Details

series10.9m (80.6%)

Calls

331 calls:

3.9s
(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (+ (* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* i a)))) (* b (fma (- a) i (* a i))))))
3.6s
(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (+ (* b (- (* c z) (* i a))) (* b (fma (- a) i (* a i))))))
3.0s
(fma t (- (* (* (* (* x 18.0) (* (cbrt y) (cbrt y))) (cbrt y)) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* j (* 27.0 k)))))
2.9s
(fma t (- (* (* z y) (* x 18.0)) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* j (* 27.0 k)))))
2.9s
(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* j (* 27.0 k)))))

sample1.4m (10.6%)

Algorithm
59×intervals
Results
30.2s262791×body80valid
18.4s208294×body80nan
11.4s21273×body1280valid
4.2s11026×body640valid
3.5s5254×body2560valid
1.4s5049×body320valid
957.0ms16512×pre80true
515.0ms2548×body160valid
113.0ms210×body5120valid

prune46.4s (5.7%)

simplify8.3s (1.0%)

Algorithm
160×egg-herbie

regimes7.3s (0.9%)

Accuracy

Total 32.9b remaining (25.4%)

Threshold costs 4.3b (3.3%)

8.5b-11.1%Linear.Matrix:det33 from linear-1.19.1.3
4.5b84.3%NMSE problem 3.2.1
4.4b83.4%The quadratic formula (r1)
2.4b31.8%Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1
2.3b15.4%cos(2*x)/(cos^2(x)*sin^2(x))

rewrite5.3s (0.7%)

Algorithm
102×rewrite-expression-head
Calls

333 calls:

252.0ms
(exp (+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))
231.0ms
(* (/ (/ (sqrt (pow (/ 1 a) 1.0)) (sqrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) y) (* (/ (sqrt (pow (/ 1 a) 1.0)) (sqrt (exp (fma y (log (/ 1 z)) (fma (log (/ 1 a)) t b))))) x))
201.0ms
(* (* (* (* x 18.0) (* (cbrt y) (cbrt y))) (cbrt y)) z)
171.0ms
(/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (* (cbrt (+ (* (+ y a) y) b)) (cbrt (+ (* (+ y a) y) b))) (* (cbrt (+ (* (+ y a) y) b)) y)) c) y) i))
95.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))
Rules
8257×times-frac
5986×*-un-lft-identity
5829×add-sqr-sqrt
5001×add-cube-cbrt
1680×add-exp-log
1647×sqrt-prod
1386×unpow-prod-down
990×add-cbrt-cube
964×prod-diff
844×associate-*l*
798×pow1
712×prod-exp
578×distribute-rgt-neg-in
543×distribute-lft-neg-in
474×add-log-exp
407×associate-/r*
403×associate-*r*
371×div-inv
357×associate-/l*
336×fma-udef
335×div-exp
334×log1p-expm1-u
333×expm1-log1p-u
317×exp-sum
288×cbrt-prod
283×distribute-lft-out--
257×cbrt-unprod
256×distribute-lft-out
250×difference-of-squares
205×sqr-pow
201×fma-neg
174×pow-prod-down
172×flip-- flip3--
171×neg-mul-1
168×cbrt-undiv
167×exp-prod
155×associate-+r+
145×log-pow pow-exp
131×unswap-sqr
130×pow-to-exp
124×associate-/r/
116×sqrt-div
114×fma-def
97×associate-*r/
92×distribute-rgt-in distribute-lft-in
86×*-commutative
84×log-prod
83×flip-+ flip3-+
79×associate-*l/
68×frac-times
66×pow1/3 sqrt-pow1
64×associate--r+
63×frac-2neg clear-num
62×sub-neg
61×pow1/2
57×tan-quot
46×diff-log
45×cbrt-div
44×rem-sqrt-square 1-exp rec-exp
43×swap-sqr
36×frac-sub
34×associate-/l/
33×associate-+l+ sum-log
30×log-div
26×sin-mult
25×associate-+l-
24×pow-prod-up neg-sub0
20×pow-sqr +-commutative cos-mult
19×pow-unpow
17×neg-log
16×pow-pow
12×rem-exp-log sub-div
11×pow-flip div-sub associate--l-
10×inv-pow pow-plus
9×pow2
8×distribute-frac-neg distribute-neg-frac
7×cube-prod
6×exp-diff sqrt-unprod
5×un-div-inv distribute-neg-in associate--l+ unpow2
4×exp-neg associate-+r- hypot-def rem-log-exp
2×cos-sum tan-sum expm1-udef
1×cube-mult cube-div unpow3 log1p-udef associate--r- log1p-expm1 frac-add expm1-log1p rem-square-sqrt rem-cbrt-cube distribute-rgt-neg-out exp-to-pow log-rec

localize2.5s (0.3%)

bsearch1.4s (0.2%)

end1.0ms (0.0%)