Details

series10.9m (48.9%)

Calls

329 calls:

3.8s
(fma (- (* (* y z) (* x 18.0)) (* a 4.0)) t (- (* c b) (fma 27.0 (* k j) (* (* x 4.0) i))))
3.7s
(fma (- (* y (* (* z x) 18.0)) (* a 4.0)) t (- (* c b) (fma 27.0 (* k j) (* (* x 4.0) i))))
3.7s
(fma (- (* y (* z (* x 18.0))) (* a 4.0)) t (- (* c b) (fma 27.0 (* k j) (* (* x 4.0) i))))
3.5s
(fma (- (* y (* (* z x) 18.0)) (* a 4.0)) t (- (* c b) (+ (* 27.0 (* k j)) (* (* x 4.0) i))))
1.6s
(/ (- (* (* (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (cos a)) (+ 1 (* (tan y) (tan z)))) (* (* (cos y) (cos z)) (* (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (sin a)))) (* (* (- 1 (* (tan y) (tan z))) (cos a)) (* (* (cos y) (cos z)) (+ 1 (* (tan y) (tan z))))))

simplify5.4m (24.3%)

prune3.0m (13.5%)

sample2.5m (11.2%)

Algorithm
59×intervals
Results
45.1s263841×body80valid
33.8s209954×body80nan
26.8s21622×body1280valid
10.9s10986×body640valid
6.7s5344×body2560valid
3.0s4963×body320valid
1.0s2487×body160valid
1.0s16512×pre80true
179.0ms236×body5120valid

regimes14.7s (1.1%)

Accuracy

Total 25.6b remaining (18.9%)

Threshold costs 4.6b (3.4%)

4.3b84.8%NMSE problem 3.2.1
4.2b15.7%Hakyll.Web.Tags:renderTagCloud from hakyll-4.7.2.3
3.6b0%Linear.Matrix:det33 from linear-1.19.1.3
3.0b7.9%Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1
2.5b0%cos(2*x)/(cos^2(x)*sin^2(x))

rewrite6.8s (0.5%)

Algorithm
99×rewrite-expression-head
Calls

331 calls:

390.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
260.0ms
(/ (- (* (* (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (cos a)) (+ 1 (* (tan y) (tan z)))) (* (* (cos y) (cos z)) (* (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (sin a)))) (* (* (- 1 (* (tan y) (tan z))) (cos a)) (* (* (cos y) (cos z)) (+ 1 (* (tan y) (tan z))))))
206.0ms
(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
150.0ms
(* (cbrt (- (+ 1.0 t) z)) (cbrt (- (+ 1.0 t) z)))
144.0ms
(/ 1 (/ (* (* sin (* cos x)) (* sin (* cos x))) (cos (* 2 x))))
Rules
5874×times-frac
5749×*-un-lft-identity
5559×add-sqr-sqrt
4783×add-cube-cbrt
2624×prod-diff
1514×add-exp-log
1290×pow1
1286×add-cbrt-cube
833×sqrt-prod
633×distribute-rgt-neg-in
613×distribute-lft-neg-in
568×cbrt-prod
541×prod-exp
514×associate-*r*
484×associate-*l*
466×add-log-exp
464×cbrt-unprod
460×pow-prod-down
374×div-inv
335×log1p-expm1-u
331×expm1-log1p-u
316×associate-/r*
309×fma-neg
278×div-exp
275×distribute-lft-out associate-/l*
235×distribute-lft-out--
212×difference-of-squares
199×distribute-rgt-in distribute-lft-in
194×neg-mul-1
193×cbrt-undiv
186×associate-*l/
170×associate-/r/
167×exp-prod
152×flip-- flip3--
132×unswap-sqr
125×exp-sum
122×associate-+r+
115×associate-*r/
107×frac-times
99×*-commutative
96×flip-+ flip3-+
92×associate-/l/
91×swap-sqr
86×sub-neg
84×associate-+l+
79×tan-quot
77×log-pow
72×frac-sub
70×associate--l+
60×cos-mult fma-udef
59×frac-2neg clear-num fma-def
57×log-prod
56×cbrt-div pow-prod-up
52×diff-log pow-sqr
51×sqrt-pow1
50×pow1/2
49×pow1/3
45×1-exp
39×pow-flip
35×rec-exp
31×pow-unpow
29×rem-sqrt-square
26×sqrt-div
24×unpow-prod-down sin-mult
22×sum-log
19×pow-plus div-sub rem-exp-log
14×neg-sub0
13×sub-div inv-pow
12×+-commutative frac-add
11×pow-exp
10×pow2
9×exp-diff neg-log associate--l-
8×sqr-pow
7×difference-of-sqr-1 associate--r+ pow-to-exp
6×associate-+l- log-div
5×distribute-neg-in
4×expm1-log1p expm1-udef associate-+r- distribute-frac-neg pow-pow distribute-neg-frac expm1-def e-exp-1
3×sqrt-unprod cos-2
2×un-div-inv tan-sum exp-neg rem-square-sqrt cos-sum rem-log-exp
1×distribute-rgt-out-- log1p-expm1 pow3 unpow1/3 rem-cbrt-cube log1p-udef

localize5.3s (0.4%)

bsearch1.5s (0.1%)

end1.0ms (0.0%)