Details

sample6.0m (69.5%)

Algorithm
78×intervals
Results
4.6m35602×body10240exit
34.2s43658×body1280valid
11.6s30690×body640valid
7.2s203713×body80valid
4.6s27304×body320valid
4.5s150733×body80nan
3.1s36098×body160valid
2.7s173754×pre80true
739.0ms3071×body2560valid
357.0ms7953×body160nan
347.0ms4149×pre10240exit
182.0ms236×body5120valid
89.0ms8237×pre80false
2.0msbody640nan

prune49.5s (9.5%)

series45.1s (8.6%)

Calls

504 calls:

4.0s
(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3)) (+ (* (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (- (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cos phi1))) (* (cos phi1) (cos phi1))))
1.7s
(/ (- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)) (+ (* (* (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)))))) (cos delta))) (* (cos delta) (cos delta))))
661.0ms
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
548.0ms
(/ (* (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)))
500.0ms
(exp (* (cbrt (log (log (+ (* 1/2 (pow x 2)) (+ x 2.0))))) (cbrt (log (log (+ (* 1/2 (pow x 2)) (+ x 2.0)))))))

bsearch20.1s (3.9%)

rewrite20.0s (3.8%)

Algorithm
145×rewrite-expression-head
Calls

504 calls:

548.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
423.0ms
(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))))
398.0ms
(* (/ (/ (cbrt a1) (/ (* (cbrt b2) (cbrt b2)) (cbrt a1))) b1) (/ (cbrt a1) (/ (cbrt b2) a2)))
343.0ms
(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3)) (+ (* (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (- (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cos phi1))) (* (cos phi1) (cos phi1))))
280.0ms
(/ (/ (+ (- (pow b 2) (pow b 2)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
Rules
7652×times-frac
6434×add-sqr-sqrt
6381×*-un-lft-identity
4172×add-cube-cbrt
2640×add-exp-log
1698×add-cbrt-cube
1380×sqrt-prod
1196×pow1
1185×associate-*r*
1116×cbrt-prod
891×associate-/l*
864×prod-exp
845×add-log-exp
807×difference-of-squares
759×div-exp
739×associate-*l/
729×flip--
728×flip3--
700×distribute-lft-out--
619×unpow-prod-down
550×associate-*l*
536×associate-/r*
422×frac-times
408×div-inv
400×cbrt-unprod
397×distribute-lft-out
391×cbrt-undiv
389×pow-exp
388×sqrt-div
357×frac-add
355×cube-prod
340×associate-*r/
291×distribute-rgt-neg-in
286×pow-to-exp
268×sqr-pow
265×pow-prod-down
251×associate-/r/
245×unswap-sqr
201×flip-+
200×flip3-+
151×associate-/l/
145×log-prod
121×clear-num frac-2neg
117×sub-neg
111×*-commutative
105×diff-log
85×unpow3 cube-mult
82×cbrt-div
77×sum-log
66×log-pow
64×tan-quot
60×div-sub
59×pow-prod-up frac-sub
57×pow-unpow
56×exp-prod
53×pow1/3
46×swap-sqr cos-mult log-div
45×pow-sqr +-commutative
43×distribute-rgt-in distribute-lft-in
38×sin-mult
37×neg-sub0
35×associate-+l-
34×pow-plus
33×pow1/2 sqrt-pow1
31×pow-pow
30×rem-sqrt-square unpow2
27×distribute-lft-neg-in pow2
26×neg-log exp-sum
25×cube-div
22×associate-+r+
21×rem-cube-cbrt
20×associate--l- rem-log-exp
19×associate--l+
17×cos-diff
16×sin-diff
14×associate--r+
13×cos-sum
11×distribute-rgt-out
neg-mul-1 distribute-rgt-neg-out distribute-neg-frac
rem-exp-log acos-asin associate--r-
distribute-frac-neg sub-div
exp-diff sin-cos-mult associate-+r-
difference-cubes sin-neg sin-sum associate-+l+
sum-cubes 1-exp rem-cbrt-cube
acos-neg distribute-rgt-out-- rec-exp
distribute-lft1-in exp-to-pow
sqrt-unprod unsub-neg tanh-undef asin-acos cube-neg tanh-def

simplify13.6s (2.6%)

Algorithm
223×egg-herbie

regimes8.5s (1.6%)

Accuracy

Total 23.8b remaining (19%)

Threshold costs 7.9b (6.3%)

5.0b31.9%Quotient of products
4.4b83.7%Cubic critical
4.2b69.9%Equirectangular approximation to distance on a great circle
1.3b94.5%Quadratic roots, full range
1.1b0%2-ancestry mixing, zero discriminant

localize2.5s (0.5%)

end1.0ms (0.0%)