Details

sample8.6m (68.8%)

Algorithm
78×intervals
Results
7.2m49374×body10240exit
34.1s44132×body1280valid
11.5s30451×body640valid
7.2s204876×body80valid
4.6s152740×body80nan
4.4s27363×body320valid
3.2s188619×pre80true
3.2s36241×body160valid
788.0ms3014×body2560valid
391.0ms4203×pre10240exit
377.0ms7851×body160nan
100.0ms8396×pre80false
97.0ms218×body5120valid
1.0msbody640nan
0.0msbody320nan

prune2.2m (17.6%)

series48.2s (6.4%)

Calls

509 calls:

1.3s
(+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3))
966.0ms
(cbrt (/ (pow (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) 3) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
794.0ms
(cbrt (/ (pow (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) 3) (pow (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) 3)))
734.0ms
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
709.0ms
(pow (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) 3)

simplify21.6s (2.9%)

Algorithm
223×egg-herbie

rewrite15.6s (2.1%)

Algorithm
145×rewrite-expression-head
Calls

509 calls:

635.0ms
(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))
542.0ms
(sqrt (+ (* (* (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
366.0ms
(* (cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))) (cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))))
250.0ms
(* (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (/ 1 (* 3.0 a)))
217.0ms
(* 2.0 (/ (pow x 2) (pow 1.0 2)))
Rules
30285×associate-*l/
20735×frac-times
19407×times-frac
16748×flip--
16747×flip3--
15667×cbrt-div
11297×*-un-lft-identity
11176×add-sqr-sqrt
7408×add-cube-cbrt
6321×associate-*r/
6204×sqrt-div
6007×frac-add
2728×add-exp-log
2010×distribute-rgt-neg-in
1759×add-cbrt-cube
1707×difference-of-squares
1574×distribute-lft-out--
1479×sqrt-prod
1325×distribute-lft-neg-in
1306×pow1
1281×neg-mul-1
1154×associate-*r*
920×prod-exp
825×add-log-exp
783×div-exp
735×associate-/l*
686×associate-/r*
659×unpow-prod-down
646×div-inv
604×associate-/r/
547×cbrt-prod
471×associate-*l*
428×cbrt-unprod
375×pow-exp
365×cbrt-undiv
355×pow-prod-down
354×distribute-lft-out
348×cube-prod
275×pow-to-exp
235×flip-+
234×flip3-+
218×sqr-pow
214×unswap-sqr
177×log-prod
131×associate-/l/
117×sub-neg
116×*-commutative
115×clear-num frac-2neg
98×frac-sub
92×diff-log
86×log-pow
84×unpow3 cube-mult exp-prod
78×unpow2
72×sum-log
69×pow-unpow
65×div-sub
60×swap-sqr
57×sqrt-pow1
53×pow1/2
51×pow1/3
48×+-commutative
47×distribute-rgt-in distribute-lft-in
45×sin-mult
42×pow-prod-up
40×pow-sqr
38×rem-sqrt-square
36×cube-div neg-sub0 tan-quot
34×pow-pow
33×log-div
30×associate-+l-
27×1-exp distribute-rgt-out
26×associate--l+
23×cos-mult
22×pow-plus rem-log-exp
20×rec-exp neg-log
17×pow2 sin-diff
16×rem-cube-cbrt distribute-frac-neg cos-diff
15×cos-sum
14×associate--l-
13×distribute-rgt-out--
12×sin-cos-mult
11×associate-+r+
10×exp-sum
sub-div
acos-asin
rem-exp-log associate--r+
distribute-lft1-in sqrt-unprod sin-sum associate-+l+
associate-+r- pow-flip rem-cbrt-cube
exp-diff acos-neg inv-pow associate--r- distribute-rgt-neg-out
un-div-inv asin-acos sqr-cos sqrt-undiv distribute-neg-frac exp-to-pow
sum-cubes rem-square-sqrt tanh-undef +-inverses tanh-def

regimes8.8s (1.2%)

Accuracy

Total 28.2b remaining (20.7%)

Threshold costs 8.6b (6.3%)

13.9b0.9%Equirectangular approximation to distance on a great circle
3.4b69.1%Quotient of products
1.2b0%2-ancestry mixing, zero discriminant
1.0b96.4%Quadratic roots, full range
1.0b95.5%Cubic critical

bsearch5.3s (0.7%)

localize2.4s (0.3%)

end1.0ms (0.0%)