Details

simplify12.7m (40.4%)

sample11.9m (37.6%)

Algorithm
78×intervals
Results
8.6m52640×body10240exit
1.3m44147×body1280valid
28.8s30669×body640valid
17.9s204615×body80valid
13.8s27484×body320valid
13.4s152194×body80nan
9.6s191160×pre80true
8.0s36041×body160valid
1.9s3042×body2560valid
1.2s7792×body160nan
562.0ms227×body5120valid
463.0ms4146×pre10240exit
2.0ms2×body640nan

prune3.7m (11.8%)

series1.6m (5.0%)

Calls

453 calls:

4.3s
(fma (- (pow (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))) 3)) (pow (sin phi1) 3) (* (pow (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))) 3) (pow (sin phi1) 3)))
3.0s
(/ (* (- (* 1.0 (sqrt 1.0)) (* (sqrt m) m)) (* (- (/ m (/ v (- 1.0 m))) 1.0) (+ (sqrt 1.0) (sqrt m)))) (+ (* (sqrt 1.0) (sqrt 1.0)) (+ (* (sqrt m) (sqrt m)) (* (sqrt 1.0) (sqrt m)))))
2.8s
(* (sqrt (hypot (* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi2 phi1) 2.0))))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))) R))
2.5s
(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) 3))
2.3s
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))) R)

regimes55.5s (2.9%)

Accuracy

Total 52.4b remaining (32.1%)

Threshold costs 6.2b (3.8%)

7.6b45.5%Quadratic roots, narrow range
6.4b11.8%Quadratic roots, medium range
6.2b12.4%Cubic critical, medium range
5.6b51.5%Quotient of products
5.4b60.9%Cubic critical, narrow range

rewrite27.0s (1.4%)

Algorithm
145×rewrite-expression-head
Calls

453 calls:

1.6s
(* (- (- (/ (* 1.0 m) v) (/ m (/ v m))) 1.0) m)
890.0ms
(/ (* (- (* 1.0 (sqrt 1.0)) (* (sqrt m) m)) (* (- (/ m (/ v (- 1.0 m))) 1.0) (+ (sqrt 1.0) (sqrt m)))) (+ (* (sqrt 1.0) (sqrt 1.0)) (+ (* (sqrt m) (sqrt m)) (* (sqrt 1.0) (sqrt m)))))
775.0ms
(- (- (/ 0.125 (* x (* x x))) (/ 0.5 x)) (/ 0.0625 (pow x 5)))
680.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)
526.0ms
(* (- (/ m (/ v (- 1.0 m))) 1.0) (fma 1.0 (sqrt 1.0) (* (sqrt m) m)))
Rules
8613×*-un-lft-identity
8408×times-frac
7702×add-sqr-sqrt
6068×add-cube-cbrt
3225×prod-diff
2753×add-exp-log
2039×add-cbrt-cube
1914×pow1
1700×sqrt-prod
929×prod-exp
839×div-exp
829×distribute-lft-out
766×associate-*r*
628×add-log-exp
584×div-inv
575×cbrt-unprod
572×difference-of-squares
508×cbrt-undiv associate-*l*
474×associate-/l*
456×expm1-log1p-u
455×log1p-expm1-u
454×associate-/r/
453×insert-posit16
442×distribute-lft-out--
440×associate-/r*
434×fma-neg
404×cbrt-prod
386×pow-prod-down
316×pow-prod-up
271×pow-exp
232×flip--
231×flip3--
219×flip-+
218×flip3-+
190×pow-to-exp
185×pow-sqr
182×unswap-sqr
181×associate-+r+
176×log-prod
173×sqrt-div
170×frac-times
167×pow-plus
165×swap-sqr
161×fma-def
158×unpow-prod-down
150×associate-*r/
147×associate-*l/
137×distribute-rgt-neg-in
124×tan-quot
120×distribute-lft-in distribute-rgt-in
114×pow2
113×*-commutative distribute-lft-neg-in
110×associate--l+
105×frac-2neg clear-num
99×log-pow
86×associate-/l/
74×sub-neg
64×cos-sum
60×sqrt-pow1 pow1/2
58×sqr-pow
55×diff-log
54×cube-prod
37×div-sub fma-udef
36×sum-log
33×pow1/3 log-div
32×rem-sqrt-square
31×neg-mul-1
30×1-exp rec-exp
27×rem-log-exp
26×cbrt-div cube-mult unpow3
25×+-commutative
22×sin-sum
21×pow-unpow
18×sin-diff
17×exp-prod
16×neg-sub0 frac-sub
15×cos-diff
14×associate-+l-
13×sin-mult
11×neg-log
10×pow-flip
9×cos-mult associate--r+ acos-asin
8×pow3 pow-pow
7×sin-cos-mult inv-pow
6×rem-cube-cbrt
5×expm1-log1p expm1-udef associate--l- exp-sum
3×associate-+l+ exp-diff log1p-expm1 log1p-udef distribute-frac-neg sqrt-unprod un-div-inv distribute-neg-frac acos-neg frac-add associate--r-
2×remove-posit16 cube-unmult hypot-udef asin-acos rem-exp-log rem-square-sqrt
1×difference-cubes tanh-undef associate-+r- tanh-def cube-div exp-to-pow hypot-def distribute-neg-in exp-lft-cube rem-cbrt-cube distribute-rgt-out

localize13.1s (0.7%)

bsearch1.6s (0.1%)

end1.0ms (0.0%)