Details

simplify4.2m (31.4%)

series3.0m (22.3%)

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)))
871.0ms
(/ (+ i (* y (+ c (* y (+ (* (+ a y) y) b))))) (+ t (* (+ (* y (+ (* y (+ z (* x y))) 27464.7644705)) 230661.510616) y)))
671.0ms
(* (/ (/ (- 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))

sample3.0m (22.3%)

Algorithm
60×intervals
Results
1.2m336023×body80valid
24.7s208371×body80nan
21.2s21285×body1280valid
7.4s11034×body640valid
4.1s5239×body2560valid
3.1s5235×body320valid
1.1s16512×pre80true
844.0ms2502×body160valid
549.0ms244×body5120valid

prune1.9m (13.9%)

regimes39.6s (4.9%)

Accuracy

Total 42.1b remaining (26.2%)

Threshold costs 5.0b (3.1%)

11.2b-33%Linear.Matrix:det44 from linear-1.19.1.3
5.5b24.4%Linear.Matrix:det33 from linear-1.19.1.3
4.5b84.3%The quadratic formula (r1)
3.7b0%cos(2*x)/(cos^2(x)*sin^2(x))
3.3b43.8%Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1

rewrite25.4s (3.1%)

Algorithm
103×rewrite-expression-head
Calls

352 calls:

1.4s
(+ (- (/ (/ (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))))))
1.4s
(* (/ (/ (- 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 y) (cos y)) (sin z)) (cos z)))) (/ (sin a) (cos a))) (/ (sin z) (* (cos z) (- 1 (/ (* (/ (sin y) (cos y)) (sin z)) (cos z))))))
809.0ms
(* (* (/ x y) (* (cbrt (- 1 z)) (* (cbrt (* (cbrt (- 1 z)) (cbrt (- 1 z)))) (cbrt (cbrt (- 1 z)))))) (cbrt (- 1 z)))
638.0ms
(/ (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
3854×times-frac
3716×*-un-lft-identity
3683×add-exp-log
3420×add-sqr-sqrt
3347×frac-times
2491×flip3-- flip--
2451×prod-exp
2345×add-cube-cbrt
1516×associate-*r/
1474×associate-*l*
1290×add-cbrt-cube
1147×associate-*l/
1045×cbrt-prod
907×pow1
899×associate-/r/
664×associate-*r*
555×add-log-exp
543×pow-exp
511×pow-to-exp
478×cbrt-unprod
472×div-exp
452×distribute-lft-out--
355×difference-of-squares
271×distribute-lft-out
264×pow-prod-down
243×associate-/r*
226×distribute-rgt-neg-in
220×distribute-lft-neg-in
209×sqrt-prod
208×associate-/l*
201×frac-sub
189×cbrt-undiv div-inv
141×flip-+ flip3-+ unswap-sqr
139×sub-neg
120×distribute-rgt-in *-commutative distribute-lft-in
116×swap-sqr
108×sqrt-div
90×pow1/3
81×log-prod
74×neg-mul-1
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
40×associate-/l/
34×associate-+l+
33×rem-sqrt-square
31×1-exp rec-exp
30×sin-mult
28×log-pow
26×pow-prod-up
25×cos-mult sqr-pow +-commutative
24×associate--r+
23×associate-+l-
19×associate--l+
17×pow-plus distribute-neg-frac
16×pow-unpow pow-pow
15×tan-quot
14×sub-div exp-prod log-div pow-sqr
9×pow2
8×exp-sum rem-exp-log
7×pow-flip neg-sub0
6×inv-pow div-sub
5×unpow-prod-up neg-log un-div-inv
4×exp-diff associate--l-
3×associate-+r- distribute-rgt-neg-out pow3 rem-log-exp
2×distribute-lft-neg-out distribute-frac-neg sqrt-unprod tan-sum cos-sum e-exp-1 pow-sub
1×distribute-rgt-out-- rem-square-sqrt rem-cbrt-cube unpow1/3

bsearch9.1s (1.1%)

localize7.8s (1.0%)

end1.0ms (0.0%)