Details

simplify6.2m (42.7%)

sample5.0m (34.8%)

Algorithm
78×intervals
Results
1.9m21677×body10240exit
1.3m44002×body1280valid
27.1s30671×body640valid
18.0s202829×body80valid
14.5s152220×body80nan
11.6s27697×body320valid
10.1s35848×body160valid
8.4s159048×pre80true
2.3s2961×body2560valid
1.3s7872×body160nan
594.0ms230×body5120valid
517.0ms4103×pre10240exit
258.0ms8220×pre80false

prune1.1m (7.5%)

series1.0m (7.0%)

Calls

483 calls:

1.8s
(+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) 3))
884.0ms
(/ (* (* m (+ (sqrt 1.0) (sqrt m))) (- (sqrt 1.0) (sqrt m))) v)
791.0ms
(/ (* (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
(pow (log (/ (sqrt (+ 1.0 x)) (- 1.0 x))) 3)
710.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite25.9s (3.0%)

Algorithm
146×rewrite-expression-head
Calls

483 calls:

796.0ms
(pow (+ (log x) (- (log 2) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))))) 3)
678.0ms
(cbrt (pow (+ (log x) (- (log 2) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))))) 3))
609.0ms
(* (pow (- (/ (- 1.0 m) (/ v m)) 1.0) 1) m)
505.0ms
(log (exp (- (/ (pow x0 3) (pow (- 1.0 x1) 6)) (pow x0 3))))
484.0ms
(- (log 2) (- (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x))) (log x)))
Rules
5820×times-frac
5398×*-un-lft-identity
5337×add-sqr-sqrt
3321×add-cube-cbrt
2936×add-exp-log
1872×add-cbrt-cube
1147×pow1
1000×prod-exp
883×div-exp
842×flip--
841×flip3--
779×difference-of-squares
777×associate-*l/
766×associate-*r*
751×add-log-exp
655×distribute-lft-out--
648×cbrt-prod
601×associate-/r*
595×unpow-prod-down
580×associate-/l*
545×sqrt-prod
498×frac-times
490×associate-*l*
480×cbrt-unprod
462×sqrt-div
459×div-inv
452×associate-*r/
449×cbrt-undiv
435×frac-add
412×distribute-lft-out
388×cube-prod
380×pow-exp
281×pow-to-exp
280×pow-prod-down
259×associate-/r/
228×log-prod
220×sqr-pow
210×unswap-sqr
182×flip-+
181×flip3-+
158×log-pow
148×distribute-rgt-neg-in
116×clear-num sub-neg frac-2neg
113×exp-prod
111×*-commutative
108×associate-/l/
103×cbrt-div
88×diff-log
79×swap-sqr
60×pow-unpow
59×pow1/3
55×sum-log
52×unpow3 cube-mult
48×distribute-rgt-in distribute-lft-in
44×div-sub
40×pow1/2 sqrt-pow1
38×+-commutative
37×rem-sqrt-square
35×unpow2 1-exp rec-exp
32×log-div
28×pow-pow
26×pow-prod-up pow-sqr
25×cos-mult rem-log-exp
22×distribute-rgt-out
21×tan-quot associate-+r+
20×sin-mult
19×cos-diff
18×rem-cube-cbrt
17×cube-div frac-sub associate--l+
16×neg-sub0
15×sum-cubes sin-diff
14×pow-plus
12×neg-log exp-sum cos-sum
11×associate-+r- acos-asin pow2
10×associate--r+
9×sin-cos-mult associate--l- associate-+l- pow-flip distribute-frac-neg
8×associate-+l+
7×pow3 rem-cbrt-cube
6×acos-neg associate--r-
5×un-div-inv sin-sum
4×exp-diff rem-exp-log inv-pow asin-acos
3×distribute-lft-neg-in distribute-lft-neg-out
2×difference-cubes distribute-lft1-in distribute-rgt-neg-out
1×unsub-neg tanh-undef neg-mul-1 tanh-def

bsearch25.7s (3.0%)

regimes13.0s (1.5%)

Accuracy

Total 30.3b remaining (21.2%)

Threshold costs 6.6b (4.6%)

6.2b11%Cubic critical, medium range
3.9b71.5%Equirectangular approximation to distance on a great circle
3.6b0%Cubic critical, wide range
3.5b0%Quadratic roots, wide range
3.0b72.5%Quotient of products

localize4.3s (0.5%)

end1.0ms (0.0%)