Details

sample13.1m (53.7%)

Algorithm
78×intervals
Results
9.7m57980×body10240exit
1.3m43377×body1280valid
28.6s30820×body640valid
19.2s205314×body80valid
13.8s152373×body80nan
12.7s27645×body320valid
9.4s197717×pre80true
9.4s35875×body160valid
2.0s3021×body2560valid
941.0ms8049×body160nan
710.0ms4025×pre10240exit
269.0ms261×body5120valid
1.0ms1×body640nan
1.0ms1×body320nan

simplify6.1m (25.2%)

prune2.5m (10.5%)

series1.7m (7.0%)

Calls

442 calls:

23.7s
(* (hypot (* (- lambda1 lambda2) (- (* (cos (* phi1 0.5)) (cos (* phi2 0.5))) (* (sin (* phi1 0.5)) (sin (* phi2 0.5))))) (- phi1 phi2)) R)
22.6s
(* (hypot (* (- lambda1 lambda2) (fma (cos (* phi1 0.5)) (cos (* phi2 0.5)) (- (* (sin (* phi1 0.5)) (sin (* phi2 0.5)))))) (- phi1 phi2)) R)
1.0s
(/ (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))) (+ (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))))
754.0ms
(* (hypot (* (- lambda1 lambda2) (cos (* 0.5 (+ phi1 phi2)))) (- phi1 phi2)) R)
723.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)

regimes22.6s (1.6%)

Accuracy

Total 52.2b remaining (30.4%)

Threshold costs 6.2b (3.6%)

7.8b44.1%Quadratic roots, narrow range
7.6b44.6%Cubic critical, narrow range
6.4b8.2%Quadratic roots, medium range
5.3b42.2%Quotient of products
4.9b28.9%Cubic critical, medium range

rewrite17.9s (1.2%)

Algorithm
143×rewrite-expression-head
Calls

442 calls:

684.0ms
(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)))))
537.0ms
(* (* (+ (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)))
430.0ms
(* (- (/ m (/ v (- 1.0 m))) 1.0) (- 1.0 m))
429.0ms
(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
384.0ms
(* (/ (/ (/ a1 b1) (cbrt b2)) (cbrt b2)) (/ a2 (cbrt b2)))
Rules
26856×times-frac
18638×*-un-lft-identity
17151×add-sqr-sqrt
12674×add-cube-cbrt
5052×prod-diff
3420×sqrt-prod
2474×add-exp-log
1867×difference-of-squares
1765×distribute-lft-out--
1730×distribute-rgt-neg-in
1589×add-cbrt-cube
1554×cbrt-prod
1257×distribute-lft-neg-in
1222×distribute-lft-out
1199×neg-mul-1
1101×pow1 associate-*l*
1091×div-inv
1079×associate-/r/
798×div-exp
770×prod-exp
716×distribute-rgt-in distribute-lft-in
694×associate-*r*
634×add-log-exp
604×associate-/r*
591×associate-/l*
525×flip--
524×flip3--
448×fma-neg
445×log1p-expm1-u
442×expm1-log1p-u
431×cbrt-undiv
392×cbrt-unprod
349×log-prod
311×flip-+
310×flip3-+
265×pow-exp
227×unswap-sqr
213×pow-prod-down
202×frac-times
185×pow-to-exp
180×fma-def
175×swap-sqr
146×associate-*l/
130×cbrt-div
125×associate-*r/
105×*-commutative
102×frac-2neg clear-num
90×sqrt-div pow-prod-up
89×sub-neg
75×frac-sub
69×associate-/l/
67×diff-log
62×cos-sum
56×pow-sqr
55×pow-plus
54×log-pow
53×div-sub
52×pow1/3
48×unpow-prod-down
46×sqrt-pow1 pow1/2
39×rem-log-exp
37×pow2 sin-mult
34×fma-udef
33×log-div
28×sum-log 1-exp tan-quot
27×rem-sqrt-square
23×rec-exp
22×sin-sum exp-prod
20×cos-mult +-commutative
18×sin-diff
17×associate--l+
13×distribute-frac-neg
12×neg-sub0 frac-add
11×sin-cos-mult
10×exp-sum sub-div associate-+l-
9×acos-asin cos-diff
6×sqrt-undiv pow-unpow pow3 sqr-pow
5×expm1-udef distribute-lft-neg-out exp-diff neg-log associate--r+ exp-to-pow rem-exp-log acos-neg
4×pow-flip sqrt-unprod
3×expm1-log1p hypot-udef asin-acos rem-square-sqrt rem-cbrt-cube
2×associate-+l+ associate--l- log1p-udef pow-pow inv-pow
1×associate-+r- unsub-neg distribute-rgt-out-- cube-unmult distribute-rgt-neg-out log1p-expm1 tanh-def un-div-inv tanh-undef sqr-cos distribute-rgt-out

localize6.9s (0.5%)

bsearch4.7s (0.3%)

end1.0ms (0.0%)