Details

series21.1m (69.4%)

Calls

317 calls:

2.1m
(* (fma z t (fma x y (fma c i (* a b)))) (fma z t (fma x y (fma c i (* a b)))))
5.3s
(/ (fma x (* x x) (* (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) (* (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))) (+ (* x x) (- (* (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))) (* x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))))
3.2s
(fma (- (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))) (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))) (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))))))
3.2s
(fma (- (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))) (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))) (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (cbrt (* (* (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))) (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j))))) (cbrt (fma 4.0 (fma t a (* x i)) (* 27.0 (* k j)))))))))
1.2s
(cbrt (* (- (* z y) (* t a)) (* (cbrt x) (cbrt x))))

simplify4.8m (15.8%)

sample2.1m (6.8%)

Algorithm
58×intervals
Results
36.5s250303×body80valid
24.9s205527×body80nan
22.0s21375×body1280valid
8.6s11091×body640valid
5.7s5212×body2560valid
2.2s5195×body320valid
1.3s16512×pre80true
719.0ms2513×body160valid
127.0ms204×body5120valid

prune1.7m (5.6%)

regimes22.5s (1.2%)

Accuracy

Total 35.1b remaining (26.7%)

Threshold costs 5.2b (4%)

7.7b9%Linear.Matrix:det33 from linear-1.19.1.3
6.1b-0.3%Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1
4.5b84.4%The quadratic formula (r1)
4.4b84.5%NMSE problem 3.2.1
2.5b-15.4%fabs fraction 1

rewrite13.1s (0.7%)

Algorithm
99×rewrite-expression-head
Calls

323 calls:

910.0ms
(* (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) (* (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))
653.0ms
(* (/ 1 (* (cbrt (- (+ t 1.0) z)) (cbrt (- (+ t 1.0) z)))) (* (/ (- y z) (cbrt (- (+ t 1.0) z))) (- a x)))
600.0ms
(* (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
584.0ms
(/ (fma x (* x x) (* (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) (* (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))) (+ (* x x) (- (* (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))) (* x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))))
560.0ms
(* (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
Rules
7114×times-frac
6773×*-un-lft-identity
5845×add-sqr-sqrt
4651×add-cube-cbrt
3622×add-exp-log
2509×prod-exp
1465×prod-diff
1286×cbrt-prod
1074×add-cbrt-cube
820×distribute-rgt-neg-in
768×pow1
759×distribute-lft-neg-in
577×pow-exp
576×pow-to-exp
509×distribute-lft-out
493×div-exp
491×associate-*r*
485×distribute-rgt-in distribute-lft-in
474×add-log-exp
472×associate-*l* distribute-lft-out--
423×associate-/r*
421×difference-of-squares
360×div-inv
353×swap-sqr
344×associate-/l*
339×cbrt-unprod
323×expm1-log1p-u log1p-expm1-u
253×flip3-- flip--
252×sqrt-prod
242×fma-neg
229×neg-mul-1
180×cbrt-undiv
170×associate-/r/
159×exp-prod
157×associate-+r+
155×pow-prod-down
141×associate--r+
132×frac-times
121×unswap-sqr
112×log-pow
103×tan-quot
96×pow1/3
84×frac-sub
83×associate-*r/
82×sqrt-div unpow-prod-down
76×sub-neg
73×associate-*l/
72×*-commutative
60×frac-2neg clear-num
59×fma-def
56×diff-log
53×cbrt-div fma-udef
46×sqrt-pow1
41×associate-/l/
40×log-prod
38×pow-prod-up
37×pow1/2
35×exp-sum
34×sqr-pow flip-+ flip3-+ rem-sqrt-square
28×associate-+l+
27×pow-plus
26×pow-sqr
25×1-exp
23×sum-log
21×rec-exp
19×pow2
17×div-sub sin-mult
16×cos-mult pow-unpow distribute-neg-frac distribute-frac-neg
15×neg-sub0
13×+-commutative
12×sub-div rem-exp-log
10×frac-add
pow-pow associate-+l- log-div
exp-diff associate--l-
associate--l+ pow3 neg-log
pow-flip associate-+r- inv-pow exp-neg
tan-sum distribute-rgt-out-- unpow1/3 cos-sum rem-cbrt-cube
unpow-prod-up quot-tan distribute-lft-neg-out cube-unmult distribute-rgt-neg-out log-rec sqrt-unprod sqr-neg rem-log-exp associate--r- e-exp-1

localize6.8s (0.4%)

bsearch1.6s (0.1%)

end1.0ms (0.0%)