Details

simplify6.4m (39.6%)

sample6.0m (37.2%)

Algorithm
78×intervals
Results
2.8m26306×body10240exit
1.3m44062×body1280valid
30.6s30590×body640valid
20.7s202821×body80valid
13.5s151501×body80nan
12.5s27500×body320valid
8.3s36204×body160valid
8.2s163295×pre80true
2.5s3073×body2560valid
930.0ms7916×body160nan
436.0ms4177×pre10240exit
170.0ms231×body5120valid
3.0msbody640nan

prune1.9m (11.7%)

series58.3s (6.0%)

Calls

459 calls:

1.5s
(expm1 (- (* (cos delta) (cos delta)) (cbrt (* (* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) (* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))))
1.3s
(/ (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
969.0ms
(hypot (* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2)) (- phi1 phi2))
937.0ms
(- (* (cos delta) (cos delta)) (cbrt (* (* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) (* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))))
876.0ms
(/ (* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

regimes26.2s (2.7%)

Accuracy

Total 55.2b remaining (33%)

Threshold costs 5.3b (3.1%)

7.8b42.5%Quadratic roots, narrow range
7.7b42.6%Cubic critical, narrow range
6.8b0%Quadratic roots, medium range
6.7b0%Cubic critical, medium range
4.2b87.6%Cubic critical

rewrite19.5s (2.0%)

Algorithm
146×rewrite-expression-head
Calls

459 calls:

1.1s
(cbrt (* (* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) (* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
1.0s
(cbrt (* (* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) (* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
443.0ms
(- (* (cos delta) (cos delta)) (cbrt (* (* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) (* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))))
410.0ms
(* m (- 1.0 m))
402.0ms
(* (- (* (/ 1 (/ (/ v m) (- (* (* 1.0 1.0) 1.0) (* (* m m) m)))) (/ 1 (+ (* 1.0 1.0) (+ (* m m) (* 1.0 m))))) 1.0) m)
Rules
9086×times-frac
9037×*-un-lft-identity
8215×add-sqr-sqrt
6317×add-cube-cbrt
2808×prod-diff
2658×add-exp-log
2399×sqrt-prod
1744×add-cbrt-cube
1337×pow1
859×distribute-lft-out
851×div-exp
817×prod-exp
788×associate-*l*
715×difference-of-squares
639×associate-*r*
611×add-log-exp
607×associate-/l*
566×associate-/r*
545×fma-neg
544×div-inv
513×distribute-lft-out--
504×associate-/r/
463×log1p-expm1-u
460×expm1-log1p-u
419×cbrt-undiv cbrt-unprod
366×cbrt-prod
301×associate-*r/
279×flip--
278×flip3--
275×associate-*l/
268×pow-prod-down
266×pow-exp
258×frac-times
236×log-prod
225×sqrt-div
221×sin-mult
217×flip-+
216×flip3-+
199×unswap-sqr
192×pow3
186×pow-to-exp
182×distribute-rgt-in distribute-lft-in
153×log-pow
130×cos-mult
122×frac-2neg clear-num
120×unpow-prod-down
116×swap-sqr
115×*-commutative associate-/l/
114×pow-prod-up
100×cbrt-div sub-neg
95×difference-cubes
90×distribute-rgt-neg-in distribute-lft-neg-in
77×frac-sub
75×associate--l+
69×sqrt-pow1
67×pow1/2 diff-log
66×1-exp rec-exp
63×pow-plus
61×pow-sqr
60×cos-sum
46×log-div
44×exp-sum div-sub
43×sin-cos-mult exp-prod
41×pow2
34×fma-def
33×sub-div
32×pow1/3 tan-quot
31×fma-udef rem-log-exp
30×pow-flip sqr-pow associate--r+ neg-mul-1
29×rem-sqrt-square
23×distribute-rgt-out
22×sin-sum
18×sin-diff
16×inv-pow
15×sum-log cube-unmult
14×hypot-def
12×+-commutative
11×cos-diff
acos-asin
exp-diff associate--l- frac-add
pow-unpow rem-exp-log
expm1-log1p expm1-udef associate--r-
distribute-lft1-in distribute-rgt1-in cube-prod distribute-frac-neg sqr-sin
associate-+l+ associate-+r+ log1p-expm1 log1p-udef un-div-inv rem-cbrt-cube
neg-sub0 associate-+r- pow-pow hypot-udef asin-acos associate-+l- sqr-cos count-2
distribute-rgt-neg-out sqrt-unprod tanh-def tanh-undef sum-cubes acos-neg

localize6.5s (0.7%)

bsearch498.0ms (0.1%)

end1.0ms (0.0%)