Details

sample13.0m (59.1%)

Algorithm
78×intervals
Results
9.8m58323×body10240exit
1.2m43377×body1280valid
27.9s30820×body640valid
18.0s205335×body80valid
15.1s152373×body80nan
13.4s27645×body320valid
8.9s198081×pre80true
8.9s35875×body160valid
3.0s3021×body2560valid
698.0ms8049×body160nan
590.0ms4025×pre10240exit
266.0ms261×body5120valid
1.0msbody640nan
1.0msbody320nan

simplify5.1m (23.2%)

prune2.1m (9.5%)

series53.6s (4.1%)

Calls

438 calls:

1.2s
(/ (- (* (cos delta) (cos delta)) (* (log1p (expm1 (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))) (log1p (expm1 (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))))) (+ (cos delta) (log1p (expm1 (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))))))
912.0ms
(hypot (* (cos (/ (+ phi2 phi1) 2.0)) (- lambda1 lambda2)) (- phi1 phi2))
727.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
725.0ms
(* (hypot (* (cos (/ (+ phi2 phi1) 2.0)) (- lambda1 lambda2)) (- phi1 phi2)) R)
725.0ms
(- (* (cos delta) (cos delta)) (* (log1p (expm1 (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))) (log1p (expm1 (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))))))

regimes21.9s (1.7%)

Accuracy

Total 56.0b remaining (31.6%)

Threshold costs 5.2b (2.9%)

7.8b44.1%Quadratic roots, narrow range
7.6b44.8%Cubic critical, narrow range
6.4b8.2%Quadratic roots, medium range
5.2b47.5%Quotient of products
4.9b28.9%Cubic critical, medium range

rewrite21.6s (1.6%)

Algorithm
143×rewrite-expression-head
Calls

438 calls:

4.3s
(* (+ (/ (/ m (/ (/ v (+ 1.0 m)) (- 1.0 m))) (+ 1.0 m)) (- 1.0)) (- 1.0 m))
826.0ms
(cbrt (* (* (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
526.0ms
(- (- (/ 0.125 (* (* x x) x)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))
519.0ms
(* (* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))) (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
461.0ms
(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
Rules
15280×times-frac
14998×*-un-lft-identity
12170×add-sqr-sqrt
9038×add-cube-cbrt
4944×prod-diff
2508×add-exp-log
2061×sqrt-prod
1775×distribute-lft-out
1630×add-cbrt-cube
1320×difference-of-squares
1196×distribute-lft-out--
1020×associate-/r/
988×pow1
864×prod-exp
736×div-inv
726×div-exp
643×associate-/l*
623×add-log-exp
574×fma-neg
561×associate-/r*
550×associate-*r*
477×associate-*l*
443×log1p-expm1-u
440×expm1-log1p-u
434×cbrt-unprod
389×associate--l+
384×flip-+ flip--
383×flip3-- flip3-+
375×cbrt-undiv
368×distribute-rgt-in distribute-lft-in
360×cbrt-prod
345×log-prod
265×pow-exp
205×pow-prod-down
189×frac-times
185×pow-to-exp
170×fma-def
163×swap-sqr
162×unswap-sqr
132×distribute-rgt-neg-in
130×associate-*r/
111×associate-*l/
110×distribute-lft-neg-in
109×cbrt-div
106×exp-prod
105×*-commutative
104×unpow-prod-down
101×frac-2neg clear-num
92×sqrt-div sub-neg
70×diff-log
67×frac-sub pow-prod-up
58×cos-sum
55×associate-/l/
50×log-pow
46×pow-plus
45×pow-sqr
40×pow1/3
38×neg-mul-1 rem-log-exp
37×1-exp rec-exp
35×sqrt-pow1 pow1/2
32×div-sub
30×fma-udef tan-quot log-div
26×pow2 sqr-pow
24×sum-log rem-sqrt-square
22×sin-sum
18×sin-diff
17×neg-sub0
16×+-commutative
11×sin-cos-mult
10×sin-mult
associate-+l- cos-diff
sqrt-undiv pow3 un-div-inv
exp-neg
expm1-log1p expm1-udef exp-diff pow-unpow neg-log log1p-udef
pow-flip acos-asin
log1p-expm1 inv-pow
distribute-frac-neg sqrt-unprod associate--r+ exp-to-pow asin-acos rem-cbrt-cube
associate--l- cos-mult distribute-rgt-out-- pow-pow hypot-udef rem-exp-log rem-square-sqrt frac-add
associate-+r- unsub-neg distribute-rgt-neg-out tanh-undef tanh-def acos-neg sqr-cos

localize6.1s (0.5%)

bsearch5.0s (0.4%)

end1.0ms (0.0%)