Details

simplify6.6m (40.8%)

sample6.4m (39.0%)

Algorithm
78×intervals
Results
3.1m26914×body10240exit
1.3m43596×body1280valid
30.2s30450×body640valid
20.1s202965×body80valid
14.2s153461×body80nan
13.6s27959×body320valid
8.8s35956×body160valid
7.1s164300×pre80true
1.9s3110×body2560valid
1.3s8154×body160nan
511.0ms4113×pre10240exit
229.0ms8261×pre80false
122.0ms215×body5120valid

prune1.3m (8.2%)

series1.1m (6.7%)

Calls

487 calls:

1.4s
(log (sqrt (exp (* (+ (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))))))
1.0s
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (+ lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))
876.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (+ lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))
805.0ms
(/ (* (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)))
766.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (* (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite30.5s (3.1%)

Algorithm
145×rewrite-expression-head
Calls

487 calls:

934.0ms
(- (pow (/ (- (+ (/ 1.0 x) 3.0)) x) 1) (/ 3.0 (pow x 3)))
678.0ms
(* (* (- (/ m (/ v (- 1.0 m))) 1.0) (+ (sqrt 1.0) (sqrt m))) (- (sqrt 1.0) (sqrt m)))
596.0ms
(log (exp (- (/ (pow x0 3) (pow (- 1.0 x1) 6)) (pow x0 3))))
578.0ms
(* (- (/ m (/ v (- 1.0 m))) 1.0) (+ (sqrt 1.0) (sqrt m)))
566.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (* (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
Rules
7130×times-frac
5713×*-un-lft-identity
5577×add-sqr-sqrt
3790×add-cube-cbrt
3739×add-exp-log
2656×associate-*l/
2006×add-cbrt-cube
1852×flip--
1851×flip3--
1728×frac-times
1355×prod-exp
1347×cbrt-div
1318×div-exp
1112×pow1
875×sqrt-div
812×associate-*r/
809×frac-add
794×associate-/l*
742×add-log-exp
716×sqrt-prod
715×difference-of-squares
648×associate-*r*
625×associate-/r*
611×pow-exp
529×associate-*l*
521×unpow-prod-down
518×cbrt-unprod
511×cbrt-undiv
491×distribute-lft-out--
465×distribute-lft-out
432×pow-to-exp
427×distribute-rgt-neg-in
410×div-inv
389×associate-/r/
349×cube-prod
341×cbrt-prod
310×distribute-lft-neg-in
264×pow-prod-down
207×flip-+
206×flip3-+
196×log-prod
174×log-pow
165×sqr-pow
144×unswap-sqr
125×clear-num frac-2neg
121×exp-prod sub-neg
112×associate-/l/
111×*-commutative
89×1-exp
81×diff-log
70×sqrt-pow1
69×log-div
52×rec-exp sum-log cos-mult
51×distribute-rgt-in pow-unpow distribute-lft-in
49×pow1/2
44×div-sub
38×+-commutative sin-mult associate--l+
35×unpow3 cube-mult
34×swap-sqr
32×rem-sqrt-square frac-sub
31×rem-log-exp
30×pow-prod-up
29×pow1/3 tan-quot
26×sin-cos-mult exp-sum
21×pow-sqr
19×pow-plus
18×neg-mul-1 pow-pow
17×associate-+r+ neg-sub0
16×sin-diff
15×rem-cube-cbrt cos-diff distribute-frac-neg
14×associate--l- distribute-rgt-out
12×cos-sum associate--r-
11×pow-flip
10×acos-asin sub-div neg-log associate-+l- pow2
cube-div associate-+l+ inv-pow sum-cubes
exp-diff associate-+r- rem-cbrt-cube associate--r+
un-div-inv rem-exp-log sin-sum
acos-neg unpow2 asin-acos exp-to-pow
distribute-rgt-neg-out distribute-neg-frac
sqrt-pow2 sub0-neg distribute-lft1-in sqrt-unprod sqrt-undiv
difference-cubes sin-neg distribute-rgt-out-- sqr-sin rem-square-sqrt tanh-undef tanh-def

regimes11.9s (1.2%)

Accuracy

Total 29.5b remaining (21.6%)

Threshold costs 5.5b (4%)

7.0b0%Cubic critical, medium range
4.6b84.2%Quadratic roots, full range
4.0b71.9%Equirectangular approximation to distance on a great circle
3.4b0%Quadratic roots, wide range
2.3b79.1%Quotient of products

bsearch5.9s (0.6%)

localize4.1s (0.4%)

end1.0ms (0.0%)