Details

prune7.7m (39.5%)

simplify4.9m (25.3%)

sample3.7m (18.9%)

Algorithm
60×intervals
Results
1.5m335311×body80valid
27.9s206939×body80nan
25.4s21587×body1280valid
11.9s10990×body640valid
5.5s5320×body2560valid
3.3s5156×body320valid
1.0s16512×pre80true
866.0ms2496×body160valid
213.0ms230×body5120valid

series1.3m (6.9%)

Calls

356 calls:

2.0s
(cbrt (* (/ (- y z) (- (+ t 1.0) z)) (- a x)))
1.8s
(cbrt (* (/ (- y z) (- (+ t 1.0) z)) (- a x)))
1.7s
(cbrt (* (/ (- y z) (- (+ t 1.0) z)) (- a x)))
1.4s
(/ (- (* (* z (sqrt (+ t a))) (+ b c)) (* (* (pow (cbrt t) 3) (- (* b b) (* c c))) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))) (* (pow (cbrt t) 3) (+ b c)))
1.3s
(- (* (* z (sqrt (+ t a))) (+ b c)) (* (* (pow (cbrt t) 3) (- (* b b) (* c c))) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))

regimes44.3s (3.8%)

Accuracy

Total 42.2b remaining (26.9%)

Threshold costs 4.6b (2.9%)

14.6b-0.9%Linear.Matrix:det44 from linear-1.19.1.3
8.4b10.1%Linear.Matrix:det33 from linear-1.19.1.3
3.0b88.9%The quadratic formula (r1)
2.2b0%Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2
1.7b0%cos(2*x)/(cos^2(x)*sin^2(x))

rewrite40.6s (3.5%)

Algorithm
107×rewrite-expression-head
Calls

356 calls:

1.6s
(/ (/ (/ (/ (pow a (- 1.0)) (pow (/ 1 z) y)) (exp (+ (* (- (log a)) t) b))) y) (/ 1 x))
659.0ms
(* (* (* (cbrt (- y z)) (cbrt (- y z))) (/ (cbrt (- y z)) (- (+ t 1.0) z))) (- a x))
548.0ms
(/ (/ (/ (pow a (- 1.0)) (pow (/ 1 z) y)) (exp (+ (* (- (log a)) t) b))) (/ y x))
539.0ms
(/ (* (cbrt (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t)) (cbrt (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t))) (/ (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i) (cbrt (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t))))
497.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
Rules
145301×times-frac
55176×add-sqr-sqrt
54899×*-un-lft-identity
54003×add-cube-cbrt
35295×unpow-prod-down
7522×exp-sum
6007×sqr-pow
5079×add-exp-log
4256×div-inv
2910×associate-/l*
2739×div-exp
1985×prod-exp
1501×add-cbrt-cube
1072×associate-*l*
882×pow1
839×pow-exp
644×associate-*r/
590×associate-*r*
568×pow-to-exp
564×add-log-exp
514×frac-times
492×frac-sub
486×flip-- flip3--
448×cbrt-unprod
388×distribute-rgt-neg-in
387×associate-/r*
372×sqrt-prod
356×flip-+ flip3-+
354×1-exp rec-exp
324×cbrt-undiv
318×distribute-lft-neg-in
299×difference-of-squares
294×distribute-lft-out--
292×associate-*l/
266×cbrt-prod
258×sqrt-div
239×pow-prod-down
229×unswap-sqr
182×associate-/l/
171×cbrt-div
155×distribute-lft-out
133×sub-neg
124×*-commutative
121×distribute-rgt-in associate-/r/ distribute-lft-in
118×log-prod
103×neg-mul-1
79×pow-unpow
66×clear-num frac-2neg
65×associate-+r+
64×sum-log
60×sqrt-pow1 diff-log
56×swap-sqr
53×pow1/3
52×pow1/2 tan-quot
49×exp-prod
44×pow-pow
42×associate-+l+
39×log-pow
32×rem-sqrt-square
29×+-commutative
28×unpow-prod-up associate--r+
26×frac-add
22×sin-mult
21×neg-sub0 associate--l+
18×cos-mult log-div
17×pow-sub associate-+l-
15×pow-prod-up
14×neg-log
13×pow-sqr div-sub
12×associate--l-
11×pow-flip
9×rem-exp-log sub-div
8×un-div-inv inv-pow cube-prod
7×associate-+r- pow2 pow-plus
5×rem-log-exp
4×distribute-lft-neg-out sqrt-unprod
3×exp-diff associate--r- distribute-frac-neg pow-neg
2×sqrt-pow2 distribute-neg-frac rem-square-sqrt tan-sum cos-sum exp-to-pow
1×unpow3 cube-unmult cube-mult

bsearch16.7s (1.4%)

localize7.5s (0.6%)

end1.0ms (0.0%)