Details

simplify50.3m

Calls

30022 calls:

Slowest
3.2s
(/ (* (* (* (- (* a (/ c b)) b) (- (* a (/ c b)) b)) (- (* a (/ c b)) b)) (* (* 2 2) 2)) (* (* (* 2 a) (* 2 a)) (* 2 a)))
2.3s
(/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* (* (* x x) x) (* (* sin sin) sin)) (* (* cos cos) cos)) (* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos)))))
2.0s
(/ (* (* (* 2 2) 2) (* (* c c) c)) (* (* (* (- (* a (/ c b)) b) 2) (* (- (* a (/ c b)) b) 2)) (* (- (* a (/ c b)) b) 2)))
1.8s
(/ (* (* (cos (* 2 x)) (cos (* 2 x))) (cos (* 2 x))) (* (* (* (* sin sin) sin) (* (* (* x x) x) (* (* cos cos) cos))) (* (* (* sin (* x cos)) (* sin (* x cos))) (* sin (* x cos)))))
1.6s
(/ (* (* (* (- (* a (/ c b)) b) (- (* a (/ c b)) b)) (- (* a (/ c b)) b)) (* (* 2 2) 2)) (* (* (* 2 2) 2) (* (* a a) a)))

rewrite10.7m

Algorithm
100×rewrite-expression-head
Calls

347 calls:

Slowest
4.9m
(* (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (/ 1 (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))
3.1m
(/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
39.3s
(/ (- (* (* (+ (* (cos y) (sin z)) (* (cos z) (sin y))) (cos a)) (+ (+ (* (* (tan z) (tan y)) (* (tan z) (tan y))) (* (tan z) (tan y))) 1)) (* (* (cos z) (* (cos y) (sin a))) (- 1 (* (* (tan z) (tan y)) (* (* (tan z) (tan y)) (* (tan z) (tan y))))))) (* (cos a) (* (- 1 (* (tan y) (tan z))) (* (* (cos y) (cos z)) (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z)))))))))
13.3s
(* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y)
13.3s
(* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y)
Rules
1244367×cbrt-prod
1040904×add-sqr-sqrt
555031×times-frac
505433×unswap-sqr
343624×associate-*r*
272340×*-un-lft-identity
256099×swap-sqr
230923×add-cube-cbrt
186950×associate-*l*
63981×*-commutative
25896×frac-times
25745×associate-/l*
14817×associate-/r*
14659×distribute-lft-out
12304×cbrt-div
7834×frac-sub
7413×distribute-lft-out--
7311×distribute-rgt-neg-in
7152×distribute-lft-neg-in
5824×difference-of-squares
3835×associate-/l/
3365×associate-*r/
3310×flip-+ flip3-+
3280×distribute-neg-frac
2889×clear-num
2731×frac-2neg
2238×associate-*l/
1826×add-cbrt-cube
1796×frac-add
1785×neg-mul-1
1717×sqrt-prod
1641×add-exp-log
1418×flip3-- flip--
1361×pow1
865×cbrt-unprod
611×div-inv
607×add-log-exp
584×prod-exp
494×pow-prod-down
438×sqrt-div
384×un-div-inv
380×associate-/r/
356×cbrt-undiv
347×insert-posit16
288×div-exp
221×exp-prod
218×exp-sum
203×log-prod
202×associate--l+
168×distribute-rgt-in distribute-lft-in
148×tan-quot
143×sub-neg
141×pow-unpow
137×associate-+r+
117×sqrt-pow1
90×pow-pow
87×pow-prod-up
84×diff-log
74×rem-sqrt-square
73×associate-+l+
67×sum-log
65×pow1/2
60×+-commutative
58×pow1/3
52×pow-sqr
50×log-pow
43×cos-mult 1-exp
41×rec-exp
40×difference-of-sqr-1 sin-mult
31×div-sub
29×unpow-prod-down
28×pow-plus
26×rem-exp-log
25×associate-+l-
24×sub-div associate--r+
23×pow-exp
21×neg-sub0
20×pow2
18×exp-diff
17×associate--l- neg-log
15×pow-flip
14×distribute-frac-neg
13×sqr-pow pow-to-exp inv-pow
12×distribute-rgt-out
10×distribute-rgt-out-- remove-double-div log-div
8×unpow-prod-up
6×distribute-lft1-in distribute-neg-in pow-sub
5×pow3
4×associate-+r- cos-2 tan-sum sqr-neg cos-sum
3×distribute-lft-neg-out sqrt-unprod
2×exp-neg rem-square-sqrt rem-cbrt-cube
1×distribute-rgt-neg-out unpow1/3

prune5.9m

sample3.2m

Algorithm
54×intervals
Results
1.7m291416×body80valid
30.9s200217×body80nan
19.3s17608×body1280valid
9.2s8882×body640valid
6.8s5159×body2560valid
3.0s4487×body320valid
981.0ms2299×body160valid
315.0ms8512×pre80true
202.0ms234×body5120valid

series1.1m

Calls

347 calls:

Slowest
12.1s
(+ (- (* c b) (+ (* (* 27.0 j) k) (* (* x 4.0) i))) (* (- (* (* y x) (* 18.0 z)) (* a 4.0)) t))
4.9s
(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
4.8s
(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
1.6s
(/ (- (* (* (+ (* (cos y) (sin z)) (* (cos z) (sin y))) (cos a)) (+ (+ (* (* (tan z) (tan y)) (* (tan z) (tan y))) (* (tan z) (tan y))) 1)) (* (* (cos z) (* (cos y) (sin a))) (- 1 (* (* (tan z) (tan y)) (* (* (tan z) (tan y)) (* (tan z) (tan y))))))) (* (cos a) (* (- 1 (* (tan y) (tan z))) (* (* (cos y) (cos z)) (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z)))))))))
713.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

regimes26.5s

Accuracy

Total 35.8b remaining (30.9%)

11.9b-35.3%Linear.Matrix:det44 from linear-1.19.1.3
7.7b25.9%Linear.Matrix:det33 from linear-1.19.1.3
5.3b80.9%The quadratic formula (r1)
2.6b0%cos(2*x)/(cos^2(x)*sin^2(x))
2.3b26.7%Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1

bsearch5.8s

localize3.7s

end1.0ms