Details

sample22.5m (57.3%)

Algorithm
76×intervals
Results
19.1m137451×body10240exit
1.1m36295×body1280valid
28.1s199099×body80valid
27.2s26295×body640valid
21.8s153200×body80nan
15.4s26175×body320valid
11.9s35057×body160valid
9.6s163492×pre80true
2.8s3127×body2560valid
1.6s7902×body160nan
1.1s4144×pre10240exit
253.0ms228×body5120valid

simplify9.9m (25.3%)

prune5.7m (14.4%)

series35.7s (1.5%)

Calls

419 calls:

597.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2)))))))) (* (- phi1 phi2) (- phi1 phi2))))
578.0ms
(sqrt (+ (* (* (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))
575.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))
555.0ms
(/ (* (pow (/ 1 (+ 1 (exp (- s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)) (* (pow (/ 1 (+ 1 (exp (- t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- t))))) c_n)))
530.0ms
(* (* e (cos v)) (* e (cos v)))

rewrite16.2s (0.7%)

Algorithm
130×rewrite-expression-head
Calls

419 calls:

544.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2)))))))) (* (- phi1 phi2) (- phi1 phi2))))
421.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))
371.0ms
(sqrt (+ (* (* (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))
355.0ms
(- (- (* (log (- 1 (/ 1 (+ 1 (exp (- s)))))) c_n) (* c_p (log (+ 1 (exp (- s)))))) (- (* c_n (log (- 1 (/ 1 (+ 1 (exp (- t))))))) (* (log (+ 1 (exp (- t)))) c_p)))
316.0ms
(- (log (exp (/ 2 (+ (exp (* -2 x)) 1)))) 1)
Rules
30422×associate-*l/
20759×frac-times
16570×flip--
16569×flip3--
15613×cbrt-div
6219×associate-*r/
6143×sqrt-div
6030×frac-add
4593×*-un-lft-identity
4414×add-sqr-sqrt
3998×times-frac
2928×add-exp-log
2677×add-cube-cbrt
1776×sqrt-prod
1634×add-cbrt-cube
1160×pow1 prod-exp
968×div-exp
727×difference-of-squares
696×pow-exp
671×add-log-exp
602×associate-*r*
561×associate-*l*
457×cbrt-unprod associate-/r*
449×associate-/l*
419×insert-posit16
404×distribute-lft-out
377×distribute-lft-out--
348×pow-to-exp
335×cbrt-undiv
311×pow-prod-down
259×swap-sqr
248×div-inv
193×log-prod
174×flip-+
173×flip3-+ unswap-sqr
157×associate-/r/
151×cbrt-prod
135×1-exp rec-exp
109×*-commutative
108×frac-2neg clear-num
96×sub-neg
90×log-pow
87×diff-log
81×exp-prod
74×associate-/l/
69×difference-of-sqr-1
68×associate--l+
64×pow-prod-up
60×unpow-prod-down
59×distribute-rgt-in distribute-lft-in
58×sqrt-pow1 pow1/2
56×associate--r+
52×log-div
45×sum-log
43×pow-sqr
40×pow1/3
36×+-commutative
35×pow-plus
33×rem-sqrt-square
31×frac-sub
30×div-sub
26×rem-log-exp
23×tan-quot
21×pow2
13×pow-flip acos-asin
12×difference-of-sqr--1 inv-pow cos-diff
10×sqr-pow cos-sum associate-+l-
sqrt-undiv distribute-rgt-out
cube-prod associate--l-
sin-mult
pow-unpow exp-sum distribute-frac-neg pow-pow rem-exp-log acos-neg
exp-diff sqrt-unprod associate--r-
associate-+r+ exp-to-pow
distribute-rgt-neg-in
neg-sub0 sin-sum cube-unmult sum-cubes rem-square-sqrt cube-mult distribute-rgt1-in
remove-posit16 cos-mult distribute-lft1-in sin-cos-mult pow3 neg-log tanh-undef tanh-def asin-acos sin-diff

regimes13.4s (0.6%)

Accuracy

Total 65.6b remaining (35.2%)

Threshold costs 3.3b (1.8%)

11.0b-0.7%Quotient of products
8.1b38.8%Equirectangular approximation to distance on a great circle
7.1b47.9%Quadratic roots, narrow range
7.1b48.1%Cubic critical, narrow range
6.0b12.2%Cubic critical, medium range

localize4.9s (0.2%)

bsearch1.5s (0.1%)

end1.0ms (0.0%)