Details

simplify12.2m (54.6%)

prune3.9m (17.6%)

sample3.6m (16.3%)

Algorithm
60×intervals
Results
1.8m336548×body80valid
34.5s209576×body80nan
24.5s21376×body1280valid
10.3s11225×body640valid
6.2s5151×body2560valid
3.5s4999×body320valid
1.2s16512×pre80true
1.0s2506×body160valid
286.0ms227×body5120valid

series1.1m (4.7%)

Calls

345 calls:

3.5s
(- (- (+ (- (* (* (* x 18.0) y) (* z t)) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k))
3.4s
(- (- (+ (- (* (* (* x 18.0) y) (* z t)) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* 27.0 (* j k)))
3.3s
(- (- (+ (- (* (* x 18.0) (* y (* z t))) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k))
926.0ms
(/ (* r (sin b)) (/ (- (* (* (cos a) (cos b)) (* (* (cos a) (cos b)) (* (cos a) (cos b)))) (* (* (sin b) (sin a)) (* (* (sin b) (sin a)) (* (sin b) (sin a))))) (+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin b) (sin a)) (+ (* (sin b) (sin a)) (* (cos a) (cos b)))))))
709.0ms
(* (* (- y z) (* (/ 1 (* (cbrt (- (+ t 1.0) z)) (* (cbrt (* (cbrt (- (+ t 1.0) z)) (cbrt (- (+ t 1.0) z)))) (cbrt (cbrt (- (+ t 1.0) z)))))) (/ 1 (cbrt (- (+ t 1.0) z))))) (- a x))

rewrite53.0s (4.0%)

Algorithm
102×rewrite-expression-head
Calls

345 calls:

8.1s
(- (- (+ (- (* (* (* x 18.0) y) (* z t)) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k))
8.0s
(* (* (- y z) (* (/ 1 (* (cbrt (- (+ t 1.0) z)) (* (cbrt (* (cbrt (- (+ t 1.0) z)) (cbrt (- (+ t 1.0) z)))) (cbrt (cbrt (- (+ t 1.0) z)))))) (/ 1 (cbrt (- (+ t 1.0) z))))) (- a x))
7.0s
(- (- (+ (- (* (* (* x 18.0) y) (* z t)) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* 27.0 (* j k)))
5.2s
(- (- (+ (- (* (* x 18.0) (* y (* z t))) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k))
3.4s
(* (* (- y z) (* (/ 1 (* (cbrt (- (+ t 1.0) z)) (cbrt (- (+ t 1.0) z)))) (/ 1 (cbrt (- (+ t 1.0) z))))) (- a x))
Rules
3265×associate-*l/
2902×associate-*r/
2694×add-sqr-sqrt
2653×times-frac
2576×*-un-lft-identity
2153×add-exp-log
2028×frac-times
2026×add-cube-cbrt
1992×frac-sub
1908×flip3-- flip--
1513×add-cbrt-cube
1387×pow1
946×prod-exp
864×sqrt-div
839×flip-+ flip3-+
676×cbrt-unprod
627×associate-/l/
579×add-log-exp
548×associate-*r*
500×pow-prod-down
434×associate-*l*
389×div-exp
345×insert-posit16
331×cbrt-prod
273×associate-/r*
254×cos-mult
248×cbrt-undiv
243×associate-/l*
237×distribute-rgt-neg-in sqrt-prod
227×distribute-lft-neg-in
198×sin-mult
192×cbrt-div
175×difference-of-squares
166×distribute-lft-out--
154×div-inv
152×associate-/r/
143×distribute-lft-out
138×sub-div
123×log-prod
121×unswap-sqr
117×*-commutative
116×sub-neg
106×distribute-rgt-in distribute-lft-in
95×frac-add
85×diff-log
83×1-exp rec-exp
77×pow1/3
75×neg-mul-1
64×sum-log
59×frac-2neg clear-num
56×pow-prod-up
55×log-pow
52×pow-sqr
49×associate-+l+
48×associate-+r+
42×exp-prod
41×associate--l+
40×sqrt-pow1 pow1/2
36×swap-sqr rem-sqrt-square
31×exp-diff
30×un-div-inv
29×pow-plus
26×associate-+l-
24×rem-exp-log
22×exp-sum cube-unmult associate--r+
21×unpow-prod-down
20×+-commutative
18×log-div
16×tan-quot
15×pow2
13×pow-flip
11×inv-pow div-sub
10×neg-sub0 difference-cubes
9×pow-unpow associate--l-
7×sqr-pow neg-log
6×pow-exp associate-+r- pow-pow distribute-neg-frac
5×pow-to-exp e-exp-1 pow-sub
3×unpow-prod-up distribute-lft-neg-out
2×quot-tan distribute-frac-neg distribute-rgt-neg-out cos-sum tan-sum distribute-rgt-out-- rem-cbrt-cube cos-2
1×pow3 difference-of-sqr-1 sqrt-unprod exp-to-pow remove-posit16

regimes27.5s (2.1%)

Accuracy

Total 42.4b remaining (27.3%)

Threshold costs 3.8b (2.5%)

10.8b-22.8%Linear.Matrix:det44 from linear-1.19.1.3
6.8b11.5%Linear.Matrix:det33 from linear-1.19.1.3
4.9b82.5%The quadratic formula (r1)
4.6b82.1%NMSE problem 3.2.1
2.9b0%cos(2*x)/(cos^2(x)*sin^2(x))

localize6.6s (0.5%)

bsearch4.9s (0.4%)

end1.0ms (0.0%)