t) (* z t))) (- (* (* x y) (* x y)) (* (* z t) (* z t)))) (- (* (* x y) (* x y)) (* (* z t) (* z t)))))
1.0s
(* (* (- (* (* x y) (* x y)) (* (* z t) (* z t))) (- (* (* x y) (* x y)) (* (* z t) (* z t)))) (- (* (* x y) (* x y)) (* (* z t) (* z t))))
1.0s
(/ (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
942.0ms
(* (* (* (sqrt (+ (+ (* x y) (* z t)) (* a b))) (sqrt (+ (+ (* x y) (* z t)) (* a b)))) (sqrt (+ (+ (* x y) (* z t)) (* a b)))) (* (* (sqrt (+ (+ (* x y) (* z t)) (* a b))) (sqrt (+ (+ (* x y) (* z t)) (* a b)))) (sqrt (+ (+ (* x y) (* z t)) (* a b)))))

sample3.3m

Algorithm
60×intervals
Results
1.5m335099×body80valid
33.4s207329×body80nan
27.7s21436×body1280valid
9.6s11005×body640valid
6.9s5265×body2560valid
3.2s5032×body320valid
911.0ms16512×pre80true
903.0ms2499×body160valid
216.0ms233×body5120valid

prune2.2m

series31.5s

Calls

345 calls:

Slowest
609.0ms
(* (* (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
537.0ms
(/ (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i) (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t))
470.0ms
(* (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i) (/ 1 (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t)))
453.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
453.0ms
(* (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))

regimes25.6s

Accuracy

Total 29.5b remaining (20.6%)

7.4b-9.4%Linear.Matrix:det44 from linear-1.19.1.3
4.4b84.4%The quadratic formula (r1)
3.0b50.5%Linear.Matrix:det33 from linear-1.19.1.3
2.1b20.6%cos(2*x)/(cos^2(x)*sin^2(x))
2.1b0%Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2

bsearch7.7s

rewrite5.1s

Algorithm
103×rewrite-expression-head
Calls

345 calls:

Slowest
263.0ms
(* (* (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
204.0ms
(* (- (* (* (cbrt (* y (* (* x 18.0) z))) (cbrt (* y (* (* x 18.0) z)))) (cbrt (* y (* (* x 18.0) z)))) (* a 4.0)) t)
188.0ms
(cbrt (* (* (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))))
132.0ms
(* (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
103.0ms
(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
Rules
1122×add-sqr-sqrt
1101×*-un-lft-identity
1018×add-cube-cbrt
605×times-frac
596×add-exp-log
586×pow1
548×add-cbrt-cube
480×add-log-exp
397×associate-*r*
385×flip3-- flip--
382×frac-times
343×insert-posit16
290×associate-*l*
231×associate-/r* associate-*l/
219×frac-sub
215×associate-*r/
184×flip-+ flip3-+
174×cbrt-prod
172×cbrt-div
147×associate-/l*
139×associate-/r/
138×sub-neg
134×div-inv
123×exp-prod
122×tan-quot
120×*-commutative
119×distribute-lft-neg-in distribute-rgt-neg-in
106×sqrt-prod
89×pow-prod-down distribute-rgt-in distribute-lft-in
85×prod-exp
77×cbrt-unprod
76×sqrt-div
63×frac-2neg clear-num
58×sin-mult
57×pow1/3
50×difference-of-squares
44×associate-/l/
40×div-exp
37×pow-prod-up
36×cbrt-undiv diff-log
33×cos-mult pow1/2
31×sum-log neg-mul-1
29×exp-sum distribute-lft-out--
28×+-commutative
27×pow-plus rem-sqrt-square
26×exp-diff
25×associate--r+
24×pow2
22×associate-+r+
21×distribute-lft-out associate--l+
20×rec-exp frac-add
19×neg-sub0
18×log-prod associate-+l-
17×div-sub
16×associate-+l+ sub-div
15×rem-exp-log
14×pow-pow unpow-prod-down
12×log-div
10×pow-flip
9×inv-pow
8×pow-exp distribute-neg-frac
7×un-div-inv log-pow
6×associate-+r- pow3 pow-to-exp associate--l-
5×distribute-frac-neg difference-of-sqr-1
4×rem-cube-cbrt rem-cbrt-cube
3×distribute-rgt-neg-out neg-log exp-neg unpow2
2×remove-posit16 cube-prod distribute-rgt-out-- unpow3 sqrt-unprod tan-sum cos-sum sqr-cos cube-div cube-mult distribute-neg-in
1×pow-unpow 2-cos sqr-sin rem-square-sqrt associate--r- cos-2 distribute-rgt-out rem-log-exp

localize3.4s

end1.0ms