Details

sample12.8m (41.2%)

Algorithm
77×intervals
Results
9.8m57417×body10240exit
1.3m42592×body1280valid
27.0s29598×body640valid
17.4s196831×body80valid
14.4s152373×body80nan
12.5s26905×body320valid
9.4s197099×pre80true
7.6s35524×body160valid
1.5s3021×body2560valid
1.2s8049×body160nan
448.0ms4025×pre10240exit
302.0ms261×body5120valid
2.0msbody640nan
1.0msbody320nan

simplify12.5m (40.2%)

prune3.6m (11.4%)

rewrite54.1s (2.9%)

Algorithm
143×rewrite-expression-head
Calls

448 calls:

4.4s
(sqrt (+ (* (* (* (sqrt (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (sqrt (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
850.0ms
(sqrt (+ (* (* (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
548.0ms
(* (/ (/ (/ 1 b1) (cbrt b2)) (cbrt (cbrt b2))) (/ a2 (cbrt b2)))
429.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
412.0ms
(* (/ (sqrt e) (/ (sqrt (+ 1.0 (* e (cos v)))) 1)) (/ (sqrt e) (/ (sqrt (+ 1.0 (* e (cos v)))) (sin v))))
Rules
387012×associate-*l/
274491×frac-times
202362×cbrt-div
195896×flip--
195895×flip3--
151912×sqrt-div
71848×associate-*r/
58561×frac-add
8913×times-frac
6737×add-sqr-sqrt
5827×*-un-lft-identity
4884×add-cube-cbrt
2806×add-exp-log
2617×cbrt-prod
1892×associate-*l*
1802×add-cbrt-cube
1131×pow1
1021×sqrt-prod
927×div-exp
912×prod-exp
706×add-log-exp
705×associate-*r*
500×associate-/r*
495×cbrt-undiv
492×cbrt-unprod
433×associate-/l* div-inv
358×difference-of-squares
354×log-prod
315×unswap-sqr
269×distribute-lft-out--
267×pow-exp
258×pow-prod-down
188×distribute-lft-out
187×pow-to-exp
139×associate-/r/
129×flip-+
128×flip3-+
124×swap-sqr
109×frac-2neg clear-num
105×*-commutative
101×cos-mult
93×sub-neg
83×diff-log
80×associate-/l/
73×pow-prod-up
59×pow1/3
57×log-pow
56×sum-log unpow-prod-down
47×pow-sqr
45×1-exp
44×log-div
43×pow-plus exp-prod
39×sqrt-pow1 pow1/2 div-sub rem-log-exp
32×distribute-rgt-in distribute-lft-in
29×frac-sub rec-exp +-commutative
28×pow2 rem-sqrt-square
26×tan-quot
20×distribute-rgt-neg-in
18×cos-diff distribute-lft-neg-in distribute-rgt-out
15×cos-sum sin-diff
14×sin-mult
11×sin-cos-mult
10×associate-+r+ associate--l+ pow3 sqr-pow acos-asin
exp-sum
associate-+l+ associate--r+
exp-diff pow-unpow neg-mul-1
associate--l- sin-sum associate-+r- cube-unmult rem-cbrt-cube
distribute-frac-neg rem-exp-log
distribute-lft1-in distribute-rgt-neg-out acos-neg
pow-flip neg-sub0 distribute-lft-neg-out sqrt-unprod pow-pow inv-pow un-div-inv exp-to-pow asin-acos associate-+l- sqr-cos
quot-tan sub-div tanh-def difference-cubes sum-cubes tanh-undef rem-square-sqrt associate--r-

series48.0s (2.6%)

Calls

448 calls:

691.0ms
(sqrt (+ (* (* (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
659.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (* (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))) (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
611.0ms
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
590.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
580.0ms
(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))

regimes21.6s (1.2%)

Accuracy

Total 56.5b remaining (32.4%)

Threshold costs 5.8b (3.3%)

7.7b44.4%Quadratic roots, narrow range
7.7b44.5%Cubic critical, narrow range
6.3b8.3%Quadratic roots, medium range
6.3b8.7%Cubic critical, medium range
5.3b45.4%Quotient of products

localize6.7s (0.4%)

bsearch5.0s (0.3%)

end1.0ms (0.0%)