Details

simplify32.8m (78.7%)

sample5.2m (12.4%)

Algorithm
78×intervals
Results
1.7m20426×body10240exit
1.4m43746×body1280valid
31.5s30691×body640valid
19.7s202771×body80valid
15.0s153013×body80nan
11.0s27749×body320valid
8.8s35759×body160valid
7.1s158253×pre80true
2.2s3100×body2560valid
969.0ms7869×body160nan
540.0ms4116×pre10240exit
200.0ms220×body5120valid
165.0ms8292×pre80false
2.0msbody640nan

prune1.6m (3.8%)

series1.1m (2.7%)

Calls

495 calls:

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 phi1)) (* (cos phi2) (* (cos lambda1) (cos lambda2))))))
946.0ms
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
896.0ms
(sqrt (/ (* (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))))
892.0ms
(sqrt (/ (* (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))))
889.0ms
(log (exp (/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (+ (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))))))

rewrite33.0s (1.3%)

Algorithm
145×rewrite-expression-head
Calls

495 calls:

1.7s
(- (pow (pow (/ (/ x0 (- 1.0 x1)) (- 1.0 x1)) 3) 3) (pow (pow x0 3) 3))
1.4s
(log (exp (/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (+ (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))))))
917.0ms
(+ x (+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) x))
894.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (cbrt (pow (sqrt (+ (exp (* -2.0 x)) 1.0)) 3))) 1.0)
808.0ms
(/ (- (pow (exp x) 3) (pow (exp (- x)) 3)) (+ (+ (exp (+ x x)) (exp (- (+ x x)))) 1))
Rules
21723×times-frac
12503×*-un-lft-identity
12181×add-sqr-sqrt
8991×add-cube-cbrt
3936×sqrt-prod
3084×add-exp-log
1926×add-cbrt-cube
1298×difference-of-squares
1275×unpow-prod-down
1187×associate-*r*
1159×flip--
1158×flip3--
1065×div-inv
1056×div-exp
1039×distribute-lft-out--
1035×pow1
939×associate-/l*
936×prod-exp
934×cube-prod
858×associate-*l/
854×frac-times
801×associate-/r*
793×add-log-exp
670×distribute-lft-out
644×frac-add
587×sqrt-div
524×cbrt-undiv
523×associate-*l*
440×associate-*r/
435×associate-/r/
411×cbrt-unprod
379×sqr-pow
374×pow-exp
355×log-pow
342×cbrt-prod
315×exp-prod
274×pow-to-exp
248×distribute-rgt-neg-in
230×cos-mult
228×log-prod
220×unswap-sqr
210×pow-prod-down
189×flip-+
188×flip3-+
165×cbrt-div
131×clear-num frac-2neg
109×sub-neg
108×*-commutative
100×associate-/l/
99×diff-log
77×unpow2
69×sqrt-pow1
64×unpow3
63×swap-sqr
62×cube-mult
61×log-div
59×sum-log
54×pow1/2
51×1-exp rec-exp
45×pow-unpow div-sub
40×+-commutative
38×pow-pow
36×tan-quot
33×exp-sum
32×rem-sqrt-square
30×pow1/3 rem-log-exp
28×distribute-rgt-out
27×cube-div
25×distribute-rgt-in distribute-lft-in
24×neg-sub0
21×pow-prod-up
19×pow-sqr sin-diff
18×rem-cube-cbrt neg-log frac-sub associate--l+
17×associate--l- sin-mult
15×cos-diff
14×pow-plus
13×difference-cubes pow2 cos-sum associate-+l-
12×sin-cos-mult
11×exp-diff
distribute-lft-neg-in
associate-+r- pow-flip associate-+r+ acos-asin associate--r+
sin-sum
inv-pow
un-div-inv distribute-lft1-in associate--r- rem-cbrt-cube
sum-cubes rem-exp-log
acos-neg sqrt-unprod distribute-neg-in distribute-rgt-out-- associate-+l+ distribute-frac-neg asin-acos neg-mul-1
pow-sub distribute-rgt-neg-out
sqrt-pow2 e-exp-1 cube-unmult unpow-prod-up unsub-neg rem-square-sqrt exp-neg sub-div tanh-undef sqr-cos exp-to-pow tanh-def

regimes15.6s (0.6%)

Accuracy

Total 35.0b remaining (26%)

Threshold costs 6.9b (5.1%)

6.1b79.1%Quadratic roots, full range
4.6b59.7%Quotient of products
3.7b0%Cubic critical, wide range
3.7b0%Quadratic roots, wide range
3.6b74.6%Equirectangular approximation to distance on a great circle

bsearch5.5s (0.2%)

localize4.7s (0.2%)

end1.0ms (0.0%)