Details

simplify5.3m (43.2%)

sample3.7m (30.0%)

Algorithm
77×intervals
Results
1.3m44120×body1280valid
29.1s15073×body10240exit
27.2s30225×body640valid
20.9s202574×body80valid
13.8s151678×body80nan
11.7s27555×body320valid
8.1s35537×body160valid
7.0s151638×pre80true
2.0s3212×body2560valid
847.0ms4091×pre10240exit
805.0ms7889×body160nan
151.0ms8099×pre80false
131.0ms262×body5120valid
4.0ms1×body640nan

prune1.3m (10.2%)

series1.1m (8.8%)

Calls

490 calls:

1.2s
(/ (+ (pow (cos phi1) 3) (pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)) (+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))) (* (cos phi1) (cos phi1))))
740.0ms
(* (cbrt (* (cbrt (/ 2.0 (+ (exp x) (exp (- x))))) (cbrt (/ 2.0 (+ (exp x) (exp (- x))))))) (cbrt (* (cbrt (/ 2.0 (+ (exp x) (exp (- x))))) (cbrt (/ 2.0 (+ (exp x) (exp (- x))))))))
694.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (log (exp (pow (cos (/ (+ phi1 phi2) 2.0)) 3))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
669.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
647.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite38.1s (5.2%)

Algorithm
140×rewrite-expression-head
Calls

490 calls:

1.2s
(/ (/ (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))) (* (* b b) (* b b)))))) (* 4.0 a)) c)
1.2s
(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))
1.1s
(* (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) (* 1.0 1.0)) (* (cbrt (+ (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))) (cbrt (+ (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3)))))
1.1s
(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))
1.1s
(* (- (/ (/ m v) (/ 1 (- 1.0 m))) 1.0) (- 1.0 m))
Rules
7613×times-frac
7132×*-un-lft-identity
7046×add-sqr-sqrt
4088×add-cube-cbrt
2442×add-exp-log
1938×add-cbrt-cube
1380×pow1
1271×difference-of-squares
1079×associate-*r*
982×distribute-lft-out--
913×associate-/l*
904×unpow-prod-down
787×add-log-exp
783×flip--
782×flip3--
774×associate-*l/
712×sqrt-prod
709×cube-prod div-exp
662×cbrt-prod
657×prod-exp
582×associate-/r*
515×associate-*l*
494×distribute-lft-out
488×cbrt-unprod
479×frac-times
457×distribute-rgt-neg-in
455×cbrt-undiv
437×log-prod
402×sqrt-div
387×associate-/r/ div-inv
347×frac-add
344×pow-prod-down
343×sqr-pow
318×associate-*r/
233×flip-+
232×flip3-+
211×cbrt-div
210×unswap-sqr
186×swap-sqr
181×distribute-lft-neg-in
134×associate-/l/
133×neg-mul-1
128×clear-num frac-2neg
112×sub-neg
109×associate-+r+
106×pow-prod-up
105×*-commutative
96×diff-log
93×1-exp
78×pow-sqr
77×pow1/3
72×log-pow
68×sum-log
66×div-sub
65×unpow3 cube-mult
60×pow-exp
55×pow-plus
53×rec-exp log-div
50×unpow2
48×pow-unpow
46×pow-to-exp
44×frac-sub
42×pow2 +-commutative
41×pow1/2 sqrt-pow1
39×distribute-rgt-in distribute-lft-in
38×cos-mult
35×associate-+l+
34×rem-sqrt-square neg-sub0
32×exp-prod associate-+l-
31×sin-cos-mult
30×rem-log-exp
29×rem-cube-cbrt
24×tan-quot
23×pow-pow difference-cubes
20×cube-div neg-log sin-diff
18×associate--l-
17×associate--l+
16×associate--r+
15×distribute-frac-neg sin-sum
14×cos-diff distribute-rgt-out
13×pow-flip sin-mult
10×cos-sum
9×associate-+r- acos-asin asin-acos
7×sum-cubes inv-pow distribute-rgt-neg-out
4×exp-diff pow-sub rem-cbrt-cube
3×acos-neg rem-exp-log log-rec exp-sum
2×un-div-inv distribute-lft1-in associate--r-
1×sqrt-undiv sin-neg sqrt-unprod unsub-neg tanh-undef tanh-def

regimes12.9s (1.8%)

Accuracy

Total 30.3b remaining (23.2%)

Threshold costs 7.6b (5.8%)

11.5b-4.3%Quotient of products
4.0b72.1%Equirectangular approximation to distance on a great circle
3.9b-68.6%(- (/ x0 (- 1 x1)) x0)
2.3b91.4%Cubic critical
1.0b95.7%Quadratic roots, full range

localize4.6s (0.6%)

bsearch1.1s (0.1%)

end1.0ms (0.0%)