Details

simplify6.6m (38.6%)

sample4.9m (28.5%)

Algorithm
78×intervals
Results
1.6m20426×body10240exit
1.3m43746×body1280valid
27.1s30691×body640valid
20.8s202771×body80valid
14.9s153013×body80nan
12.6s27749×body320valid
8.0s158253×pre80true
7.9s35759×body160valid
2.7s3100×body2560valid
838.0ms7869×body160nan
432.0ms4116×pre10240exit
248.0ms8292×pre80false
167.0ms220×body5120valid
2.0msbody640nan

prune3.6m (20.9%)

series1.2m (6.8%)

Calls

493 calls:

5.7s
(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)) (+ (* (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (- (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (cos phi1))) (* (cos phi1) (cos phi1))))
2.0s
(sqrt (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n) (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n) (/ (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (+ 1 (* c_p (+ (log 0.5) (* 0.5 t))))))))
2.0s
(sqrt (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n) (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n) (/ (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (+ 1 (* c_p (+ (log 0.5) (* 0.5 t))))))))
1.9s
(+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3))
880.0ms
(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite31.8s (3.1%)

Algorithm
147×rewrite-expression-head
Calls

493 calls:

1.4s
(sqrt (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n) (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n) (/ (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (+ 1 (* c_p (+ (log 0.5) (* 0.5 t))))))))
1.2s
(sqrt (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n) (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n) (/ (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (+ 1 (* c_p (+ (log 0.5) (* 0.5 t))))))))
568.0ms
(+ x (- (- x (/ 0.125 (pow x 3))) (/ 0.5 x)))
478.0ms
(log (exp (- (/ (pow x0 3) (pow (- 1.0 x1) 6)) (pow x0 3))))
451.0ms
(* (- (/ (- (* 1.0 m) (pow m 3)) (* v (+ 1.0 m))) 1.0) (- 1.0 m))
Rules
71110×times-frac
40583×add-sqr-sqrt
35646×*-un-lft-identity
28611×unpow-prod-down
23979×add-cube-cbrt
18333×sqrt-prod
6537×difference-of-squares
3746×sqr-pow
3476×distribute-lft-out--
3049×add-exp-log
2334×distribute-lft-out
1964×associate-/r/
1911×add-cbrt-cube
1816×div-inv
1169×flip--
1168×flip3--
1082×flip-+
1081×flip3-+
1026×pow1
1008×prod-exp
985×div-exp
936×frac-times
889×associate-*l/
802×add-log-exp
778×associate-*r*
737×associate-/r*
730×associate-/l*
629×frac-add
590×sqrt-div
555×associate-*l*
488×associate-*r/
470×cbrt-undiv
461×cbrt-unprod
344×pow-exp
328×log-prod
325×cbrt-prod
269×cube-prod
247×pow-to-exp
236×cos-mult
210×pow-prod-down
206×distribute-rgt-neg-in
161×cbrt-div
160×unswap-sqr
158×log-pow
143×sub-neg
128×rem-sqrt-square
125×clear-num frac-2neg
111×*-commutative
95×associate-/l/ diff-log
91×exp-prod
87×1-exp
82×associate-+r+
74×frac-sub
71×distribute-rgt-in distribute-lft-in
69×sum-log sqrt-pow1
61×swap-sqr
58×rec-exp log-div
54×pow1/2
51×+-commutative
50×distribute-lft-neg-in
44×div-sub
40×unpow3
39×associate--l+
36×cube-mult
31×rem-log-exp
30×pow-unpow distribute-rgt-out
28×tan-quot
24×neg-mul-1
23×neg-sub0
22×exp-sum
21×sin-mult
19×sin-diff
18×pow-prod-up
17×pow1/3 unpow2
16×cube-div pow-sqr neg-log associate-+l-
15×cos-diff
14×associate--l- associate-+l+ pow-pow
13×sum-cubes associate-+r- cos-sum
12×sin-cos-mult pow2 pow-plus
11×rem-cube-cbrt
10×associate--r+
inv-pow distribute-rgt-out-- pow-flip
acos-asin
exp-diff sin-sum
distribute-frac-neg distribute-lft1-in associate--r-
distribute-neg-frac rem-cbrt-cube
acos-neg un-div-inv sqrt-unprod distribute-neg-in asin-acos log-rec
sub0-neg rem-exp-log distribute-rgt-neg-out
difference-cubes unsub-neg rem-square-sqrt sub-div tanh-undef sqr-cos exp-to-pow tanh-def

regimes13.0s (1.3%)

Accuracy

Total 36.5b remaining (26.4%)

Threshold costs 5.7b (4.1%)

7.4b46.4%Quadratic roots, narrow range
6.1b79.1%Quadratic roots, full range
4.6b57.4%Quotient of products
3.8b73.4%Equirectangular approximation to distance on a great circle
3.7b0%Cubic critical, wide range

bsearch4.8s (0.5%)

localize4.0s (0.4%)

end1.0ms (0.0%)