Details

simplify9.1m (54.3%)

sample4.8m (28.8%)

Algorithm
77×intervals
Results
1.7m42973×body1280valid
42.4s31301×body640valid
28.7s201437×body80valid
27.8s14854×body10240exit
23.0s152623×body80nan
18.3s27952×body320valid
12.6s36233×body160valid
9.1s150526×pre80true
3.7s2949×body2560valid
1.4s8027×body160nan
911.0ms4101×pre10240exit
254.0ms192×body5120valid
2.0ms1×body320nan
1.0ms1×body640nan

prune1.4m (8.3%)

series43.5s (4.4%)

Calls

447 calls:

1.2s
(/ (- (* (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))))))))
817.0ms
(- (* (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))))))))
782.0ms
(- (* (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))))))))
735.0ms
(- (* (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)))))))))
671.0ms
(cbrt (/ 1/2 a))

regimes18.4s (1.8%)

Accuracy

Total 64.6b remaining (30.9%)

Threshold costs 4.9b (2.3%)

7.6b44.2%Cubic critical, narrow range
7.6b44.5%Quadratic roots, narrow range
7.0b53.7%Equirectangular approximation to distance on a great circle
6.2b6.1%Cubic critical, medium range
6.2b6.3%Quadratic roots, medium range

rewrite15.6s (1.6%)

Algorithm
139×rewrite-expression-head
Calls

447 calls:

409.0ms
(* (* (* -3/2 (/ (* a c) b)) (* -3/2 (/ (* a c) b))) (* -3/2 (/ (* a c) b)))
391.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (* (- lambda1 lambda2) (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (* (- phi1 phi2) (- phi1 phi2))))
382.0ms
(cbrt (* (* (* -3/2 (/ (* a c) b)) (* -3/2 (/ (* a c) b))) (* -3/2 (/ (* a c) b))))
377.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (* (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))
314.0ms
(log (exp (/ (+ (/ -1 (exp (* 3 x))) (exp (* 3 x))) (+ 1 (- (* (exp x) (exp x)) (/ -1 (* (exp x) (exp x))))))))
Rules
4513×add-sqr-sqrt
4281×times-frac
4093×*-un-lft-identity
3166×associate-*l/
2870×add-exp-log
2851×add-cube-cbrt
2485×add-cbrt-cube
2428×frac-times
2377×cbrt-div
2143×flip--
2142×flip3--
1440×pow1
1341×sqrt-prod
1109×prod-exp
1085×cbrt-unprod
1026×associate-*r*
1011×associate-*r/
993×sqrt-div
924×frac-add
693×div-exp
666×add-log-exp
659×cbrt-undiv
580×associate-*l*
570×cbrt-prod
523×difference-of-squares
481×frac-sub
447×insert-posit16
388×associate-/r*
369×associate-/l*
365×pow-prod-down
290×distribute-lft-out--
242×unswap-sqr
236×div-inv
235×distribute-lft-out
189×log-prod
165×flip-+
164×flip3-+
153×pow-prod-up
132×associate-/r/
129×exp-prod
119×*-commutative
104×sub-neg
101×swap-sqr
100×cos-mult
99×tanh-def
95×frac-2neg clear-num
93×pow-plus
91×pow-sqr
86×associate-/l/
80×diff-log
68×tan-quot
55×log-pow
51×pow2
50×sqrt-pow1
46×pow1/3
45×log-div
44×associate-+r+
43×sin-mult
39×div-sub
36×sum-log
35×distribute-rgt-in distribute-lft-in
34×pow1/2
31×rem-sqrt-square
30×difference-of-sqr-1
28×cos-diff
27×+-commutative
26×associate-+l+
19×rem-log-exp
17×1-exp associate--l+
16×unpow-prod-down
13×rec-exp cos-sum
11×pow-flip exp-sum
10×pow3
9×distribute-rgt-out-- sin-cos-mult acos-asin
8×sqr-pow sub-div rem-exp-log
7×inv-pow distribute-rgt-out
6×exp-diff sin-sum associate--r+ asin-acos associate-+l- sqr-cos
5×rem-cbrt-cube associate--r- sin-diff
4×associate--l- associate-+r- pow-exp pow-to-exp
3×distribute-frac-neg acos-neg
2×cube-unmult pow-div un-div-inv distribute-rgt1-in
1×sqrt-undiv tanh-undef exp-to-pow

localize7.2s (0.7%)

bsearch693.0ms (0.1%)

end1.0ms (0.0%)