Details

sample10.3m

Algorithm
72×intervals
Results
7.4m81004×body10240exit
51.6s32894×body1280valid
26.7s198293×body80valid
23.6s24765×body640valid
19.6s151777×body80nan
13.6s25141×body320valid
11.2s34918×body160valid
9.1s154147×pre80true
2.4s2982×body2560valid
1.8s7801×body160nan
1.0s4132×pre10240exit
267.0ms235×body5120valid

prune3.8m

simplify1.7m

bsearch46.1s

series45.4s

Calls

415 calls:

Slowest
668.0ms
(hypot (* (cos (* (+ phi1 phi2) 1/2)) (- lambda1 lambda2)) (- phi1 phi2))
650.0ms
(cbrt (/ 1/2 a))
642.0ms
(/ (fma (sqrt (sqrt (fma c (* -3 a) (* b b)))) (sqrt (sqrt (fma c (* -3 a) (* b b)))) (- b)) (* 3 a))
605.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
580.0ms
(/ (fma (sqrt (sqrt (fma c (* -3 a) (* b b)))) (sqrt (sqrt (fma c (* -3 a) (* b b)))) (- b)) (* 3 a))

regimes14.5s

Accuracy

Total 47.4b remaining (21.2%)

Threshold costs 3.6b (1.6%)

7.9b42.6%Quadratic roots, narrow range
6.8b23.1%Cubic critical, narrow range
4.9b82.4%Quadratic roots, full range
4.7b28.8%Quadratic roots, medium range
4.6b78%Cubic critical

rewrite10.3s

Algorithm
130×rewrite-expression-head
Calls

415 calls:

Slowest
401.0ms
(* (- (- (/ m v) (/ m (/ v m))) 1) (- 1 m))
299.0ms
(log (exp (- (/ (/ 2 (sqrt (+ 1 (exp (* -2 x))))) (sqrt (+ 1 (exp (* -2 x))))) 1)))
282.0ms
(/ (- (- (- x 1) x) 1) (* (+ x 1) (- x 1)))
280.0ms
(/ (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x))) (fma (* y x) (fma x y (log1p (exp x))) (* (log1p (exp x)) (log1p (exp x)))))
251.0ms
(/ (/ (- (/ (* 27/8 (* (* c a) (* c a))) b) (* (* 9/2 a) (* c b))) (+ (* b (+ (sqrt (fma b b (* (* a -3) c))) b)) (fma b b (* (* a -3) c)))) (* 3 a))
Rules
15349×times-frac
12193×*-un-lft-identity
11111×add-sqr-sqrt
8901×add-cube-cbrt
3918×prod-diff
2659×add-exp-log
2426×sqrt-prod
1332×add-cbrt-cube
1089×pow1
1038×distribute-lft-out
980×div-exp
964×prod-exp
924×difference-of-squares
865×div-inv
849×log-prod
693×pow-exp
674×associate-/r*
649×exp-sum
609×associate-/r/
597×add-log-exp
541×associate-*r*
520×associate-/l*
469×distribute-lft-out-- fma-neg
418×expm1-log1p-u
416×log1p-expm1-u
415×insert-posit16
401×associate-*l*
345×pow-to-exp
309×cbrt-undiv
285×flip-+
284×flip3-+
267×cbrt-unprod
197×difference-of-sqr-1
194×pow-prod-down
185×flip--
184×flip3--
176×cbrt-prod
170×sqrt-div
154×distribute-rgt-in distribute-lft-in
151×1-exp
146×rec-exp unswap-sqr
121×fma-def
107×frac-2neg clear-num pow-prod-up
106×swap-sqr
105×log-pow
87×*-commutative associate-*r/
81×exp-prod
75×frac-times
73×sub-neg
68×associate-*l/
67×pow-plus fma-udef
63×diff-log
60×tan-quot
59×associate-/l/
58×pow-sqr
46×sqrt-pow1
44×pow1/2
43×pow2
41×div-sub
40×unpow-prod-down
38×sum-log
33×sin-sum cbrt-div rem-log-exp
30×pow-flip pow1/3 cos-sum rem-sqrt-square
27×pow3
24×associate-+r+
23×frac-sub
22×log-div
20×inv-pow
19×frac-add
18×+-commutative
16×associate--l+ distribute-rgt-neg-in
15×difference-cubes
14×cube-unmult
10×acos-asin distribute-lft-neg-in
7×exp-diff log-rec expm1-def
6×pow-unpow neg-mul-1 pow-pow log1p-udef
5×distribute-frac-neg acos-neg sin-mult distribute-rgt-out
4×neg-sub0 log1p-expm1 sqr-pow associate--r+ hypot-udef associate-+l- hypot-def
3×associate-+l+ distribute-neg-frac asin-acos rem-exp-log rem-cbrt-cube
2×expm1-log1p quot-tan expm1-udef associate-+r- neg-log sqrt-unprod cos-diff associate--r-
1×remove-posit16 associate--l- cos-mult distribute-rgt1-in distribute-rgt-out-- tanh-undef tanh-def exp-to-pow rem-square-sqrt sin-diff unsub-neg

localize4.5s

end2.0ms