Details

simplify20.9m

Calls

10248 calls:

Slowest
2.3s
(/ (* (* (* -2 -2) -2) (* (* (* (* a c) (* a c)) (* a c)) (/ (* (* 1 1) 1) (* (* b b) b)))) (* (* (* 2 2) 2) (* (* a a) a)))
2.3s
(/ (* (* (* -2 -2) -2) (* (* (* (* a a) a) (* (* c c) c)) (/ (* (* 1 1) 1) (* (* b b) b)))) (* (* (* 2 2) 2) (* (* a a) a)))
2.2s
(/ (* (* (* -2 -2) -2) (* (* (* (* a a) a) (* (* c c) c)) (* (* (/ 1 b) (/ 1 b)) (/ 1 b)))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
2.2s
(/ (* (* (* -2 -2) -2) (* (* (* (* a c) (* a c)) (* a c)) (* (* (/ 1 b) (/ 1 b)) (/ 1 b)))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
2.2s
(/ (* (* (* -2 -2) -2) (* (* (* (* a c) (* a c)) (* a c)) (* (* (/ 1 b) (/ 1 b)) (/ 1 b)))) (* (* (* 2 2) 2) (* (* a a) a)))

sample10.4m

Algorithm
71×intervals
Results
7.4m76577×body10240exit
53.3s32440×body1280valid
27.1s198322×body80valid
21.9s24518×body640valid
21.4s153270×body80nan
14.5s25154×body320valid
12.1s34879×body160valid
9.9s150289×pre80true
2.6s3025×body2560valid
2.0s7886×body160nan
931.0ms4102×pre10240exit
368.0ms231×body5120valid

prune2.5m

series33.9s

Calls

409 calls:

Slowest
611.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2))) (* (cbrt (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2))))) (* (- phi1 phi2) (- phi1 phi2))))
599.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cbrt (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2))))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
570.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
558.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
447.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))

rewrite14.5s

Algorithm
127×rewrite-expression-head
Calls

409 calls:

Slowest
576.0ms
(+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x)))
425.0ms
(log (+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))))
409.0ms
(- (exp x) (exp (- x)))
391.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2))) (* (cbrt (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2))))) (* (- phi1 phi2) (- phi1 phi2))))
320.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
Rules
3423×*-un-lft-identity
3354×add-sqr-sqrt
2425×times-frac
2016×add-exp-log
1961×add-cube-cbrt
1939×associate-*l/
1888×flip--
1887×flip3--
1879×frac-times
1655×add-cbrt-cube
1519×cbrt-div
1236×pow1
922×sqrt-div
887×frac-add
836×associate-*r/
655×associate-*l*
646×prod-exp
635×add-log-exp
613×cbrt-prod
595×associate-*r*
551×difference-of-squares
485×cbrt-unprod
461×div-exp
409×insert-posit16
390×sqrt-prod
369×associate-/r*
356×cbrt-undiv
324×distribute-lft-out
304×associate-/l*
275×distribute-lft-out--
262×pow-prod-down
211×swap-sqr
201×div-inv
194×flip-+
193×flip3-+
167×unswap-sqr
166×log-prod
142×difference-of-sqr-1
140×associate-/r/
133×pow-prod-up
124×log-pow
104×*-commutative
102×sub-neg
97×frac-2neg clear-num
92×sqrt-pow1
85×pow-sqr
80×exp-prod
76×diff-log
75×associate-/l/
72×pow1/2
68×pow1/3
67×pow-plus
60×tan-quot
57×1-exp rec-exp
55×unpow-prod-down
48×pow2
41×sum-log log-div
37×sqr-pow
34×rem-sqrt-square
29×associate-+r+
28×distribute-rgt-in +-commutative distribute-lft-in
24×distribute-rgt-neg-in
23×rem-log-exp
20×sin-mult
18×frac-sub div-sub
17×pow-flip
16×inv-pow
12×exp-sum
11×cos-sum cos-diff
10×neg-mul-1 distribute-lft-neg-in
exp-diff associate--l+ associate-+l- acos-asin
un-div-inv
associate-+l+ neg-sub0 pow-exp pow3 pow-to-exp
sqrt-unprod
associate--l- distribute-frac-neg neg-log rem-square-sqrt rem-cbrt-cube
log-rec rem-exp-log acos-neg distribute-rgt-out
sin-sum associate-+r- distribute-rgt-neg-out sin-PI/3 distribute-rgt-out--
remove-posit16 cos-mult sin-cos-mult tanh-undef tanh-def asin-acos unsub-neg sin-diff distribute-rgt1-in

regimes12.0s

Accuracy

Total 56.8b remaining (31.9%)

8.6b38.4%Cubic critical, narrow range
7.6b45.2%Quadratic roots, narrow range
6.7b3.6%Cubic critical, medium range
6.4b6.2%Quadratic roots, medium range
5.2b53%Quotient of products

localize4.2s

bsearch1.4s

end1.0ms