Details

simplify12.9m (49.6%)

sample6.5m (25.1%)

Algorithm
77×intervals
Results
3.0m25797×body10240exit
1.4m43626×body1280valid
31.1s31115×body640valid
20.6s194594×body80valid
17.2s145370×body80nan
14.3s27857×body320valid
10.1s35981×body160valid
8.4s163544×pre80true
2.8s3039×body2560valid
1.4s7926×body160nan
655.0ms4152×pre10240exit
238.0ms289×body5120valid

prune3.2m (12.2%)

series1.3m (4.8%)

Calls

458 calls:

1.4s
(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (* (- phi1 phi2) (- phi1 phi2))))
1.3s
(sqrt (+ (* (* (* (* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2))) (* (cbrt (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2.0)))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (* (- phi1 phi2) (- phi1 phi2))))
1.3s
(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))
1.2s
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
1.2s
(/ (* (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)))

rewrite51.8s (3.3%)

Algorithm
140×rewrite-expression-head
Calls

458 calls:

6.1s
(sqrt (+ (* (* (* (* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2))) (* (cbrt (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2.0)))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (* (- phi1 phi2) (- phi1 phi2))))
1.6s
(* (* (+ (/ 1.0 (- x 1.0)) (/ x (+ 1.0 x))) (+ (/ 1.0 (- x 1.0)) (/ x (+ 1.0 x)))) (+ (/ 1.0 (- x 1.0)) (/ x (+ 1.0 x))))
1.1s
(- (- (/ 0.125 (* (* x x) x)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))
1.0s
(cbrt (* (* (* -1.5 -1.5) -1.5) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))))
701.0ms
(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (* (- phi1 phi2) (- phi1 phi2))))
Rules
4948×times-frac
4736×add-sqr-sqrt
4350×*-un-lft-identity
3268×add-cube-cbrt
2936×add-exp-log
2374×associate-*l/
2141×add-cbrt-cube
2139×sqrt-prod
1852×flip--
1851×flip3--
1806×frac-times
1343×cbrt-div
1324×pow1
1111×prod-exp
966×sqrt-div
922×frac-add
800×associate-*r*
788×div-exp
734×add-log-exp
706×cbrt-unprod
668×associate-*r/
667×associate-*l*
504×associate-/r*
458×insert-posit16
457×cbrt-undiv
354×difference-of-squares
340×associate-/l*
337×pow-prod-down
308×div-inv
305×cbrt-prod
297×distribute-lft-out--
273×pow-exp
240×swap-sqr
238×distribute-lft-out
235×unswap-sqr
203×log-prod
193×flip-+ pow-to-exp
192×flip3-+
128×*-commutative
119×pow-prod-up
106×unpow-prod-down associate-/r/
102×frac-2neg clear-num
98×sub-neg
96×associate-/l/
89×diff-log
87×pow-plus
82×sqrt-pow1
80×exp-prod
79×log-pow
69×sum-log
67×pow1/3
66×pow1/2
59×pow-sqr
45×distribute-rgt-in distribute-lft-in
41×log-div
40×1-exp associate--l+
38×pow2
36×rem-sqrt-square
34×frac-sub
32×rec-exp sqr-pow +-commutative
29×rem-log-exp
27×tan-quot
25×div-sub
23×sin-mult
19×cos-mult
16×sin-diff
15×associate-+r+ cos-diff
12×pow-flip associate--r+
10×cos-sum
9×associate--l-
8×pow3 distribute-rgt-neg-in
7×sin-cos-mult inv-pow
6×sqrt-undiv pow-unpow sqrt-unprod acos-asin
5×exp-sum
4×exp-diff sin-sum un-div-inv rem-exp-log
3×associate-+l+ neg-sub0 distribute-lft-neg-in cube-unmult distribute-rgt-neg-out associate-+l- rem-square-sqrt
2×remove-posit16 associate-+r- neg-log pow-pow asin-acos sqr-cos rem-cbrt-cube associate--r- distribute-rgt-out
1×tanh-undef tanh-def difference-cubes exp-to-pow neg-mul-1

regimes50.0s (3.2%)

Accuracy

Total 68.3b remaining (31.5%)

Threshold costs 5.8b (2.7%)

13.5b9.7%Equirectangular approximation to distance on a great circle
7.4b46%Cubic critical, narrow range
7.4b46.5%Quadratic roots, narrow range
6.4b7.3%Quadratic roots, medium range
6.3b7.4%Cubic critical, medium range

localize22.7s (1.5%)

bsearch4.3s (0.3%)

end1.0ms (0.0%)