Details

sample13.1m (62.8%)

Algorithm
78×intervals
Results
9.8m58772×body10240exit
1.2m43306×body1280valid
29.9s30588×body640valid
18.8s205098×body80valid
14.1s27969×body320valid
12.7s152559×body80nan
9.5s198124×pre80true
8.3s36128×body160valid
2.3s3125×body2560valid
721.0ms7892×body160nan
563.0ms4142×pre10240exit
263.0ms250×body5120valid
189.0ms8365×pre80false
1.0msbody640nan

simplify4.3m (20.6%)

prune1.4m (6.7%)

series1.0m (4.9%)

Calls

499 calls:

1.3s
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* c_p (+ (log (/ 1.0 2.0)) (* (/ 1.0 2.0) t))) 1) (pow (/ (- (pow 1.0 3) (pow (/ 1.0 (+ 1.0 (exp (- t)))) 3)) (+ (* (/ 1.0 (+ 1.0 (exp (- t)))) (+ (/ 1.0 (+ 1.0 (exp (- t)))) 1.0)) (* 1.0 1.0))) c_n)))
891.0ms
(pow E (log (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))))))
784.0ms
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* c_p (+ (log (/ 1.0 2.0)) (* (/ 1.0 2.0) t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
736.0ms
(- (* (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))))))))
706.0ms
(- (pow (cos delta) 2) (+ (* (pow (sin delta) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (+ (* 2 (* (sin delta) (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))))) (* (pow (pow (sin phi1) (sqrt 4)) (sqrt 4)) (pow (cos delta) 2)))))

rewrite43.7s (3.5%)

Algorithm
146×rewrite-expression-head
Calls

499 calls:

4.6s
(- (pow (cos delta) 2) (+ (* (pow (sin delta) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (+ (* 2 (* (sin delta) (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))))) (* (pow (pow (sin phi1) (sqrt 4)) (sqrt 4)) (pow (cos delta) 2)))))
4.5s
(- (pow (cos delta) 2) (+ (* (pow (sin delta) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (+ (* 2 (* (sin delta) (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))))) (* (pow (sin phi1) 4) (pow (cos delta) 2)))))
1.5s
(- (/ x (sqrt 1.0)) (- (/ (/ (pow x 3) (pow (sqrt 1.0) 3)) 6) (log (sqrt 1.0))))
831.0ms
(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))))
804.0ms
(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))))
Rules
18113×times-frac
11419×add-sqr-sqrt
11245×*-un-lft-identity
7762×add-cube-cbrt
3393×add-exp-log
1927×add-cbrt-cube
1575×difference-of-squares
1501×sqrt-prod
1456×distribute-lft-out--
1227×div-exp
1199×associate-*r*
1152×associate-/l*
1126×unpow-prod-down
1064×prod-exp
1038×pow1
1033×associate-*l/
952×div-inv
926×flip--
925×flip3--
847×add-log-exp
791×cube-prod
717×associate-/r*
698×associate-*l*
634×frac-times
605×distribute-rgt-neg-in
546×frac-add
509×cbrt-undiv
468×sqrt-div
467×pow-exp
458×associate-*r/
416×cbrt-unprod
390×associate-/r/
342×sqr-pow
339×pow-to-exp
281×distribute-lft-out
249×log-div
219×unswap-sqr
209×pow-prod-down
202×flip-+
201×flip3-+
194×frac-sub
182×log-prod
166×cbrt-prod
164×unpow3 cube-mult
133×associate-/l/
125×sub-neg
123×clear-num frac-2neg
122×un-div-inv
114×diff-log
112×*-commutative
99×swap-sqr
94×1-exp
93×unpow2
75×sum-log
71×exp-diff log-pow
66×pow-sub
65×cbrt-div
64×rec-exp
58×exp-prod
57×div-sub
51×pow-unpow
42×+-commutative
40×distribute-lft-neg-in
39×pow1/2 distribute-rgt-in distribute-lft-in sqrt-pow1
35×rem-sqrt-square
32×sin-cos-mult
31×associate-+l-
30×pow1/3 cos-mult
27×neg-sub0
26×associate-+l+ tan-quot
22×rem-log-exp
20×pow-pow
19×pow-sqr neg-log sin-mult pow-prod-up associate--r+
18×associate--l+ sin-diff
17×rem-cube-cbrt pow-flip exp-sum
16×associate-+r+
15×cos-diff
14×associate--l- pow-plus
13×distribute-rgt-out
12×pow2
11×cos-sum rem-exp-log inv-pow
10×acos-asin neg-mul-1
cube-div sin-sum distribute-frac-neg
associate-+r-
unpow-prod-up associate--r-
difference-cubes asin-acos exp-to-pow
acos-neg
distribute-rgt-neg-out
distribute-lft1-in sub-div sum-cubes rem-cbrt-cube distribute-neg-frac
e-exp-1 distribute-rgt-out-- tanh-undef sqr-cos tanh-def log-rec

regimes14.3s (1.1%)

Accuracy

Total 32.2b remaining (26.4%)

Threshold costs 7.6b (6.2%)

11.8b-8.8%Quotient of products
8.7b52.2%Equirectangular approximation to distance on a great circle
3.1b89.1%Quadratic roots, full range
1.0b95.5%Cubic critical
0.8b0%2-ancestry mixing, zero discriminant

localize4.6s (0.4%)

bsearch1.3s (0.1%)

end1.0ms (0.0%)