Details

sample9.8m (50.4%)

Algorithm
78×intervals
Results
6.5m43146×body10240exit
1.3m43543×body1280valid
27.6s30155×body640valid
20.2s204782×body80valid
14.1s27534×body320valid
14.1s150444×body80nan
10.1s36307×body160valid
8.3s181334×pre80true
2.0s2960×body2560valid
1.4s7786×body160nan
789.0ms4158×pre10240exit
234.0ms8146×pre80false
222.0ms262×body5120valid

simplify6.7m (34.4%)

prune1.1m (5.7%)

series59.0s (5.1%)

Calls

487 calls:

1.2s
(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
998.0ms
(* (* (sqrt (+ x (sqrt 1.0))) (sqrt (+ (sqrt x) (sqrt (sqrt 1.0))))) (sqrt (- (sqrt x) (sqrt (sqrt 1.0)))))
772.0ms
(/ (* (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)))
734.0ms
(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
659.0ms
(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))))

rewrite27.8s (2.4%)

Algorithm
145×rewrite-expression-head
Calls

487 calls:

941.0ms
(* (- (/ 1 (/ (/ v (- 1.0 m)) m)) 1.0) m)
806.0ms
(* (* (- (- (* 1.0 (/ m v)) (/ (pow m 2) v)) 1.0) (+ (sqrt 1.0) (sqrt m))) (- (sqrt 1.0) (sqrt m)))
694.0ms
(* (/ 2.0 (+ (pow (exp x) 3) (exp (* x -3)))) (+ (* (exp x) (exp x)) (- (* (exp (- x)) (exp (- x))) (* (exp x) (exp (- x))))))
681.0ms
(* (- (- (* 1.0 (/ m v)) (/ (pow m 2) v)) 1.0) (+ (sqrt 1.0) (sqrt m)))
642.0ms
(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))))
Rules
6408×times-frac
5928×add-sqr-sqrt
5605×*-un-lft-identity
3726×add-cube-cbrt
2551×add-exp-log
1652×add-cbrt-cube
1091×pow1
982×associate-*r*
935×flip--
934×flip3--
918×associate-*l/
890×difference-of-squares
826×prod-exp
806×sqrt-prod
744×div-exp
738×add-log-exp
625×associate-/l*
611×distribute-lft-out--
572×frac-times
560×associate-/r*
552×unpow-prod-down
540×associate-*l*
424×associate-*r/
418×sqrt-div
408×frac-add
383×cbrt-unprod
370×pow-exp div-inv
368×associate-/r/
356×cbrt-undiv
313×distribute-lft-out
299×cbrt-prod
280×cube-prod
264×pow-to-exp
258×pow-prod-down
255×exp-prod
242×sqr-pow
237×flip-+
236×flip3-+
226×log-pow
192×log-prod
177×unswap-sqr
176×cbrt-div
116×distribute-rgt-neg-in
114×*-commutative
110×clear-num frac-2neg
109×associate-/l/
108×sub-neg
75×diff-log
69×frac-sub
64×sqrt-pow1
63×pow-unpow
61×exp-neg
54×pow1/3 neg-sub0
53×sum-log
51×pow1/2 exp-diff
47×swap-sqr
44×log-div
41×distribute-rgt-in distribute-lft-in div-sub
38×+-commutative
37×unpow3 cube-mult
36×unpow2
33×rem-sqrt-square
31×pow-prod-up rem-log-exp
30×pow-pow
25×pow-sqr
24×un-div-inv tan-quot
22×rem-cube-cbrt
21×1-exp rec-exp
19×exp-sum sin-diff
18×sub-div sin-mult
16×pow-plus
15×associate--l+
14×distribute-rgt-out pow2
13×sin-cos-mult
12×cube-div cos-diff
10×cos-sum neg-log associate-+l-
distribute-lft-neg-in acos-asin
associate--l-
associate-+l+ rem-exp-log sin-sum pow-flip cos-mult
associate-+r+ associate-+r- asin-acos
inv-pow distribute-frac-neg associate--r+
acos-neg difference-cubes sqrt-unprod distribute-rgt-out--
associate--r- neg-mul-1 rem-cbrt-cube
sub0-neg distribute-lft1-in distribute-rgt-neg-out distribute-neg-frac exp-to-pow
exp-lft-sqr rgt-mult-inverse tanh-undef tanh-def

regimes15.0s (1.3%)

Accuracy

Total 33.0b remaining (24.3%)

Threshold costs 8.2b (6.1%)

6.1b13.9%Quadratic roots, medium range
5.0b54.9%Quotient of products
4.5b84.2%Quadratic roots, full range
3.7b72.4%Equirectangular approximation to distance on a great circle
3.5b4.1%Cubic critical, wide range

bsearch5.3s (0.5%)

localize4.3s (0.4%)

end0.0ms (0.0%)