Details

sample7.1m (74.2%)

Algorithm
78×intervals
Results
5.7m41601×body10240exit
34.1s43992×body1280valid
10.9s30167×body640valid
7.1s204050×body80valid
4.5s153350×body80nan
4.4s27839×body320valid
2.9s36091×body160valid
2.8s181111×pre80true
723.0ms3052×body2560valid
356.0ms7814×body160nan
336.0ms4109×pre10240exit
93.0ms8389×pre80false
70.0ms209×body5120valid

prune52.9s (9.2%)

series46.5s (8.1%)

Calls

493 calls:

3.8s
(/ (+ (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))))
1.0s
(+ (pow (cos phi1) 3) (pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3))
732.0ms
(- (pow (pow (/ x (+ x 1.0)) 3) 3) (pow (pow (/ (+ x 1.0) (- x 1.0)) 3) 3))
642.0ms
(/ (* (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)))

rewrite24.2s (4.2%)

Algorithm
145×rewrite-expression-head
Calls

493 calls:

1.8s
(* (- (/ (/ m 1) (/ v (/ (- (* 1.0 1.0) (* m m)) (+ 1.0 m)))) 1.0) (- 1.0 m))
1.7s
(* (- (/ (/ (/ (* m (- 1.0 m)) (sqrt v)) (sqrt (sqrt v))) (sqrt (sqrt v))) 1.0) m)
718.0ms
(- (pow (pow (/ x (+ x 1.0)) 3) 3) (pow (pow (/ (+ x 1.0) (- x 1.0)) 3) 3))
717.0ms
(- (pow (pow (/ x (+ x 1.0)) 3) 3) (pow (pow (/ (+ x 1.0) (- x 1.0)) 3) 3))
425.0ms
(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))))
Rules
19236×times-frac
13845×*-un-lft-identity
11179×add-sqr-sqrt
8409×add-cube-cbrt
7469×sqrt-prod
3099×add-exp-log
1950×unpow-prod-down
1882×add-cbrt-cube
1664×cube-prod
1511×distribute-lft-out
1319×difference-of-squares
1192×associate-*r*
1130×distribute-lft-out--
1043×pow1
1025×div-exp
1005×prod-exp
941×associate-/l*
782×add-log-exp
759×flip--
758×flip3--
741×div-inv
738×associate-*l/
711×associate-/r*
510×associate-/r/
496×sqrt-div
488×cbrt-undiv
423×cbrt-unprod
414×frac-times
410×pow-exp
390×sqr-pow
387×associate-*l*
369×frac-add
323×associate-*r/
305×pow-to-exp
299×flip-+
298×flip3-+
268×cbrt-prod
247×distribute-rgt-neg-in
199×unswap-sqr
193×pow-prod-down
174×log-prod
138×associate-/l/
127×clear-num frac-2neg
126×sub-neg
104×*-commutative
100×diff-log
84×pow-unpow
78×unpow3 cube-mult 1-exp
64×log-pow
63×div-sub
53×sum-log
50×distribute-rgt-in distribute-lft-in
48×cbrt-div
47×exp-prod rec-exp
46×swap-sqr
44×pow-prod-up
42×unpow2 log-div
38×pow-pow
35×+-commutative
34×neg-sub0
33×cos-mult
31×pow1/3 sin-mult
30×pow-sqr
29×associate-+l-
28×tan-quot
27×pow1/2 rem-sqrt-square sqrt-pow1
26×pow-plus rem-log-exp
25×cube-div associate--l+
24×neg-log associate--r+
22×frac-sub
21×pow2
19×associate--l-
17×cos-diff sin-diff
16×rem-cube-cbrt associate-+r+ distribute-neg-frac
15×sum-cubes
14×acos-asin
13×distribute-rgt-out
12×sin-cos-mult distribute-frac-neg cos-sum
10×pow-flip distribute-rgt-neg-out
associate--r-
acos-neg associate-+r-
difference-cubes sin-neg inv-pow sub-div exp-sum
un-div-inv
exp-diff rem-exp-log sin-sum distribute-rgt-out--
sqrt-undiv
associate-+l+ rem-cbrt-cube
distribute-lft1-in exp-neg
remove-double-div tanh-undef asin-acos exp-to-pow tanh-def log-rec

simplify13.8s (2.4%)

Algorithm
223×egg-herbie

regimes8.4s (1.5%)

Accuracy

Total 29.8b remaining (24.9%)

Threshold costs 7.7b (6.5%)

8.7b37%Equirectangular approximation to distance on a great circle
7.3b36.2%Quotient of products
3.7b86.1%Quadratic roots, full range
1.3b0%2-ancestry mixing, positive discriminant
1.1b0%2-ancestry mixing, zero discriminant

localize2.5s (0.4%)

bsearch646.0ms (0.1%)

end1.0ms (0.0%)