Details

sample3.5m (49.7%)

Algorithm
78×intervals
Results
1.8m21813×body10240exit
48.3s43791×body1280valid
15.9s30950×body640valid
8.8s202364×body80valid
6.3s27541×body320valid
5.8s152714×body80nan
4.0s36011×body160valid
2.8s158232×pre80true
888.0ms3079×body2560valid
487.0ms4136×pre10240exit
430.0ms7993×body160nan
98.0ms8099×pre80false
80.0ms230×body5120valid
3.0msbody640nan
2.0msbody320nan

prune1.9m (26.8%)

series42.8s (10.0%)

Calls

498 calls:

1.1s
(pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3)
969.0ms
(pow (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))) (* (cbrt 1/3) (cbrt 1/3)))
854.0ms
(pow (pow (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))) (* (cbrt 1/3) (cbrt 1/3))) (cbrt 1/3))
784.0ms
(/ (cbrt (+ (pow (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) 3) (pow (* 1.0 1.0) 3))) (cbrt (+ (* (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0))))) (- (* (* 1.0 1.0) (* 1.0 1.0)) (* (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) (* 1.0 1.0))))))
663.0ms
(/ (* (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)))

rewrite22.9s (5.3%)

Algorithm
143×rewrite-expression-head
Calls

498 calls:

752.0ms
(/ (cbrt (+ (pow (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) 3) (pow (* 1.0 1.0) 3))) (cbrt (+ (* (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0))))) (- (* (* 1.0 1.0) (* 1.0 1.0)) (* (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) (* 1.0 1.0))))))
742.0ms
(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))
500.0ms
(* (* (* (- (/ (* m (- 1.0 m)) v) 1.0) (sqrt (+ (sqrt 1.0) (sqrt m)))) (sqrt (+ (sqrt 1.0) (sqrt m)))) (- (sqrt 1.0) (sqrt m)))
433.0ms
(/ (- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3)) (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) (* 1.0 1.0)))
391.0ms
(* (/ (+ (- (pow b 2) (pow b 2)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (/ 1 (* 3.0 a)))
Rules
6114×times-frac
6006×*-un-lft-identity
5570×add-sqr-sqrt
3641×add-cube-cbrt
2983×add-exp-log
1776×add-cbrt-cube
1188×pow1
1053×sqrt-prod
1049×prod-exp
1037×associate-*r*
876×associate-*l/
862×div-exp
849×flip--
848×flip3--
792×add-log-exp
773×difference-of-squares
696×associate-/l*
689×frac-times
684×unpow-prod-down
638×associate-/r*
614×distribute-lft-out--
534×distribute-lft-out
443×cbrt-unprod cube-prod
433×cbrt-prod
427×frac-add
412×associate-*l*
404×cbrt-div
397×associate-*r/
384×pow-exp
371×cbrt-undiv
354×associate-/r/
330×flip-+ div-inv
329×flip3-+
308×pow-prod-down
300×sqrt-div
279×pow-to-exp
275×distribute-rgt-neg-in
233×sqr-pow
182×log-prod
179×unswap-sqr
133×associate-/l/
125×clear-num frac-2neg
110×swap-sqr
109×*-commutative
100×sub-neg
87×diff-log
74×1-exp rec-exp
73×distribute-lft-neg-in
70×div-sub
69×sum-log
62×pow1/3
61×frac-sub
60×unpow3 cube-mult
52×pow-unpow
50×log-pow unpow2
42×+-commutative
40×log-div
39×pow1/2 neg-mul-1 sqrt-pow1
38×neg-sub0
37×associate-+l-
36×exp-prod
34×pow-prod-up
32×distribute-rgt-in pow-sqr distribute-lft-in
30×un-div-inv
29×rem-sqrt-square
27×sin-mult
25×neg-log
22×pow-pow
20×pow-flip rem-log-exp
19×cube-div
18×tan-quot sin-diff
17×cos-diff pow-plus
16×distribute-rgt-out associate--l+ associate--r+
14×associate--l- sum-cubes
13×rem-cube-cbrt pow2 acos-asin
12×cos-sum
11×sin-cos-mult inv-pow distribute-frac-neg associate-+r-
cos-mult
difference-cubes associate-+r+ associate--r-
acos-neg asin-acos
rem-exp-log sin-sum exp-sum rem-cbrt-cube
exp-diff associate-+l+ distribute-rgt-neg-out
distribute-lft1-in sub-div
distribute-neg-out sin-neg unpow1/3 sqrt-unprod unsub-neg rem-square-sqrt tanh-undef sqr-cos cube-neg exp-to-pow tanh-def

regimes18.4s (4.3%)

Accuracy

Total 26.6b remaining (20.7%)

Threshold costs 7.1b (5.5%)

6.9b40.2%Quotient of products
3.8b72.6%Equirectangular approximation to distance on a great circle
3.2b89%Quadratic roots, full range
3.2b89.1%Cubic critical
1.3b0%2-ancestry mixing, positive discriminant

simplify13.6s (3.2%)

Algorithm
221×egg-herbie

localize2.4s (0.6%)

bsearch707.0ms (0.2%)

end1.0ms (0.0%)