Details

simplify6.6m (38.6%)

sample4.9m (28.7%)

Algorithm
78×intervals
Results
1.6m20426×body10240exit
1.3m43746×body1280valid
30.2s30691×body640valid
18.8s202771×body80valid
14.7s153013×body80nan
13.0s27749×body320valid
8.6s35759×body160valid
7.1s158253×pre80true
2.3s3100×body2560valid
1.3s7869×body160nan
633.0ms4116×pre10240exit
211.0ms8292×pre80false
141.0ms220×body5120valid
1.0msbody640nan

prune3.6m (21.1%)

series1.0m (6.0%)

Calls

489 calls:

2.1s
(sqrt (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n) (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n) (/ (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (+ 1 (* c_p (+ (log 0.5) (* 0.5 t))))))))
2.1s
(sqrt (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n) (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n) (/ (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (+ 1 (* c_p (+ (log 0.5) (* 0.5 t))))))))
1.1s
(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3)) (+ (* (cos phi1) (cos phi1)) (* (* (cos phi2) (* (cos lambda1) (cos lambda2))) (- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1)))))
810.0ms
(log (exp (/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (+ (/ (* x x) (* (+ x 1.0) (+ x 1.0))) (/ (+ (* (+ x 1.0) (/ (+ x 1.0) (- x 1.0))) x) (- x 1.0))))))
809.0ms
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* (log 0.5) c_p) (+ (* 0.5 (* t c_p)) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

rewrite34.6s (3.4%)

Algorithm
147×rewrite-expression-head
Calls

489 calls:

1.7s
(log (exp (/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (+ (/ (* x x) (* (+ x 1.0) (+ x 1.0))) (/ (+ (* (+ x 1.0) (/ (+ x 1.0) (- x 1.0))) x) (- x 1.0))))))
1.4s
(sqrt (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n) (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n) (/ (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (+ 1 (* c_p (+ (log 0.5) (* 0.5 t))))))))
1.1s
(sqrt (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n) (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n) (/ (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (+ 1 (* c_p (+ (log 0.5) (* 0.5 t))))))))
613.0ms
(log (exp (- (/ (pow x0 3) (pow (- 1.0 x1) 6)) (pow x0 3))))
593.0ms
(* (- (- (* 1.0 (/ m v)) (/ (pow m 2) v)) 1.0) m)
Rules
71971×times-frac
41170×add-sqr-sqrt
36851×*-un-lft-identity
28901×unpow-prod-down
24114×add-cube-cbrt
18427×sqrt-prod
6736×difference-of-squares
3805×sqr-pow
3758×distribute-lft-out--
3150×add-exp-log
2543×distribute-lft-out
1979×add-cbrt-cube
1959×associate-/r/
1830×div-inv
1138×flip--
1137×flip3--
1051×prod-exp
1036×pow1
1003×div-exp
985×flip-+
984×flip3-+
856×frac-times
849×associate-*l/
771×associate-*r*
770×add-log-exp
766×associate-/r*
689×associate-/l*
618×frac-add
590×sqrt-div
570×cube-prod
498×cbrt-undiv
491×associate-*l*
488×cbrt-unprod
474×log-pow
440×associate-*r/
406×exp-prod
363×pow-exp
333×cbrt-prod
328×log-prod
255×pow-to-exp
230×cos-mult
215×pow-prod-down
163×cbrt-div
148×distribute-rgt-neg-in unswap-sqr
130×sub-neg
128×rem-sqrt-square clear-num frac-2neg
107×*-commutative
94×associate-/l/
92×diff-log
73×associate-+r+
69×sqrt-pow1
61×swap-sqr
59×log-div
56×sum-log
54×pow1/2
50×1-exp rec-exp
48×distribute-rgt-in distribute-lft-in
45×+-commutative
43×div-sub
42×unpow3
40×cube-mult
36×pow-unpow
32×rem-log-exp
28×distribute-rgt-out tan-quot
22×exp-sum
21×associate--l+
20×cube-div
19×sin-diff
18×pow-prod-up sin-mult pow-pow
17×rem-cube-cbrt pow1/3 neg-sub0
16×pow-sqr
15×cos-diff
14×sin-cos-mult associate-+l+ associate-+l-
13×associate--l- neg-log cos-sum
12×inv-pow pow-flip pow-plus
11×pow2
associate-+r- frac-sub
exp-diff acos-asin associate--r+
sin-sum
difference-cubes
distribute-lft1-in unpow2 associate--r-
sum-cubes rem-cbrt-cube
distribute-frac-neg acos-neg un-div-inv sqrt-unprod distribute-neg-in distribute-rgt-out-- asin-acos log-rec
sub0-neg rem-exp-log distribute-rgt-neg-out
unsub-neg rem-square-sqrt sub-div tanh-undef sqr-cos exp-to-pow tanh-def

regimes13.7s (1.3%)

Accuracy

Total 33.1b remaining (25.8%)

Threshold costs 6.1b (4.7%)

6.0b82.2%Quadratic roots, full range
4.6b57.4%Quotient of products
3.8b73.4%Equirectangular approximation to distance on a great circle
3.7b0%Cubic critical, wide range
3.7b0%Quadratic roots, wide range

bsearch4.6s (0.5%)

localize4.3s (0.4%)

end1.0ms (0.0%)