Details

sample3.5m (32.0%)

Algorithm
60×intervals
Results
1.6m335897×body80valid
31.3s209084×body80nan
27.8s21202×body1280valid
11.7s11193×body640valid
6.2s5250×body2560valid
3.8s5218×body320valid
1.5s16512×pre80true
1.3s2523×body160valid
605.0ms200×body5120valid

prune3.3m (30.1%)

simplify2.3m (20.9%)

series47.7s (7.3%)

Calls

333 calls:

982.0ms
(/ (- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))
839.0ms
(- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0)))))
696.0ms
(/ 1 (/ (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i) (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t)))
680.0ms
(* (/ (- y z) (- (+ t 1.0) z)) (- a x))
669.0ms
(/ 1 (* (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i) (/ 1 (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t))))

regimes33.2s (5.1%)

Accuracy

Total 37.3b remaining (25.3%)

Threshold costs 3.6b (2.4%)

11.3b-8.9%Linear.Matrix:det44 from linear-1.19.1.3
6.0b-7.3%Linear.Matrix:det33 from linear-1.19.1.3
4.3b84.2%The quadratic formula (r1)
2.4b11.9%cos(2*x)/(cos^2(x)*sin^2(x))
2.2b60.9%Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1

rewrite18.5s (2.8%)

Algorithm
101×rewrite-expression-head
Calls

333 calls:

892.0ms
(* (* (- x) (/ 1 (* (cbrt (- (+ t 1.0) z)) (cbrt (- (+ t 1.0) z))))) (/ (- y z) (cbrt (- (+ t 1.0) z))))
884.0ms
(/ (- (* (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (cos a) (cos b))) (* (* (sin b) (sin a)) (* (* (sin b) (sin a)) (* (sin b) (sin a))))) (+ (* (* (sin b) (sin a)) (+ (* (sin b) (sin a)) (* (cos a) (cos b)))) (* (* (cos a) (cos b)) (* (cos a) (cos b)))))
817.0ms
(/ (- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))
561.0ms
(- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0)))))
540.0ms
(/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (* (cbrt (+ (* (+ (* (+ y a) y) b) y) c)) (cbrt (+ (* (+ (* (+ y a) y) b) y) c))) (* (cbrt (+ (* (+ (* (+ y a) y) b) y) c)) y)) i))
Rules
2874×*-un-lft-identity
2806×add-sqr-sqrt
2253×times-frac
1836×add-cube-cbrt
1716×add-exp-log
1482×pow1
1423×add-cbrt-cube
1069×associate-*r/
1064×associate-*l/
812×associate-*r*
776×flip3-- flip--
745×frac-times
678×frac-sub
632×prod-exp
562×add-log-exp
547×pow-prod-down
524×cbrt-unprod
445×associate-*l*
356×associate-/r*
347×distribute-lft-out--
333×insert-posit16
313×cbrt-prod
306×difference-of-squares
300×div-exp
292×sqrt-div
285×flip-+ flip3-+
272×associate-/l/
258×associate-/l*
212×cbrt-undiv
210×distribute-lft-out
194×distribute-rgt-neg-in
190×cos-mult
186×sqrt-prod
164×distribute-lft-neg-in
160×associate-/r/
158×sin-mult
146×cbrt-div
145×unswap-sqr
137×div-inv
125×tan-quot sub-neg
122×*-commutative
104×distribute-rgt-in distribute-lft-in
94×pow-prod-up
71×diff-log
69×pow1/3
68×pow-sqr
67×log-prod frac-2neg clear-num
64×1-exp rec-exp
59×sum-log swap-sqr
48×pow-plus neg-mul-1
40×frac-add
35×sub-div exp-prod
32×associate-+r+
31×log-pow
30×exp-sum
27×associate--r+
26×sqrt-pow1
25×associate-+l+ pow1/2
24×pow-flip
23×+-commutative
22×un-div-inv rem-sqrt-square
21×rem-exp-log
20×pow2
18×pow-unpow associate--l+
16×inv-pow
15×div-sub
14×neg-sub0
13×associate-+l-
12×distribute-lft-neg-out unpow-prod-down
9×associate-+r- pow3 neg-log
8×exp-diff distribute-neg-frac log-div
7×associate--l-
5×distribute-frac-neg
4×pow-exp cube-unmult sqr-pow difference-cubes pow-pow pow-to-exp
3×rem-cbrt-cube unsub-neg
2×distribute-rgt-neg-out tan-sum cos-sum
1×cos-2 difference-of-sqr-1 sqrt-unprod unpow2 remove-posit16 sqr-cos

localize6.2s (0.9%)

bsearch5.6s (0.9%)

end1.0ms (0.0%)