Details

prune12.3m (50.1%)

rewrite4.0m (16.2%)

Algorithm
104×rewrite-expression-head
Calls

352 calls:

2.9m
(* (/ (/ (/ (cbrt (cbrt (cos (* 2.0 x)))) (cbrt (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x)))))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)) x))
23.7s
(* (/ (/ (/ (cbrt (cos (* 2.0 x))) (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))) (* (cbrt x) (cbrt x))) (pow cos 2.0)) (/ (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)) x))
5.0s
(* (* (/ (/ (/ (cbrt (cbrt (cos (* 2.0 x)))) (cbrt (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x)))))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (* (cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x))) (cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)))) 1)) (/ (cbrt (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x))) x))
3.9s
(* (* (/ x y) (exp (- (- (+ (* (- (log z)) y) (- (log (pow a t))))) b))) (pow (/ 1 (pow a 1.0)) 1.0))
3.6s
(* (/ (/ (/ (cbrt (* (cbrt (cos (* 2.0 x))) (cbrt (cos (* 2.0 x))))) (* (cbrt (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))) (cbrt (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x))))))) (cbrt x)) (pow cos (/ 2.0 2))) (* (/ (/ (/ (cbrt (cbrt (cos (* 2.0 x)))) (cbrt (/ (pow sin (/ 2.0 2)) (cbrt (cos (* 2.0 x)))))) (cbrt x)) (pow cos (/ 2.0 2))) (/ (/ (/ (cbrt (cos (* 2.0 x))) (pow sin (/ 2.0 2))) (cbrt x)) x)))
Rules
129876×times-frac
73364×cbrt-prod
68853×add-sqr-sqrt
46287×*-un-lft-identity
43488×add-cube-cbrt
31051×associate-*r/
28709×frac-times
23383×unpow-prod-down
22485×flip-+ flip3-+
21787×associate-*l*
14396×associate-*l/
11138×add-exp-log
10459×frac-sub
10428×frac-add
9477×sqr-pow
7900×flip3-- flip--
7138×div-exp
5413×associate-/l/
3444×unswap-sqr
3313×associate-*r*
3016×prod-exp
1987×add-cbrt-cube
1121×div-inv
1101×distribute-lft-out--
1022×pow-exp
986×pow-to-exp
950×cbrt-undiv
899×difference-of-squares
858×associate-/l*
804×pow1
739×associate-/r*
717×distribute-rgt-neg-in
685×distribute-lft-neg-in
662×cbrt-unprod
590×add-log-exp
516×associate-/r/
510×cube-prod
398×distribute-lft-out
276×sqrt-prod
260×sqrt-div
253×cbrt-div
226×neg-mul-1
221×pow-prod-down
153×distribute-rgt-in distribute-lft-in
133×log-prod
127×sub-neg
113×*-commutative
111×1-exp
95×diff-log
88×associate--r+
86×log-pow
84×exp-prod
81×frac-2neg clear-num
59×associate--l+
58×tan-quot
53×unpow3 cube-mult
47×rec-exp
44×sum-log pow1/3
36×pow-unpow distribute-rgt-out--
33×sin-mult
30×neg-sub0
29×sqrt-pow1 pow1/2
28×associate-+r+
26×pow-pow
25×cos-mult +-commutative
23×sub-div
22×neg-log
21×rem-sqrt-square div-sub distribute-neg-in
18×swap-sqr associate--l-
14×exp-diff
11×pow-flip inv-pow
10×sum-cubes
exp-sum
associate-+l+ unpow-prod-up exp-neg rem-exp-log associate-+l-
associate--r-
distribute-neg-frac unpow2
pow-prod-up un-div-inv distribute-frac-neg rem-log-exp pow-sqr
associate-+r- rem-cube-cbrt log-div
pow2 pow-plus cube-div
sqrt-unprod tan-sum cos-sum
distribute-lft-neg-out unsub-neg unpow1/2 cube-neg difference-cubes rem-square-sqrt rem-cbrt-cube pow-sub

sample3.1m (12.5%)

Algorithm
59×intervals
Results
1.2m326408×body80valid
24.8s207865×body80nan
19.6s20379×body1280valid
7.6s10070×body640valid
6.1s5311×body2560valid
2.8s4599×body320valid
1.7s16512×pre80true
688.0ms2159×body160valid
177.0ms225×body5120valid

simplify3.0m (12.3%)

series1.3m (5.4%)

Calls

352 calls:

4.0s
(+ (* (/ z (* (cbrt t) (cbrt t))) (* (sqrt (+ t a)) (+ c b))) (* (* (cbrt t) (- (* c c) (* b b))) (- a (- (/ (/ 2.0 3.0) t) (/ 5.0 6.0)))))
3.8s
(+ (pow (+ (* z t) (* x y)) 3) (pow (* b a) 3))
3.6s
(+ (pow (+ (* z t) (* x y)) 3) (pow (* b a) 3))
2.9s
(/ (- (* (+ (* (* (* b b) (- (pow 1.0 3) (pow (* 3.0 a) 3))) (+ (* 1.0 (- 1.0 a)) (* a a))) (* (* (* a a) (+ (pow 1.0 3) (pow a 3))) (+ (* (* 3.0 a) (+ (* 3.0 a) 1.0)) (* 1.0 1.0)))) (* 4.0 (+ (pow (+ (pow b 2) (* a a)) 2.0) 1.0))) (* (* (- (* 1.0 1.0) (pow (+ (pow b 2) (* a a)) (* 2 2.0))) (+ (* 1.0 (- 1.0 a)) (* a a))) (+ (* (* 3.0 a) (+ (* 3.0 a) 1.0)) (* 1.0 1.0)))) (* (+ (* (* 3.0 a) (+ (* 3.0 a) 1.0)) (* 1.0 1.0)) (* (+ (* 1.0 (- 1.0 a)) (* a a)) (+ (pow (+ (pow b 2) (* a a)) 2.0) 1.0))))
2.7s
(- (* (+ (* (* (* b b) (- (pow 1.0 3) (pow (* 3.0 a) 3))) (+ (* 1.0 (- 1.0 a)) (* a a))) (* (* (* a a) (+ (pow 1.0 3) (pow a 3))) (+ (* (* 3.0 a) (+ (* 3.0 a) 1.0)) (* 1.0 1.0)))) (* 4.0 (+ (pow (+ (pow b 2) (* a a)) 2.0) 1.0))) (* (* (- (* 1.0 1.0) (pow (+ (pow b 2) (* a a)) (* 2 2.0))) (+ (* 1.0 (- 1.0 a)) (* a a))) (+ (* (* 3.0 a) (+ (* 3.0 a) 1.0)) (* 1.0 1.0))))

regimes35.7s (2.4%)

Accuracy

Total 52.6b remaining (33.5%)

Threshold costs 3.0b (1.9%)

14.5b-10.5%Linear.Matrix:det44 from linear-1.19.1.3
8.3b1.5%Linear.Matrix:det33 from linear-1.19.1.3
5.8b1.9%Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2
4.8b83.2%The quadratic formula (r1)
3.7b86.9%NMSE problem 3.2.1

bsearch8.6s (0.6%)

localize7.6s (0.5%)

end1.0ms (0.0%)