Details

series5.6m (30.0%)

Calls

347 calls:

2.7m
(pow (cbrt (/ (- (+ f n)) (- f n))) 6)
1.9m
(pow (cbrt (/ (+ f n) (- f n))) 6)
3.3s
(/ (- (* (* z (/ (sqrt (+ t a)) (cbrt t))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* (* (cbrt t) (cbrt t)) (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))) (* (* (cbrt t) (cbrt t)) (* (- a (/ 5.0 6.0)) (* t 3.0))))
3.1s
(- (* (* z (/ (sqrt (+ t a)) (cbrt t))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* (* (cbrt t) (cbrt t)) (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0)))))
1.4s
(- (* x x) (* (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))

end5.3m (28.2%)

simplify3.2m (17.2%)

sample2.5m (13.2%)

Algorithm
60×intervals
Results
52.3s297276×body80valid
25.1s207336×body80nan
19.3s21239×body1280valid
6.9s10924×body640valid
4.5s5320×body2560valid
3.1s5206×body320valid
804.0ms16512×pre80true
653.0ms2585×body160valid
133.0ms203×body5120valid

prune1.2m (6.3%)

rewrite27.1s (2.4%)

Algorithm
104×rewrite-expression-head
Calls

347 calls:

1.3s
(/ (* (* (sqrt (/ (pow a (- 1.0)) (exp (- (- b (* (log a) t)) (* (log z) y))))) x) (sqrt (/ (pow a (- 1.0)) (exp (+ (+ (* (- (log z)) y) (* (- (log a)) t)) b))))) y)
1.2s
(/ (- (* (* z (/ (sqrt (+ t a)) (cbrt t))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* (* (cbrt t) (cbrt t)) (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))) (* (* (cbrt t) (cbrt t)) (* (- a (/ 5.0 6.0)) (* t 3.0))))
725.0ms
(- (* (* z (/ (sqrt (+ t a)) (cbrt t))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* (* (cbrt t) (cbrt t)) (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0)))))
648.0ms
(+ (log (+ x y)) (+ (+ (log (sqrt z)) (- (log (sqrt z)) t)) (* (- a 0.5) (log t))))
586.0ms
(/ (+ (* (+ (* (* (cbrt (* (+ (* (+ (* x y) z) y) 27464.7644705) y)) (cbrt (* (+ (* (+ (* x y) z) y) 27464.7644705) y))) (cbrt (* (+ (* (+ (* x y) z) y) 27464.7644705) y))) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
Rules
4612×times-frac
3924×add-sqr-sqrt
3900×*-un-lft-identity
2867×add-exp-log
2851×add-cube-cbrt
1512×prod-exp
1306×add-cbrt-cube
783×pow1
746×associate-*l/
731×associate-*r/
720×flip3-- flip--
714×associate-*r*
600×cbrt-prod
594×frac-times
579×distribute-rgt-neg-in
560×div-exp
552×distribute-lft-neg-in
542×add-log-exp
539×associate-*l*
503×frac-sub
463×cbrt-div
396×cbrt-unprod
386×associate-/l*
382×associate-/r/
358×difference-of-squares
345×distribute-lft-out--
337×unpow-prod-down
323×associate-/r*
290×pow-exp
288×pow-to-exp
276×flip-+ flip3-+
253×div-inv
239×cbrt-undiv
212×sqrt-prod
199×distribute-lft-out
188×pow-prod-down
169×neg-mul-1
168×associate-/l/
154×sub-neg
143×unswap-sqr
137×distribute-rgt-in distribute-lft-in
134×cube-prod
117×*-commutative
90×log-prod
80×sqrt-div
71×clear-num frac-2neg
66×pow-unpow
62×diff-log
61×1-exp associate-+r+ rec-exp
58×sum-log
48×pow1/3
44×exp-prod
43×log-pow
40×tan-quot sqrt-pow1
39×pow1/2 sin-mult exp-sum
34×sqr-pow
33×associate-+l+
30×associate--r+
29×cos-mult
28×rem-sqrt-square
24×pow-pow
22×frac-add +-commutative swap-sqr
21×associate--l+
20×associate-+l-
16×distribute-neg-frac
15×sub-div div-sub
13×distribute-lft-neg-out
12×rem-exp-log
11×exp-diff neg-sub0
10×log-div
9×pow-flip
8×pow-prod-up inv-pow distribute-frac-neg
7×un-div-inv associate-+r-
6×pow-sqr distribute-rgt-neg-out
5×cube-div associate--l-
4×rem-cube-cbrt unpow3 neg-log pow-sub cube-mult
3×pow2 unsub-neg pow-plus
2×cos-sum sqrt-unprod unpow-prod-up tan-sum rem-cbrt-cube
1×rem-square-sqrt distribute-rgt-out cube-neg pow-neg rem-log-exp

regimes19.7s (1.7%)

Accuracy

Total 29.8b remaining (22.9%)

Threshold costs 4.7b (3.6%)

7.0b28.4%Linear.Matrix:det33 from linear-1.19.1.3
5.8b4.3%Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1
2.8b-10%Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2
2.0b47.9%Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1
1.7b0%cos(2*x)/(cos^2(x)*sin^2(x))

bsearch7.1s (0.6%)

localize4.7s (0.4%)