Details

simplify4.2m (32.2%)

series3.0m (22.5%)

Calls

352 calls:

1.8m
(/ 1 (/ (+ i (* y (+ c (* y (+ (* (+ a y) y) b))))) (+ t (* (+ (* y (+ (* y (+ z (* x y))) 27464.7644705)) 230661.510616) y))))
5.7s
(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
5.4s
(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
887.0ms
(/ (+ i (* y (+ c (* y (+ (* (+ a y) y) b))))) (+ t (* (+ (* y (+ (* y (+ z (* x y))) 27464.7644705)) 230661.510616) y)))
792.0ms
(* (/ (/ (- y z) (* (cbrt (- (+ t 1.0) z)) (cbrt (- (+ t 1.0) z)))) (cbrt (- (+ t 1.0) z))) (- a x))

sample2.7m (20.9%)

Algorithm
60×intervals
Results
1.2m336023×body80valid
23.3s208371×body80nan
19.1s21285×body1280valid
8.4s11034×body640valid
5.0s5239×body2560valid
2.9s5235×body320valid
1.2s2502×body160valid
689.0ms16512×pre80true
515.0ms244×body5120valid

prune1.9m (14.5%)

regimes37.8s (4.8%)

Accuracy

Total 40.7b remaining (25.6%)

Threshold costs 5.0b (3.1%)

11.2b-33%Linear.Matrix:det44 from linear-1.19.1.3
4.5b84.3%The quadratic formula (r1)
4.1b43.9%Linear.Matrix:det33 from linear-1.19.1.3
3.7b0%cos(2*x)/(cos^2(x)*sin^2(x))
3.3b43.8%Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1

rewrite25.0s (3.2%)

Algorithm
103×rewrite-expression-head
Calls

352 calls:

1.3s
(* (/ (/ (- y z) (* (cbrt (- (+ t 1.0) z)) (* (cbrt (* (cbrt (- (+ t 1.0) z)) (cbrt (- (+ t 1.0) z)))) (cbrt (cbrt (- (+ t 1.0) z)))))) (cbrt (- (+ t 1.0) z))) (- a x))
1.2s
(+ (- (/ (/ (sin y) (cos y)) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z))))) (/ (sin a) (cos a))) (/ (sin z) (* (cos z) (- 1 (/ (* (/ (sin y) (cos y)) (sin z)) (cos z))))))
1.1s
(+ (- (/ (/ (sin y) (cos y)) (- 1 (/ (* (/ (sin y) (cos y)) (sin z)) (cos z)))) (/ (sin a) (cos a))) (/ (sin z) (* (cos z) (- 1 (/ (* (/ (sin y) (cos y)) (sin z)) (cos z))))))
927.0ms
(* (* (/ x y) (* (cbrt (- 1 z)) (* (cbrt (* (cbrt (- 1 z)) (cbrt (- 1 z)))) (cbrt (cbrt (- 1 z)))))) (cbrt (- 1 z)))
579.0ms
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))) x)))
Rules
6658×cbrt-div
4824×*-un-lft-identity
4710×times-frac
3994×add-sqr-sqrt
3719×add-exp-log
3347×frac-times
2681×add-cube-cbrt
2491×flip3-- flip--
2437×prod-exp
1549×associate-*l*
1516×associate-*r/
1326×add-cbrt-cube
1147×associate-*l/
1080×cbrt-prod
924×pow1
899×associate-/r/
777×associate-*r*
628×distribute-lft-out--
613×distribute-rgt-neg-in
555×add-log-exp
551×distribute-lft-neg-in
543×pow-exp
514×div-exp
511×pow-to-exp
492×cbrt-unprod
475×difference-of-squares
397×distribute-lft-out
312×swap-sqr
266×pow-prod-down
247×associate-/r*
244×associate-/l*
209×sqrt-prod
203×cbrt-undiv
201×frac-sub
197×div-inv
141×flip-+ neg-mul-1 flip3-+ unswap-sqr
139×sub-neg
120×distribute-rgt-in *-commutative distribute-lft-in
108×sqrt-div
90×pow1/3
81×log-prod
69×sum-log
65×unpow-prod-down
60×sqrt-pow1
57×frac-add
56×frac-2neg clear-num diff-log
47×associate-+r+
45×pow1/2
42×associate-/l/
34×associate-+l+
33×rem-sqrt-square
32×pow-prod-up
31×1-exp rec-exp
30×sin-mult
28×log-pow
25×cos-mult sqr-pow +-commutative
24×associate--r+
23×pow-plus associate-+l-
19×associate--l+
16×pow-unpow pow-pow pow-sqr
15×tan-quot distribute-frac-neg
14×sub-div exp-prod log-div
11×pow2
9×neg-sub0
8×exp-sum div-sub rem-exp-log
7×pow-flip distribute-lft-neg-out distribute-rgt-neg-out
6×inv-pow distribute-neg-frac
5×unpow-prod-up pow3 neg-log un-div-inv
4×exp-diff associate--l-
3×associate-+r- rem-log-exp
2×sqrt-unprod tan-sum sqr-neg cos-sum rem-cbrt-cube e-exp-1 pow-sub
1×distribute-rgt-out-- rem-square-sqrt unpow1/3

localize7.9s (1.0%)

bsearch7.7s (1.0%)

end1.0ms (0.0%)