Details

series6.7m (36.2%)

Calls

360 calls:

2.3m
(- (* (+ (+ (* x y) (* z t)) (* a b)) (+ (+ (* x y) (* z t)) (* a b))) (* (* c i) (* c i)))
1.7m
(+ (* (+ (+ (* x y) (* z t)) (* a b)) (+ (* x y) (* z t))) (- (* (+ (+ (* x y) (* z t)) (* a b)) (* a b)) (* (* c i) (* c i))))
1.5m
(- (* (+ (+ (* x y) (* z t)) (* a b)) (+ (+ (* x y) (* z t)) (* a b))) (* (* c i) (* c i)))
1.7s
(- (* (+ (+ (* x y) (* z t)) (* a b)) (* a b)) (* (* c i) (* c i)))
976.0ms
(/ (- (* (+ (+ (* x y) (* z t)) (* a b)) (+ (+ (* x y) (* z t)) (* a b))) (* (* c i) (* c i))) (- (+ (+ (* x y) (* z t)) (* a b)) (* c i)))

simplify4.0m (21.6%)

prune3.6m (19.5%)

sample3.0m (16.1%)

Algorithm
60×intervals
Results
1.3m335577×body80valid
25.1s207865×body80nan
17.5s21181×body1280valid
7.8s11103×body640valid
4.3s5311×body2560valid
2.5s5177×body320valid
1.0s16512×pre80true
691.0ms2488×body160valid
173.0ms225×body5120valid

regimes34.9s (3.1%)

Accuracy

Total 36.1b remaining (23%)

Threshold costs 4.6b (2.9%)

9.4b-8.3%Linear.Matrix:det44 from linear-1.19.1.3
4.8b83.3%The quadratic formula (r1)
4.0b0%Linear.Matrix:det33 from linear-1.19.1.3
3.6b87.2%NMSE problem 3.2.1
2.2b0%cos(2*x)/(cos^2(x)*sin^2(x))

rewrite28.7s (2.6%)

Algorithm
106×rewrite-expression-head
Calls

360 calls:

3.0s
(* (* (- y z) (* (* (cbrt (/ 1 (- (+ t 1.0) z))) (cbrt (/ 1 (- (+ t 1.0) z)))) (cbrt (/ 1 (- (+ t 1.0) z))))) (- a x))
1.1s
(* (+ (* (+ (* (* (cbrt (* (+ (* (+ (* x y) z) y) 27464.7644705) y)) (cbrt (* (+ (* (+ (* x y) z) y) 27464.7644705) y))) (cbrt (* (+ (* (+ (* x y) z) y) 27464.7644705) y))) 230661.510616) y) t) (/ 1 (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))
929.0ms
(/ (cbrt (* (* (* (- (tan y) (tan z)) (- (tan y) (tan z))) (- (tan y) (tan z))) (* (* (+ (tan z) (tan y)) (+ (tan z) (tan y))) (+ (tan z) (tan y))))) (- (tan y) (tan z)))
926.0ms
(cbrt (* (* (* (- (tan y) (tan z)) (- (tan y) (tan z))) (- (tan y) (tan z))) (* (* (+ (tan z) (tan y)) (+ (tan z) (tan y))) (+ (tan z) (tan y)))))
678.0ms
(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
Rules
29069×frac-times
24663×tan-quot
8356×cbrt-div
7304×associate-*l/
6545×flip3-- flip--
6340×frac-sub
6308×flip-+ flip3-+
6200×frac-add
5935×times-frac
5095×add-exp-log
4702×add-sqr-sqrt
4469×*-un-lft-identity
4211×associate-*r/
4172×associate-/l/
3671×prod-exp
3421×add-cube-cbrt
1374×add-cbrt-cube
871×pow1
814×pow-exp pow-to-exp
726×cbrt-prod
699×div-exp
605×add-log-exp
559×associate-*r*
527×associate-/r*
521×associate-*l*
519×cbrt-unprod
382×difference-of-squares
344×sqrt-prod
337×associate-/l*
335×distribute-lft-out--
295×distribute-rgt-neg-in
286×div-inv
267×distribute-lft-neg-in
257×cbrt-undiv
225×pow-prod-down
203×distribute-lft-out
166×associate-/r/
150×sub-neg
142×unswap-sqr
117×neg-mul-1
107×*-commutative
103×distribute-rgt-in distribute-lft-in
83×diff-log
72×frac-2neg clear-num
70×sqrt-div
67×log-prod unpow-prod-down
64×exp-prod
62×exp-sum
60×1-exp rec-exp
55×sum-log pow1/3
51×log-pow
46×associate-+r+
40×associate--l+
34×sqrt-pow1
33×pow1/2
32×sin-mult
30×rem-sqrt-square
29×associate-+l+
27×pow-unpow rem-exp-log
26×cos-mult
25×sqr-pow
24×swap-sqr associate--r+
23×+-commutative
19×sub-div distribute-rgt-out--
17×associate-+l-
15×exp-diff div-sub pow-prod-up
13×neg-sub0 pow-pow
11×pow-sqr
10×un-div-inv log-div
9×associate--l- pow-flip neg-log pow-plus inv-pow
8×associate-+r- pow2
2×pow3 distribute-frac-neg tan-sum distribute-neg-frac exp-neg cos-sum rem-log-exp
1×cube-unmult sqrt-unprod exp-to-pow unpow1/3 rem-cbrt-cube

localize7.7s (0.7%)

bsearch3.5s (0.3%)

end1.0ms (0.0%)