Details

sample7.4m (73.2%)

Algorithm
78×intervals
Results
6.0m29210×body10240exit
34.2s43438×body1280valid
11.9s30721×body640valid
7.3s204649×body80valid
4.9s27181×body320valid
4.8s152821×body80nan
3.3s180950×pre80true
3.2s35962×body160valid
792.0ms3100×body2560valid
442.0ms14758×body80overflowed
391.0ms4141×pre10240exit
382.0ms7935×body160nan
98.0ms7928×pre80false
63.0ms205×body5120valid
0.0msbody320nan

prune1.0m (10.4%)

series55.2s (9.1%)

Calls

506 calls:

1.9s
(* (/ 1 (sqrt (+ (* (- (log 1.0) (* 2.0 (/ (pow x 2) (pow 1.0 2)))) (- (- (log 1.0) (* 2.0 (/ (pow x 2) (pow 1.0 2)))) (* 2.0 (+ (pow x 2) x)))) (* (* 2.0 (+ (pow x 2) x)) (* 2.0 (+ (pow x 2) x)))))) (/ (+ (pow (* 2.0 (+ (pow x 2) x)) 3) (pow (- (log 1.0) (* 2.0 (/ (pow x 2) (pow 1.0 2)))) 3)) (sqrt (+ (* (- (log 1.0) (* 2.0 (/ (pow x 2) (pow 1.0 2)))) (- (- (log 1.0) (* 2.0 (/ (pow x 2) (pow 1.0 2)))) (* 2.0 (+ (pow x 2) x)))) (* (* 2.0 (+ (pow x 2) x)) (* 2.0 (+ (pow x 2) x)))))))
1.8s
(/ (+ (pow (* 2.0 (+ (pow x 2) x)) 3) (pow (- (log 1.0) (* 2.0 (/ (pow x 2) (pow 1.0 2)))) 3)) (+ (* (- (log 1.0) (* 2.0 (/ (pow x 2) (pow 1.0 2)))) (- (- (log 1.0) (* 2.0 (/ (pow x 2) (pow 1.0 2)))) (* 2.0 (+ (pow x 2) x)))) (* (* 2.0 (+ (pow x 2) x)) (* 2.0 (+ (pow x 2) x)))))
848.0ms
(/ (- (* (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))))))))) (+ (cos delta) (* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
844.0ms
(/ (- (* (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)))))))) (+ (cos delta) (* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
816.0ms
(/ (- (* (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)))))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

rewrite15.4s (2.5%)

Algorithm
144×rewrite-expression-head
Calls

506 calls:

797.0ms
(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))
759.0ms
(* (/ 1 (sqrt (+ (* (- (log 1.0) (* 2.0 (/ (pow x 2) (pow 1.0 2)))) (- (- (log 1.0) (* 2.0 (/ (pow x 2) (pow 1.0 2)))) (* 2.0 (+ (pow x 2) x)))) (* (* 2.0 (+ (pow x 2) x)) (* 2.0 (+ (pow x 2) x)))))) (/ (+ (pow (* 2.0 (+ (pow x 2) x)) 3) (pow (- (log 1.0) (* 2.0 (/ (pow x 2) (pow 1.0 2)))) 3)) (sqrt (+ (* (- (log 1.0) (* 2.0 (/ (pow x 2) (pow 1.0 2)))) (- (- (log 1.0) (* 2.0 (/ (pow x 2) (pow 1.0 2)))) (* 2.0 (+ (pow x 2) x)))) (* (* 2.0 (+ (pow x 2) x)) (* 2.0 (+ (pow x 2) x)))))))
571.0ms
(* (+ (sqrt (/ m (/ v (- 1.0 m)))) (sqrt 1.0)) (* (- (sqrt (/ m (/ v (- 1.0 m)))) (sqrt 1.0)) m))
421.0ms
(/ (+ (pow (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) 3) (sqrt (pow 1.0 3))) (sqrt (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) (* 1.0 1.0))))
287.0ms
(* (- (sqrt (/ m (/ v (- 1.0 m)))) (sqrt 1.0)) m)
Rules
11587×times-frac
8729×add-sqr-sqrt
8344×*-un-lft-identity
5253×add-cube-cbrt
3490×add-exp-log
2938×associate-*r/
2104×add-cbrt-cube
1793×sqrt-prod
1757×flip--
1756×flip3--
1614×frac-times
1532×difference-of-squares
1443×associate-*r*
1435×frac-add
1323×associate-*l/
1250×sqrt-div
1207×flip-+ distribute-lft-out--
1206×flip3-+
1191×pow1
1186×div-exp
1146×prod-exp
1044×associate-/l*
1025×associate-/r/
817×associate-/r*
812×distribute-rgt-neg-in
808×unpow-prod-down
801×add-log-exp
632×frac-sub
596×associate-*l* cube-prod
548×cbrt-undiv
502×cbrt-unprod
441×div-inv
369×pow-exp
344×cbrt-prod
338×distribute-lft-neg-in
332×distribute-lft-out
295×pow-prod-down
273×sqr-pow
268×pow-to-exp
190×neg-mul-1
179×cbrt-div
170×unswap-sqr
162×associate-/l/
150×log-prod
137×clear-num frac-2neg
121×sub-neg
102×*-commutative
101×1-exp
98×diff-log
88×rec-exp
83×div-sub
70×pow-unpow
64×swap-sqr
63×unpow3 cube-mult
62×sum-log
60×distribute-rgt-in distribute-lft-in
54×sin-mult
52×associate--l+
49×pow1/2 sqrt-pow1
44×pow1/3
41×unpow2 +-commutative cos-mult
40×rem-sqrt-square
39×pow-pow
38×log-div
36×cube-div
35×log-pow pow-prod-up
33×pow-sqr
31×exp-prod
30×associate-+r+ neg-sub0
27×associate-+l-
23×rem-cube-cbrt
20×tan-quot
19×distribute-rgt-out sin-diff
18×distribute-frac-neg sum-cubes
17×associate-+l+ pow-plus
15×sin-sum neg-log rem-log-exp
14×associate-+r- cos-diff acos-asin
13×pow-flip exp-sum
12×associate--l- pow2 sub-div
11×difference-cubes tanh-def
10×cos-sum un-div-inv inv-pow
sin-cos-mult associate--r- associate--r+
acos-neg rem-exp-log distribute-rgt-neg-out
rem-cbrt-cube distribute-neg-frac
exp-diff sub0-neg
sqrt-pow2 sin-neg sqr-cos
distribute-lft1-in sqrt-unprod unsub-neg asin-acos sqrt-undiv
pow3 distribute-rgt-out-- rem-square-sqrt tanh-undef cube-neg

simplify15.4s (2.5%)

Algorithm
222×egg-herbie

regimes8.6s (1.4%)

Accuracy

Total 21.6b remaining (19.3%)

Threshold costs 6.8b (6.1%)

5.6b50.5%Quotient of products
4.2b69.4%Equirectangular approximation to distance on a great circle
1.4b94.1%Cubic critical
1.3b0%2-ancestry mixing, positive discriminant
1.2b95.1%Quadratic roots, full range

localize2.4s (0.4%)

bsearch2.2s (0.4%)

end1.0ms (0.0%)