Details

simplify25.7m

Calls

13050 calls:

Slowest
1.8s
(/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* (* (* cos sin) (* cos sin)) (* cos sin)) (* (* x x) x)) (* (* (* (* cos sin) x) (* (* cos sin) x)) (* (* cos sin) x))))
1.7s
(* (* (* (fma i c (fma a b (fma x y (* z t)))) (fma i c (fma a b (fma x y (* z t))))) (fma i c (fma a b (fma x y (* z t))))) (* (* (fma i c (fma a b (fma x y (* z t)))) (fma i c (fma a b (fma x y (* z t))))) (fma i c (fma a b (fma x y (* z t))))))
1.7s
(/ (/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos)))) (* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos))))
1.6s
(/ (/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos)))) (* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos))))
1.6s
(/ (/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos)))) (* (* (* sin sin) sin) (* (* (* x cos) (* x cos)) (* x cos))))

prune3.7m

series3.7m

Calls

330 calls:

Slowest
2.6m
(* (fma i c (fma a b (fma x y (* z t)))) (fma i c (fma a b (fma x y (* z t)))))
1.7s
(fma (/ (+ (tan y) (tan z)) (- (pow 1 3) (pow (/ (* (tan y) (sin z)) (cos z)) 3))) (+ (* 1 1) (+ (* (/ (* (tan y) (sin z)) (cos z)) (/ (* (tan y) (sin z)) (cos z))) (* 1 (/ (* (tan y) (sin z)) (cos z))))) (- (* (tan a) 1)))
970.0ms
(fma j (- (* t c) (* y i)) (- (* (- (* z y) (* t a)) x) (* (- (* z c) (* i a)) b)))
956.0ms
(fma j (fma t c (- (* y i))) (- (* (- (* z y) (* t a)) x) (* (- (* z c) (* i a)) b)))
850.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))

sample2.6m

Algorithm
57×intervals
Results
49.7s243632×body80valid
33.5s205283×body80nan
28.2s20685×body1280valid
12.6s10431×body640valid
5.7s4237×body2560valid
4.0s4821×body320valid
1.7s16512×pre80true
1.0s2451×body160valid
647.0ms119×body5120valid

regimes17.4s

Accuracy

Total 21.1b remaining (18.1%)

5.1b0%Linear.Matrix:det33 from linear-1.19.1.3
2.6b90%NMSE problem 3.2.1
2.4b18.7%cos(2*x)/(cos^2(x)*sin^2(x))
2.2b59.8%Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1
1.3b0%Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1

rewrite15.5s

Algorithm
99×rewrite-expression-head
Calls

338 calls:

Slowest
2.4s
(- (+ (- (* (* (* x 18.0) y) (* z t)) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i))
1.8s
(- (+ (- (* (* x 18.0) (* y (* z t))) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i))
867.0ms
(+ (- (+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z))) t) (* (- a 0.5) (log t)))
449.0ms
(/ (sqrt (+ a t)) (/ t z))
308.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
Rules
16132×times-frac
12214×*-un-lft-identity
11126×add-sqr-sqrt
9652×add-cube-cbrt
5176×prod-diff
2098×sqrt-prod
1324×add-exp-log
1176×add-cbrt-cube
1115×pow1
834×div-inv
675×distribute-lft-out
658×distribute-lft-out--
643×fma-neg
556×difference-of-squares
525×add-log-exp
517×cbrt-prod
461×associate-*r*
443×associate-*l*
407×associate-/r*
394×prod-exp
378×cbrt-unprod
339×log1p-expm1-u
338×expm1-log1p-u insert-posit16
325×pow-prod-down
294×distribute-rgt-neg-in
281×distribute-lft-neg-in
265×div-exp
260×associate-/l*
259×flip3-- flip--
254×associate-/r/
203×associate-+r+
196×cbrt-undiv
183×swap-sqr
174×log-pow
148×exp-prod
140×unswap-sqr
113×pow1/3
111×cbrt-div
108×associate-*l/
107×associate--r+
99×distribute-rgt-in distribute-lft-in
93×frac-times
88×associate-+l+
85×*-commutative
82×fma-def
79×log-prod neg-mul-1
73×sqrt-pow1 exp-sum
70×diff-log
66×sub-neg
62×frac-2neg clear-num
61×frac-sub
60×pow-prod-up
56×associate-*r/
52×sqrt-div
51×flip-+ flip3-+
49×fma-udef
48×pow-sqr
42×associate-/l/
39×sum-log
38×1-exp rec-exp pow1/2
36×tan-quot
33×frac-add
31×pow-plus
25×rem-sqrt-square
21×distribute-rgt-out--
20×sin-mult
19×pow2
18×rem-exp-log
16×pow-flip associate-+l-
15×div-sub
14×cos-mult +-commutative sub-div inv-pow distribute-neg-frac
12×neg-sub0
10×exp-diff associate--l- associate--l+ neg-log unpow-prod-down log-div
7×cube-prod
5×associate-+r- pow3
4×pow-exp cos-2 difference-of-sqr-1 pow-unpow expm1-def
3×expm1-log1p expm1-udef rem-cube-cbrt un-div-inv
2×remove-posit16 sqr-pow sqrt-unprod pow-pow pow-to-exp tan-sum cos-sum distribute-frac-neg rem-log-exp rem-cbrt-cube
1×remove-double-div log1p-expm1 log1p-udef unpow3 cube-mult rem-square-sqrt cube-div acos-asin associate--r-

localize5.9s

bsearch2.3s

end1.0ms