Details

rewrite14.5m (38.6%)

Algorithm
99×rewrite-expression-head
Calls

324 calls:

5.0m
(/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
34.1s
(- (* (/ (* (cbrt z) (cbrt z)) (* (cbrt t) (cbrt t))) (/ (* (cbrt z) (sqrt (+ t a))) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
26.2s
(/ (* x (* (cbrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) (cbrt (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))))) (* (cbrt y) (cbrt y)))
9.1s
(/ (- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a))) (* (- 1 (/ (cbrt (* (* (* (tan z) (sin y)) (* (tan z) (tan y))) (* (tan z) (sin y)))) (cbrt (* (cos y) (cos y))))) (cos a)))
7.2s
(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
Rules
449242×frac-sub
402218×add-sqr-sqrt
393879×frac-times
314421×associate-/l*
301993×associate-/r*
272876×*-un-lft-identity
220294×cbrt-prod
192263×add-cube-cbrt
163745×associate-*l*
146805×associate-*r*
116693×flip-+ flip3-+
95496×unswap-sqr
94463×associate-*r/
84939×flip3-- flip--
63275×times-frac
58158×swap-sqr
42522×sqrt-prod
29478×*-commutative
25021×clear-num
24866×frac-2neg
21172×distribute-lft-out
20427×distribute-lft-out--
17342×associate-/l/
17339×difference-of-squares
13790×sqrt-div
13482×cbrt-div
13109×associate-*l/
10760×distribute-rgt-neg-in
10654×distribute-lft-neg-in
3484×distribute-neg-frac
2655×neg-mul-1
2162×exp-sum
1842×associate--l+
1634×log-prod
1549×associate-/r/
1428×add-exp-log
1311×add-cbrt-cube
1201×pow1
883×distribute-rgt-in distribute-lft-in
857×associate-+r+
845×frac-add
843×associate-+l+
643×add-log-exp
574×div-inv
509×prod-exp
486×un-div-inv
484×cbrt-unprod
462×tan-quot
364×pow-prod-down
324×insert-posit16
288×sub-neg
264×div-exp
236×cbrt-undiv
185×+-commutative
179×exp-prod
126×log-pow
120×sum-log
88×diff-log
59×pow1/3 pow-prod-up
52×1-exp rec-exp
49×sqrt-pow1 pow1/2
48×unpow-prod-down
39×rem-exp-log pow-sqr
33×rem-sqrt-square
31×pow-unpow
30×sin-mult
27×div-sub
26×cos-mult sub-div
25×pow-plus e-exp-1
23×associate-+l-
19×pow-exp
18×exp-diff
16×neg-sub0 associate--r+
15×cube-prod
13×pow2
12×pow-flip pow-pow
11×distribute-frac-neg inv-pow pow-to-exp
10×sqr-pow difference-of-sqr-1 log-div
9×remove-double-div pow3 neg-log associate--l-
7×distribute-lft-neg-out
6×cube-div rem-cbrt-cube
5×associate-+r-
4×tan-sum cos-sum
3×sqr-neg
2×sqrt-unprod sqrt-pow2 exp-to-pow rem-log-exp
1×unpow3 cube-mult unpow2 rem-square-sqrt sqr-cos cos-2 distribute-rgt-out

simplify12.5m (33.3%)

prune5.5m (14.6%)

sample3.5m (9.4%)

Algorithm
58×intervals
Results
1.7m318386×body80valid
29.8s198430×body80nan
27.8s21134×body1280valid
10.5s10865×body640valid
6.6s5351×body2560valid
3.4s5159×body320valid
1.4s16512×pre80true
1.0s2555×body160valid
183.0ms205×body5120valid

series46.3s (2.1%)

Calls

324 calls:

767.0ms
(/ (- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a))) (* (- 1 (cbrt (* (* (* (tan z) (tan y)) (* (tan z) (tan y))) (* (tan z) (tan y))))) (cos a)))
760.0ms
(/ (- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a))) (* (- 1 (* (tan z) (tan y))) (cos a)))
701.0ms
(* (/ (- y z) (- (+ t 1.0) z)) (- a x))
667.0ms
(- (* (+ (* x y) (* z t)) (+ (* x y) (* z t))) (* (* a b) (* a b)))
656.0ms
(/ (- (* (+ (tan z) (tan y)) (cos a)) (* (- 1 (* (tan z) (tan y))) (sin a))) (* (- 1 (/ (cbrt (* (* (* (tan z) (sin y)) (* (tan z) (tan y))) (* (tan z) (sin y)))) (cbrt (* (cos y) (cos y))))) (cos a)))

regimes32.2s (1.4%)

Accuracy

Total 38.4b remaining (30.8%)

Threshold costs 3.7b (2.9%)

11.2b-2%Linear.Matrix:det44 from linear-1.19.1.3
5.2b81.2%The quadratic formula (r1)
4.0b-48.8%cos(2*x)/(cos^2(x)*sin^2(x))
3.8b6.4%Linear.Matrix:det33 from linear-1.19.1.3
3.0b0%Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1

bsearch6.5s (0.3%)

localize6.4s (0.3%)

end0.0ms (0.0%)