Details

sample7.6m (42.9%)

Algorithm
78×intervals
Results
4.5m33337×body10240exit
1.3m43487×body1280valid
28.7s30724×body640valid
19.2s203273×body80valid
15.5s151837×body80nan
13.1s27892×body320valid
8.9s36078×body160valid
6.0s170932×pre80true
1.6s3103×body2560valid
826.0ms7662×body160nan
474.0ms4163×pre10240exit
132.0ms223×body5120valid

simplify5.6m (31.5%)

prune2.8m (16.1%)

series50.5s (4.8%)

Calls

448 calls:

1.0s
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))) R)
742.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
732.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))) R))
633.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))
605.0ms
(/ (* (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)))

rewrite22.4s (2.1%)

Algorithm
144×rewrite-expression-head
Calls

448 calls:

2.8s
(- (/ (/ (/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)
1.3s
(* (+ (- (/ (* 1 (/ m (+ 1.0 m))) (/ v (* (+ 1.0 m) (- 1.0 m)))) 1.0) (fma 1.0 -1 1.0)) m)
565.0ms
(* (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))) (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))
547.0ms
(cbrt (* (* (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))) (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0)))) (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0)))))
547.0ms
(- (- (/ 0.125 (* (* x x) x)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))
Rules
45636×times-frac
35868×sqrt-prod
35396×*-un-lft-identity
25390×add-sqr-sqrt
23677×add-cube-cbrt
11187×prod-diff
5255×distribute-lft-out
3111×fma-neg
2232×add-exp-log
1784×sqrt-div
1578×add-cbrt-cube
1415×associate-/r/
974×pow1
922×div-inv
821×associate-/l*
750×flip-+
749×flip3-+
707×prod-exp
671×difference-of-squares
655×div-exp
635×add-log-exp
571×distribute-lft-out--
530×associate-*r*
470×associate-/r*
452×expm1-log1p-u log1p-expm1-u
424×associate--l+
396×associate-*l*
379×cbrt-unprod
361×cbrt-undiv
317×cbrt-prod
294×flip--
293×flip3--
265×pow-exp
253×distribute-rgt-in distribute-lft-in
218×frac-times
194×pow-prod-down
193×distribute-rgt-neg-in associate-*r/
189×fma-def
185×pow-to-exp
175×distribute-lft-neg-in
168×swap-sqr
150×log-prod
140×associate-*l/
131×unpow-prod-down
120×unswap-sqr
119×cbrt-div
115×exp-prod
110×frac-2neg clear-num
94×associate-/l/
91×*-commutative
88×sub-neg
82×associate-+r+
65×frac-add
64×pow-prod-up
62×cos-sum diff-log
56×frac-sub
55×log-pow
53×pow1/3 neg-mul-1
46×pow-sqr
42×div-sub
39×pow-plus
36×sum-log
35×sqr-pow
33×fma-udef log-div
28×sqrt-pow1 pow1/2
26×pow2 +-commutative tan-quot sin-mult
25×rem-sqrt-square
22×sin-sum
20×rem-log-exp
19×neg-sub0
18×exp-sum sin-diff
17×1-exp
13×cos-diff
11×rec-exp
9×associate--r+ associate-+l-
8×expm1-log1p expm1-udef exp-diff distribute-frac-neg log1p-expm1 neg-log acos-asin log1p-udef
7×sin-cos-mult exp-neg
6×associate-+l+ pow-unpow
5×distribute-rgt-neg-out pow3
4×associate--l- acos-neg associate--r-
3×distribute-neg-frac rem-cbrt-cube
2×pow-flip cos-mult cube-unmult pow-pow inv-pow asin-acos pow-div rem-exp-log un-div-inv distribute-rgt-out
1×associate-+r- unsub-neg tanh-undef tanh-def hypot-udef distribute-rgt-out--

regimes20.0s (1.9%)

Accuracy

Total 56.3b remaining (30.7%)

Threshold costs 6.7b (3.6%)

7.6b45%Quadratic roots, narrow range
6.9b0%Quadratic roots, medium range
6.8b0%Cubic critical, medium range
5.7b49.4%Quotient of products
5.6b58.6%Cubic critical, narrow range

localize6.2s (0.6%)

bsearch951.0ms (0.1%)

end1.0ms (0.0%)