Details

simplify10.4m

Calls

5058 calls:

Slowest
2.1s
(/ (* (* (* -3/2 (* a c)) (* -3/2 (* a c))) (* -3/2 (* a c))) (* (* (* (* 3 a) b) (* (* 3 a) b)) (* (* 3 a) b)))
1.7s
(/ (* (* (* -2 (* a c)) (* -2 (* a c))) (* -2 (* a c))) (* (* (* (* 2 a) b) (* (* 2 a) b)) (* (* 2 a) b)))
1.4s
(* (* (* (* (+ 1 (exp x)) (+ 1 (exp x))) (* (+ 1 (exp x)) (+ 1 (exp x)))) (* (+ 1 (exp x)) (+ 1 (exp x)))) (* (* (+ 1 (exp x)) (+ 1 (exp x))) (+ 1 (exp x))))
1.2s
(sqrt (+ (* (* (* (- (pow lambda1 3) (pow lambda2 3)) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))) (+ phi1 phi2))) (* (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* lambda1 lambda2))) (* (- (pow phi1 3) (pow phi2 3)) (- (* phi1 phi1) (* phi2 phi2))))))
1.1s
(sqrt (+ (* (* (* (- (pow lambda1 3) (pow lambda2 3)) (cos (/ (+ phi1 phi2) 2))) (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2)))) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2)))) (* (* (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* lambda1 lambda2))) (+ lambda1 lambda2)) (* (- (pow phi1 3) (pow phi2 3)) (- phi1 phi2)))))

sample9.5m

Algorithm
71×intervals
Results
6.6m76485×body10240exit
51.5s32826×body1280valid
24.5s197544×body80valid
21.3s152332×body80nan
21.2s24108×body640valid
14.5s25251×body320valid
12.7s35273×body160valid
10.5s150171×pre80true
3.1s3097×body2560valid
1.9s7809×body160nan
1.1s4095×pre10240exit
274.0ms244×body5120valid

prune1.7m

series23.6s

Calls

407 calls:

Slowest
734.0ms
(cbrt (* 2 a))
581.0ms
(sqrt (+ (* (* (cos (* (+ phi1 phi2) 1/2)) (cos (* (+ phi1 phi2) 1/2))) (+ (* lambda1 lambda1) (* lambda2 (- lambda2 (* 2 lambda1))))) (* (- phi1 phi2) (- phi1 phi2))))
492.0ms
(log (- (/ -1/2 x) (+ (/ -1/8 (* (* x x) x)) (/ 1/16 (pow x 5)))))
440.0ms
(cbrt (/ (- (- g) (sqrt (- (* g g) (* h h)))) (cbrt (/ a 1/2))))
429.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

regimes13.1s

Accuracy

Total 62.3b remaining (35.9%)

10.8b39.2%Equirectangular approximation to distance on a great circle
7.6b42.4%Cubic critical, narrow range
7.3b47.2%Quadratic roots, narrow range
6.9b0.3%Quadratic roots, medium range
5.9b11.6%Cubic critical, medium range

rewrite4.0s

Algorithm
128×rewrite-expression-head
Calls

407 calls:

Slowest
402.0ms
(/ (+ x 1) (- 1 x))
84.0ms
(* (+ (* (exp x) (exp x)) (- (* (exp (- x)) (exp (- x))) (* (exp x) (exp (- x))))) (log (exp (/ 2 (+ (pow (exp x) 3) (pow (exp (- x)) 3))))))
60.0ms
(* (- (/ (* m (- 1 m)) v) 1) (- 1 m))
55.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
54.0ms
(/ (* (- (/ (* m (- 1 m)) v) 1) (- (pow 1 3) (pow m 3))) (+ (+ (* m m) m) 1))
Rules
1123×add-sqr-sqrt
1108×*-un-lft-identity
950×add-cube-cbrt
943×associate-*l/
818×flip--
817×flip3--
771×pow1
698×add-exp-log
679×frac-times
665×add-cbrt-cube
610×sqrt-div
514×add-log-exp
453×times-frac
439×associate-*r/
434×frac-add
406×insert-posit16
307×associate-*r*
263×associate-*l*
229×associate-/r* cbrt-prod
215×flip-+
214×flip3-+
209×div-inv
170×sqrt-prod
153×associate-/r/
131×associate-/l*
119×log-div
117×pow-prod-down
111×exp-diff *-commutative
107×log-prod
99×frac-2neg clear-num
97×prod-exp
95×cbrt-unprod
92×tan-quot
91×sub-neg
84×pow-prod-up
78×difference-of-squares
77×cbrt-div
72×exp-prod
70×associate-/l/
64×log-pow
62×exp-neg
59×div-exp
55×cbrt-undiv pow-plus
51×distribute-rgt-in distribute-lft-in
49×pow2
45×pow1/2
44×distribute-lft-out
41×distribute-lft-out--
40×neg-sub0
39×pow1/3
35×frac-sub
34×diff-log
33×cube-prod +-commutative unpow-prod-down
32×rem-sqrt-square
28×cos-mult
23×un-div-inv
22×div-sub
19×sum-log exp-sum
17×rem-log-exp
16×sub-div
15×difference-of-sqr-1
12×rec-exp
11×tanh-def
10×cos-diff associate--l+
associate-+r+ cos-sum acos-asin
pow-flip inv-pow
sin-sum pow-pow rem-exp-log
distribute-rgt-out-- sin-mult cube-div
associate--l- distribute-frac-neg associate-+l- distribute-rgt-out
rem-cube-cbrt pow-exp pow3 sqrt-unprod acos-neg cube-mult
quot-tan unpow3 pow-to-exp difference-cubes rem-square-sqrt distribute-rgt1-in
associate-+l+ remove-posit16 rgt-mult-inverse sin-cos-mult sub0-neg neg-mul-1 sin-PI/3 exp-to-pow tanh-undef asin-acos rem-cbrt-cube sin-diff

localize3.3s

bsearch1.7s

end1.0ms