Details

series11.5m (57.0%)

Calls

322 calls:

2.0m
(fma (fma c y0 (* y1 (- a))) (fma y2 x (* z (- y3))) (* (- (* a b) (* c i)) (- (* x y) (* z t))))
12.4s
(+ (pow (- (/ (+ (tan z) (tan y)) (fma (- (tan y)) (tan z) 1)) (tan a)) 3) (pow x 3))
8.3s
(/ (+ (pow (- (/ (+ (tan z) (tan y)) (fma (- (tan y)) (tan z) 1)) (tan a)) 3) (pow x 3)) (fma x x (* (- (/ (+ (tan z) (tan y)) (fma (- (tan y)) (tan z) 1)) (+ (tan a) x)) (- (/ (+ (tan z) (tan y)) (fma (- (tan y)) (tan z) 1)) (tan a)))))
6.0s
(sqrt (fma i c (fma z t (fma y x (* a b)))))
5.4s
(sqrt (fma i c (fma z t (fma y x (* a b)))))

simplify3.2m (15.7%)

prune2.7m (13.5%)

sample1.9m (9.6%)

Algorithm
59×intervals
Results
35.3s264300×body80valid
23.2s207380×body80nan
17.5s21308×body1280valid
9.1s11271×body640valid
6.5s5370×body2560valid
1.7s4959×body320valid
1.0s16512×pre80true
781.0ms2643×body160valid
99.0ms242×body5120valid

rewrite23.2s (1.9%)

Algorithm
100×rewrite-expression-head
Calls

324 calls:

7.6s
(* (/ (/ (cbrt (/ 1 (pow sin (/ 2.0 2)))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (/ (/ (cos (* x 2.0)) (pow sin (/ 2.0 2))) (cbrt x)) x))
3.0s
(* (/ (/ (cbrt (cbrt (/ 1 (pow sin (/ 2.0 2))))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (/ (cos (* x 2.0)) (pow sin (/ 2.0 2))) (cbrt x)))
791.0ms
(/ (+ (pow (- (/ (+ (tan z) (tan y)) (fma (- (tan y)) (tan z) 1)) (tan a)) 3) (pow x 3)) (fma x x (* (- (/ (+ (tan z) (tan y)) (fma (- (tan y)) (tan z) 1)) (+ (tan a) x)) (- (/ (+ (tan z) (tan y)) (fma (- (tan y)) (tan z) 1)) (tan a)))))
433.0ms
(* (/ (/ (cbrt (* (cbrt (/ 1 (pow sin (/ 2.0 2)))) (cbrt (/ 1 (pow sin (/ 2.0 2)))))) 1) (pow 1 (/ 2.0 2))) (/ (* (/ (/ (cbrt (cbrt (/ 1 (pow sin (/ 2.0 2))))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (/ (cos (* x 2.0)) (pow sin (/ 2.0 2))) (cbrt x))) x))
432.0ms
(+ (pow (- (/ (+ (tan z) (tan y)) (fma (- (tan y)) (tan z) 1)) (tan a)) 3) (pow x 3))
Rules
19943×times-frac
14663×add-sqr-sqrt
9941×*-un-lft-identity
8615×add-exp-log
8307×cbrt-prod
7977×add-cube-cbrt
5545×div-exp
4069×unpow-prod-down
3233×associate-*l*
2585×prod-exp
1827×sqr-pow
1516×associate-*r*
1385×add-cbrt-cube
1296×unswap-sqr
1294×prod-diff
1069×pow-exp
997×pow1
955×pow-to-exp
725×distribute-rgt-neg-in
716×distribute-lft-neg-in
633×distribute-lft-out--
610×exp-sum
472×associate-/l*
465×1-exp
460×div-inv
450×log-pow
430×cbrt-undiv
429×add-log-exp
414×cbrt-unprod
348×sqrt-prod
336×distribute-lft-out
325×expm1-log1p-u
324×log1p-expm1-u
314×cube-prod
307×associate-/r*
266×exp-prod
225×pow-prod-down
222×difference-of-squares
206×rec-exp
194×associate-+r+
190×swap-sqr
150×fma-neg
125×associate-*r/
113×cbrt-div
111×flip3-- distribute-rgt-in flip-- distribute-lft-in
109×neg-mul-1
108×associate-/r/
103×sub-neg
93×*-commutative
89×pow1/3
86×fma-def
70×frac-times
67×log-prod tan-quot
65×fma-udef
60×frac-2neg clear-num
59×associate-*l/
47×flip-+ flip3-+
46×sqrt-pow1 sqrt-div
44×pow1/2
38×associate-/l/
33×diff-log
32×exp-diff pow-unpow
31×rem-sqrt-square
28×frac-sub neg-sub0
23×pow-prod-up
21×sum-log pow-sqr
20×exp-neg
15×+-commutative
13×distribute-neg-frac sin-mult
12×pow-pow
11×cos-mult pow2 pow-plus sub-div div-sub
9×unpow3 distribute-rgt-out-- rem-exp-log cube-mult frac-add
8×pow-flip log-div
7×associate--l+ inv-pow
6×associate-+l+ distribute-frac-neg neg-log cube-div
5×rem-cube-cbrt associate-+r- un-div-inv sum-cubes distribute-neg-in
4×distribute-rgt-neg-out sqrt-unprod associate--l-
2×expm1-udef tan-sum exp-to-pow associate-+l- cos-sum
1×expm1-log1p log1p-expm1 log-rec cube-neg rem-square-sqrt rem-log-exp acos-asin rem-cbrt-cube log1p-udef

regimes18.7s (1.5%)

Accuracy

Total 37.9b remaining (26.9%)

Threshold costs 3.4b (2.4%)

9.6b19.4%Linear.Matrix:det33 from linear-1.19.1.3
5.9b4.5%Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1
4.3b14%Hakyll.Web.Tags:renderTagCloud from hakyll-4.7.2.3
3.7b87.2%NMSE problem 3.2.1
3.1b47%Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1

localize5.8s (0.5%)

bsearch2.2s (0.2%)

end1.0ms (0.0%)