Details

simplify12.3m

Calls

5220 calls:

Slowest
1.9s
(/ (* (* (* (* -3/2 (* a c)) (* -3/2 (* a c))) (* -3/2 (* a c))) (* (* (/ 1 b) (/ 1 b)) (/ 1 b))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
1.5s
(/ (* (* (* (* -3/2 (* a c)) (/ 1 b)) (* (* -3/2 (* a c)) (/ 1 b))) (* (* -3/2 (* a c)) (/ 1 b))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
1.4s
(* (* (* (* (- (* x x) 1) (- (* x x) 1)) (* (- (* x x) 1) (- (* x x) 1))) (* (- (* x x) 1) (- (* x x) 1))) (* (* (- (* x x) 1) (- (* x x) 1)) (- (* x x) 1)))
1.3s
(* (* (- (pow (* x x) 3) (pow 1 3)) (- (* (* x x) (* x x)) (* 1 1))) (- (* (* x x) (* x x)) (* 1 1)))
1.2s
(* (* (* (* (- (* x x) 1) (- (* x x) 1)) (- (* x x) 1)) (* (* (- (* x x) 1) (- (* x x) 1)) (- (* x x) 1))) (* (* (- (* x x) 1) (- (* x x) 1)) (- (* x x) 1)))

sample10.6m

Algorithm
72×intervals
Results
7.8m80794×body10240exit
49.6s33115×body1280valid
26.2s197839×body80valid
21.2s151977×body80nan
19.8s24419×body640valid
14.4s25212×body320valid
11.7s34639×body160valid
8.8s153152×pre80true
2.5s2981×body2560valid
1.7s8061×body160nan
1.0s4082×pre10240exit
265.0ms205×body5120valid

prune1.9m

series23.5s

Calls

414 calls:

Slowest
449.0ms
(/ (* (pow (/ 1 (+ 1 (exp (- s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)) (* (pow (/ 1 (+ 1 (exp (- t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- t))))) c_n)))
443.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
437.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
407.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
363.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

regimes11.8s

Accuracy

Total 61.1b remaining (34.5%)

7.3b46.4%Quadratic roots, narrow range
7.1b47.7%Cubic critical, narrow range
7.0b38.8%Quotient of products
6.9b0%Cubic critical, medium range
6.3b7.2%Quadratic roots, medium range

rewrite4.0s

Algorithm
128×rewrite-expression-head
Calls

414 calls:

Slowest
313.0ms
(/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x))))
107.0ms
(- (/ (- (/ -3 x) (/ (/ -3 x) (* (* x x) (* x x)))) (- 1 (/ 1 (* x x)))) (/ 1 (* x x)))
56.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
55.0ms
(/ (- (sqrt (+ (* (* c -4) a) (* b b))) b) (* 2 a))
54.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
Rules
1448×associate-*l/
1269×flip--
1268×flip3--
1181×add-exp-log
1055×*-un-lft-identity
1040×add-sqr-sqrt
932×add-cube-cbrt
831×frac-times
751×sqrt-div
739×pow1
668×frac-add
631×add-cbrt-cube
523×add-log-exp
474×associate-*r/
414×insert-posit16
390×prod-exp
369×times-frac
265×pow-exp
259×associate-*r*
258×log-prod
245×associate-/r* associate-*l*
227×div-exp
220×div-inv
187×sqrt-prod
185×pow-to-exp
166×associate-/r/
137×associate-/l*
119×cbrt-div
108×rec-exp
106×frac-2neg clear-num
102×*-commutative
99×cbrt-prod
97×flip-+
96×pow-prod-down flip3-+
94×sub-neg
80×cbrt-unprod
76×log-pow
75×log-div
74×associate-/l/
60×tan-quot
53×pow-prod-up
50×pow1/3 cbrt-undiv
48×difference-of-squares
44×pow1/2
43×distribute-lft-out--
39×diff-log
38×pow-plus rem-sqrt-square
37×frac-sub distribute-rgt-in distribute-lft-in
35×distribute-lft-out pow2 rem-log-exp
34×pow-flip
31×associate--l+
29×exp-prod
24×+-commutative div-sub
23×inv-pow
20×sum-log
15×difference-of-sqr-1 unpow-prod-down
14×associate--l-
11×associate-+r+ associate--r+
10×associate--r-
cos-sum acos-asin
sin-mult cos-diff distribute-rgt-out
associate-+l+ pow-pow
sin-sum exp-sum pow3 un-div-inv associate-+l-
exp-diff
rem-cbrt-cube distribute-rgt1-in
neg-sub0 distribute-rgt-out-- distribute-frac-neg distribute-rgt-neg-out sub-div acos-neg rem-exp-log
cos-mult associate-+r- unsub-neg sqrt-unprod tanh-undef tanh-def neg-mul-1 sin-PI/3 exp-to-pow asin-acos sin-diff

localize3.4s

bsearch1.8s

end1.0ms