Details

sample13.1m (58.6%)

Algorithm
78×intervals
Results
9.8m58381×body10240exit
1.3m43306×body1280valid
29.6s30587×body640valid
19.7s205068×body80valid
14.1s152559×body80nan
13.8s27969×body320valid
9.2s36128×body160valid
7.4s197701×pre80true
2.3s3124×body2560valid
680.0ms7892×body160nan
562.0ms4142×pre10240exit
275.0ms250×body5120valid
202.0ms8365×pre80false
1.0msbody640nan

simplify6.4m (28.3%)

prune1.1m (5.0%)

series1.0m (4.5%)

Calls

482 calls:

1.3s
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* (log 0.5) c_p) (+ (* 0.5 (* t c_p)) 1)) (pow (/ (- (pow 1.0 3) (pow (/ 1.0 (+ 1.0 (exp (- t)))) 3)) (+ (* (/ 1.0 (+ 1.0 (exp (- t)))) (+ 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) (* 1.0 1.0))) c_n)))
826.0ms
(- (* (cos delta) (cos delta)) (* (pow (sin phi1) 2) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
816.0ms
(pow E (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
789.0ms
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* (log 0.5) c_p) (+ (* 0.5 (* t c_p)) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
720.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite29.9s (2.2%)

Algorithm
143×rewrite-expression-head
Calls

482 calls:

2.5s
(* (- (/ (/ m (sqrt v)) (/ (sqrt v) (- 1.0 m))) 1.0) m)
871.0ms
(- (- (/ x (+ x 1.0)) (/ x (- x 1.0))) (* (/ 1 (- x 1.0)) 1.0))
737.0ms
(log (exp (- (/ (pow x0 3) (pow (- 1.0 x1) 6)) (pow x0 3))))
730.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
711.0ms
(- (pow (cos delta) 2) (+ (* (sin delta) (+ (* (sin delta) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (* (* (cos phi1) (* (cbrt (pow (pow (sin phi1) 3) 3)) (* (cos delta) (cos theta)))) 2))) (* (pow (sin phi1) 4) (pow (cos delta) 2))))
Rules
7083×times-frac
6372×add-sqr-sqrt
5770×*-un-lft-identity
3783×add-cube-cbrt
3084×add-exp-log
2169×sqrt-prod
1771×add-cbrt-cube
1044×prod-exp
1034×div-exp
1030×pow1
1017×associate-*r*
969×flip--
967×flip3--
934×associate-*l/
896×difference-of-squares
800×add-log-exp
713×distribute-lft-out--
689×cbrt-prod
635×unpow-prod-down
591×associate-*l*
575×frac-times
518×sqrt-div
485×associate-/r*
463×associate-/l*
447×pow-exp
427×associate-/r/
425×cbrt-unprod
422×cube-prod
420×cbrt-undiv
395×frac-add
384×associate-*r/ div-inv
327×swap-sqr
315×pow-to-exp
260×distribute-lft-out
247×unswap-sqr
229×sqr-pow
198×pow-prod-down
194×flip-+
192×flip3-+
181×log-div
170×log-pow
154×log-prod
152×exp-prod
143×sub-neg
112×diff-log
109×*-commutative
107×sqrt-pow1
105×clear-num frac-2neg
104×distribute-rgt-neg-in
91×associate-/l/
74×cbrt-div
73×pow1/2 exp-diff
66×pow-sub
64×1-exp
62×unpow3 cube-mult
58×sum-log
57×distribute-rgt-in distribute-lft-in
54×pow-unpow
50×frac-sub
46×pow1/3
42×pow-prod-up
38×div-sub
37×rec-exp
36×rem-sqrt-square cos-mult
35×+-commutative associate--l+
32×sin-cos-mult
30×pow-sqr
26×tan-quot
22×pow-plus rem-log-exp pow-pow
20×neg-sub0 exp-sum
18×associate--r+ sin-diff
17×rem-cube-cbrt cos-diff pow2
15×neg-log sin-mult
14×associate--l-
13×distribute-rgt-out associate-+l-
12×acos-asin cos-sum
11×associate-+r-
10×rem-exp-log
distribute-frac-neg sin-sum associate-+r+
cube-div
acos-neg sqrt-undiv unpow-prod-up associate--r-
associate-+l+ inv-pow pow-flip
asin-acos unpow2
sub-div distribute-rgt-neg-out
difference-cubes un-div-inv distribute-lft1-in sqrt-unprod rem-square-sqrt sum-cubes
rem-cbrt-cube e-exp-1 sin-neg pow3 sqr-sin tanh-undef sqr-cos exp-to-pow tanh-def

regimes13.0s (1.0%)

Accuracy

Total 35.9b remaining (28.5%)

Threshold costs 7.0b (5.6%)

15.5b27.6%Equirectangular approximation to distance on a great circle
3.9b64.6%Quotient of products
3.5b0%Quadratic roots, wide range
3.5b0%Cubic critical, wide range
1.3b64.2%2-ancestry mixing, positive discriminant

localize4.4s (0.3%)

bsearch1.2s (0.1%)

end1.0ms (0.0%)