Details

series2.3m (45.9%)

Calls

344 calls:

1.6m
(- (* (+ (+ (* x y) (* z t)) (* a b)) (+ (+ (* x y) (* z t)) (* a b))) (* (* c i) (* c i)))
826.0ms
(* (sqrt (+ (sqrt x) (sqrt 1.0))) (* (sqrt (- (sqrt x) (sqrt 1.0))) (sqrt x)))
676.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))))))
652.0ms
(/ (- (* (+ (+ (* x y) (* z t)) (* a b)) (+ (+ (* x y) (* z t)) (* a b))) (* (* c i) (* c i))) (- (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
598.0ms
(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))))

sample1.2m (24.8%)

Algorithm
60×intervals
Results
23.1s336501×body80valid
9.0s21683×body1280valid
8.1s207422×body80nan
3.0s10806×body640valid
2.4s5317×body2560valid
954.0ms5132×body320valid
439.0ms16512×pre80true
333.0ms2533×body160valid
62.0ms227×body5120valid

prune43.2s (14.4%)

rewrite16.7s (5.6%)

Algorithm
102×rewrite-expression-head
Calls

344 calls:

1.2s
(* (* (/ 1 (* (cbrt (- (+ t 1.0) z)) (cbrt (- (+ t 1.0) z)))) (/ (- y z) (cbrt (- (+ t 1.0) z)))) (- a x))
1.0s
(* (* x (sqrt (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))) (/ (sqrt (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b))))) y))
977.0ms
(/ (* (* x (sqrt (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))) (sqrt (/ (pow (/ 1 a) 1.0) (exp (+ (* y (log (/ 1 z))) (+ (* (log (/ 1 a)) t) b)))))) y)
510.0ms
(/ (+ (* (+ (* (* (cbrt (+ (* (+ (* x y) z) y) 27464.7644705)) (cbrt (+ (* (+ (* x y) z) y) 27464.7644705))) (* (cbrt (+ (* (+ (* x y) z) y) 27464.7644705)) y)) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
436.0ms
(/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (* (cbrt (+ (* (+ (* (+ y a) y) b) y) c)) (cbrt (+ (* (+ (* (+ y a) y) b) y) c))) (* (cbrt (+ (* (+ (* (+ y a) y) b) y) c)) y)) i))
Rules
7303×times-frac
5130×add-sqr-sqrt
4971×*-un-lft-identity
4159×add-cube-cbrt
1809×add-exp-log
1431×cbrt-prod
1094×add-cbrt-cube
1052×unpow-prod-down
989×pow1
825×sqrt-prod
821×associate-*r*
812×prod-exp
655×distribute-rgt-neg-in
637×distribute-lft-neg-in
582×associate-*l*
544×cube-prod
537×add-log-exp
392×associate-/l*
385×flip3-- flip--
359×associate-/r*
338×cbrt-unprod
311×div-inv
309×difference-of-squares
298×frac-times
292×div-exp
284×distribute-lft-out--
271×associate-*r/
263×pow-prod-down
232×log-prod
215×associate-*l/
212×cbrt-div
203×neg-mul-1
201×distribute-rgt-in distribute-lft-in
186×frac-sub
166×unswap-sqr
161×cbrt-undiv
155×distribute-lft-out
153×pow-exp
151×sqrt-div
150×exp-sum
133×pow-to-exp
127×sub-neg
126×associate-/r/
117×*-commutative
114×flip-+ flip3-+
92×sqrt-pow1
87×sqr-pow
83×pow1/3
70×sin-mult
64×cos-mult
62×pow1/2
59×diff-log log-pow
56×clear-num sum-log frac-2neg
50×swap-sqr
49×pow-prod-up
46×associate-+l+
44×associate-/l/
43×associate-+r+
41×exp-prod
38×pow-unpow
37×pow-sqr
31×1-exp
30×rem-sqrt-square
28×rec-exp
24×tan-quot associate--r+
23×sub-div
22×pow-plus
21×+-commutative
19×pow-flip associate--l+
17×frac-add
16×unpow3 cube-mult associate-+l-
15×inv-pow
14×neg-sub0
13×pow2
12×distribute-neg-frac
11×neg-log
10×pow-pow rem-exp-log
8×distribute-rgt-neg-out associate--l- log-div
7×div-sub log-rec
6×sqrt-unprod associate-+r-
5×exp-diff unpow2
4×distribute-neg-in
3×cube-div rem-log-exp
2×cos-sum rem-cube-cbrt un-div-inv distribute-lft-neg-out unpow-prod-up rem-square-sqrt distribute-frac-neg tan-sum exp-to-pow
1×e-exp-1 pow3 exp-neg pow-sub rem-cbrt-cube pow-neg

regimes14.0s (4.7%)

Accuracy

Total 42.7b remaining (27%)

Threshold costs 4.6b (2.9%)

11.6b-5.9%Linear.Matrix:det44 from linear-1.19.1.3
6.2b11%Linear.Matrix:det33 from linear-1.19.1.3
5.1b46.3%Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2
3.7b86.1%The quadratic formula (r1)
2.3b0%cos(2*x)/(cos^2(x)*sin^2(x))

simplify8.9s (3.0%)

Algorithm
162×egg-herbie

bsearch2.5s (0.8%)

localize2.4s (0.8%)

end1.0ms (0.0%)