Details

simplify1.4hr

Calls

36937 calls:

Slowest
2.9s
(/ (* (* (* 4 4) 4) (* (* (* c a) (* c a)) (* c a))) (* (* (* (* 2 a) (* 2 a)) (* 2 a)) (* (* (- (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (- (- b) (sqrt (- (* b b) (* (* 4 a) c))))) (- (- b) (sqrt (- (* b b) (* (* 4 a) c)))))))
2.8s
(/ (* (* (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)))))
2.4s
(/ (* 4 (* c a)) (* (* 2 a) (- (- b) (sqrt (- (* b b) (* (* 4 a) c))))))
2.1s
(fma (- (sqrt c)) (* (* 4 a) (sqrt c)) (* (sqrt c) (* (* 4 a) (sqrt c))))
2.0s
(/ (sqrt a) (* (* 2 a) (- (- b) (sqrt (- (* b b) (* (* 4 a) c))))))

prune7.1m

sample1.7m

Algorithm
50×intervals
Results
33.7s182172×body80valid
23.7s154021×body80nan
15.9s15688×body1280valid
7.1s7102×body640valid
6.8s5159×body2560valid
2.0s3412×body320valid
1.1s1704×body160valid
298.0ms8512×pre80true
228.0ms234×body5120valid

rewrite1.5m

Algorithm
94×rewrite-expression-head
Calls

313 calls:

Slowest
18.9s
(/ (* x (* (cbrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (cbrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))) (/ y (cbrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b)))))
11.1s
(- (+ (- (* (* y 18.0) (* (* x z) t)) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i))
7.2s
(- (+ (- (* (* y 18.0) (* (* x z) t)) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i))
4.6s
(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
4.2s
(+ (* (/ (/ (- y z) (* (cbrt (- (+ 1.0 t) z)) (cbrt (- (+ 1.0 t) z)))) (cbrt (- (+ 1.0 t) z))) (- a x)) x)
Rules
246833×*-un-lft-identity
128922×cbrt-prod
116116×times-frac
109944×add-sqr-sqrt
104832×exp-sum
103320×associate-*l*
92403×prod-diff
76531×add-cube-cbrt
66784×associate-*r*
64961×distribute-lft-out
32012×swap-sqr
28881×distribute-lft-out--
23386×associate--l+
18383×log-prod
14736×unswap-sqr
11242×associate-+l+
10332×distribute-rgt-in distribute-lft-in
10098×frac-times
9743×associate-/r*
9195×associate-+r+
7820×associate-/l*
4882×difference-of-squares
4007×cbrt-div
3407×distribute-neg-frac
3273×frac-sub
3069×*-commutative
3052×associate-*l/
2879×sqrt-prod
2578×frac-add
2416×associate-/l/
2180×flip3-- flip--
2142×fma-def
1908×sub-neg
1577×clear-num
1549×frac-2neg
1548×+-commutative
1468×add-cbrt-cube
1440×add-exp-log
1217×associate-*r/
1065×pow1
1056×div-inv
1010×flip-+ flip3-+
1002×associate-/r/
799×distribute-rgt-neg-in
718×distribute-lft-neg-in
622×cbrt-unprod
608×fma-neg
514×add-log-exp
472×prod-exp
358×pow-prod-down
313×expm1-log1p-u log1p-expm1-u insert-posit16
311×exp-diff
293×div-exp
288×cbrt-undiv
265×tan-quot
202×neg-mul-1
160×sqrt-div
105×sqrt-pow1
93×un-div-inv
77×pow1/3 diff-log
68×pow-unpow
66×log-pow
59×pow1/2
54×exp-prod
53×1-exp rec-exp
49×pow-prod-up
46×unpow-prod-down
43×sum-log
42×difference-of-sqr-1
41×pow-sqr
34×sin-mult
33×fma-udef
29×rem-sqrt-square
28×cos-mult sub-div
25×distribute-rgt-out
22×sqr-pow associate--r+
21×pow-flip
17×associate--l- associate-+l-
15×neg-sub0 pow-pow inv-pow div-sub
14×pow-plus rem-exp-log
12×expm1-def
11×pow-exp
10×pow2 neg-log distribute-rgt-out-- log-div
9×unpow-prod-up
7×remove-double-div pow-to-exp
5×sqrt-unprod
4×cos-sum tan-sum e-exp-1 cos-2
3×rem-square-sqrt
2×distribute-frac-neg
1×quot-tan expm1-udef associate-+r- unpow1/3 associate--r-

series49.7s

Calls

313 calls:

Slowest
814.0ms
(fma j (- (* t c) (* y i)) (- (* (* (cbrt (- (* z y) (* t a))) (cbrt (- (* z y) (* t a)))) (* (cbrt (- (* z y) (* t a))) x)) (* (- (* z c) (* i a)) b)))
798.0ms
(fma j (- (* t c) (* y i)) (- (* (- (* z y) (* t a)) x) (* (- (* z c) (* i a)) b)))
791.0ms
(/ (- (* (cos a) (+ (/ (sin z) (cos z)) (/ (sin y) (cos y)))) (* (- 1 (* (tan z) (tan y))) (sin a))) (* (- 1 (* (tan z) (tan y))) (cos a)))
706.0ms
(cbrt z)
703.0ms
(* (/ (- y z) (- (+ 1.0 t) z)) (- a x))

regimes8.3s

Accuracy

Total 15.4b remaining (13.2%)

4.1b20.1%Linear.Matrix:det33 from linear-1.19.1.3
3.8b85.7%NMSE problem 3.2.1
2.6b0%cos(2*x)/(cos^2(x)*sin^2(x))
1.0b95.9%The quadratic formula (r1)
0.8b0%Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

localize3.8s

bsearch1.5s

end1.0ms