Details

sample13.2m (58.6%)

Algorithm
78×intervals
Results
9.8m58656×body10240exit
1.3m43306×body1280valid
30.8s30587×body640valid
20.9s205088×body80valid
13.3s152559×body80nan
12.8s27969×body320valid
8.6s197997×pre80true
8.2s36128×body160valid
2.1s3125×body2560valid
1.0s7892×body160nan
727.0ms4142×pre10240exit
233.0ms250×body5120valid
231.0ms8365×pre80false
1.0ms1×body640nan

simplify6.5m (28.7%)

prune1.1m (4.9%)

series57.5s (4.3%)

Calls

475 calls:

1.5s
(/ (* (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 (/ (- (pow 1.0 3) (pow (/ 1.0 (+ 1.0 (exp (- t)))) 3)) (+ (* (/ 1.0 (+ 1.0 (exp (- t)))) (+ 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) (* 1.0 1.0))) c_n)))
859.0ms
(pow E (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
803.0ms
(- (* (cos delta) (cos delta)) (* (pow (sin phi1) 2) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
783.0ms
(/ (* (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)))
708.0ms
(/ (* (* a c) 4.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite27.8s (2.1%)

Algorithm
143×rewrite-expression-head
Calls

475 calls:

2.2s
(* (- (/ (/ m (sqrt v)) (/ (sqrt v) (- 1.0 m))) 1.0) m)
875.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
855.0ms
(- (- (/ x (+ x 1.0)) (/ x (- x 1.0))) (* (/ 1 (- x 1.0)) 1.0))
598.0ms
(+ x (- x (+ (/ 0.125 (pow x 3)) (/ 0.5 x))))
579.0ms
(+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))
Rules
6746×times-frac
5952×add-sqr-sqrt
5614×*-un-lft-identity
3636×add-cube-cbrt
3236×add-exp-log
1856×add-cbrt-cube
1453×sqrt-prod
1141×associate-*r*
1109×prod-exp
1097×div-exp
1016×pow1
909×flip--
907×flip3--
906×associate-*l/
840×difference-of-squares
775×add-log-exp
697×cbrt-prod
678×distribute-lft-out--
611×associate-*l*
588×unpow-prod-down
529×frac-times
508×sqrt-div
488×associate-/r*
456×cbrt-unprod
454×cbrt-undiv
450×pow-exp
440×cube-prod
431×associate-/l*
419×associate-/r/
395×frac-add
379×div-inv
376×associate-*r/
320×pow-to-exp
288×distribute-lft-out
250×unswap-sqr
232×sqr-pow
219×swap-sqr
203×flip-+
201×pow-prod-down flip3-+
179×log-div
151×log-prod
138×log-pow
128×sub-neg
113×*-commutative
108×clear-num frac-2neg
103×sqrt-pow1 diff-log
101×exp-prod
97×associate-/l/
85×distribute-rgt-neg-in
78×cbrt-div
73×exp-diff 1-exp
71×pow1/2
67×unpow3 cube-mult
66×pow-sub
58×sum-log
48×pow-unpow
47×distribute-rgt-in distribute-lft-in
46×rec-exp
42×pow1/3
39×div-sub
37×pow-prod-up
34×sin-cos-mult rem-sqrt-square +-commutative
32×frac-sub
29×pow-sqr
27×cos-mult
26×tan-quot
24×exp-sum associate--l+
21×rem-log-exp
20×pow-pow
18×sin-diff
17×rem-cube-cbrt cos-diff pow-plus
16×pow2 neg-sub0
15×associate-+r- associate--r+
13×distribute-rgt-out
12×associate-+r+ acos-asin neg-log sin-mult cos-sum
11×associate-+l-
10×pow-flip
9×distribute-frac-neg sin-sum associate--l-
8×cube-div rem-exp-log
6×acos-neg unpow-prod-up
5×inv-pow distribute-neg-in associate-+l+
4×asin-acos associate--r- unpow2
2×difference-cubes un-div-inv distribute-lft1-in sum-cubes distribute-rgt-neg-out
1×sqrt-undiv rem-cbrt-cube e-exp-1 sqrt-unprod sqr-sin rem-square-sqrt sub-div tanh-undef sqr-cos exp-to-pow tanh-def

regimes13.6s (1.0%)

Accuracy

Total 43.3b remaining (30.4%)

Threshold costs 6.7b (4.7%)

15.5b27.6%Equirectangular approximation to distance on a great circle
7.7b44.7%Quadratic roots, narrow range
3.9b64.6%Quotient of products
3.5b0%Quadratic roots, wide range
3.5b0%Cubic critical, wide range

localize4.2s (0.3%)

bsearch1.2s (0.1%)

end1.0ms (0.0%)