Details

simplify10.9m (42.9%)

sample9.3m (36.3%)

Algorithm
78×intervals
Results
4.8m26288×body10240exit
1.8m43571×body1280valid
41.9s30540×body640valid
26.4s202536×body80valid
19.8s27686×body320valid
19.3s150771×body80nan
13.0s36538×body160valid
10.3s163277×pre80true
3.0s3037×body2560valid
1.1s8004×body160nan
883.0ms4104×pre10240exit
178.0ms202×body5120valid
1.0msbody320nan

prune2.5m (9.9%)

series1.5m (5.9%)

Calls

455 calls:

2.7s
(expm1 (log1p (log1p (fma (fma 1/4 (- a b) 1) (sqrt E) -1))))
2.4s
(fma (* (- (* (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* (* 1.0 1.0) 1.0)) (- (* (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* (* 1.0 1.0) 1.0))) (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (- (* (* (log1p (expm1 (- (* (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* (* 1.0 1.0) 1.0)))) (- (* (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* (* 1.0 1.0) 1.0))) (* 1.0 1.0))))
2.4s
(* (hypot (* (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) (- lambda1 lambda2)) (- phi1 phi2)) R)
2.3s
(log1p (log1p (fma (fma 1/4 (- a b) 1) (sqrt E) -1)))
1.2s
(fma (* (- (* (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* (* 1.0 1.0) 1.0)) (- (* (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* (* 1.0 1.0) 1.0))) (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (- (* (* (- (* (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* (* 1.0 1.0) 1.0)) (- (* (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* (* 1.0 1.0) 1.0))) (* 1.0 1.0))))

regimes33.2s (2.2%)

Accuracy

Total 58.7b remaining (35.4%)

Threshold costs 4.2b (2.5%)

8.5b38%Quadratic roots, narrow range
8.4b38.4%Cubic critical, narrow range
6.0b14.9%Cubic critical, medium range
5.9b15%Quadratic roots, medium range
5.4b81.6%Cubic critical

rewrite33.1s (2.2%)

Algorithm
145×rewrite-expression-head
Calls

455 calls:

983.0ms
(/ (* (* (* -1.5 -1.5) -1.5) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* a a) a) (* (* 3.0 3.0) 3.0)))
946.0ms
(cbrt (/ (* (* (* -1.5 -1.5) -1.5) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* a a) a) (* (* 3.0 3.0) 3.0))))
712.0ms
(* (- (/ (/ (* (* (- 1.0 m) (+ m 1.0)) m) (+ 1.0 m)) v) 1.0) (- 1.0 m))
711.0ms
(cbrt (* (* (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
614.0ms
(* (- (/ m (/ v (- 1.0 m))) 1.0) (- 1.0 m))
Rules
13054×add-exp-log
12356×add-cbrt-cube
8692×prod-exp
8325×cbrt-unprod
7080×*-un-lft-identity
6751×add-sqr-sqrt
6493×times-frac
4769×add-cube-cbrt
2482×div-exp
2403×prod-diff
2195×cbrt-undiv
1672×pow1
1411×sqrt-prod
769×difference-of-squares
634×add-log-exp
575×distribute-lft-out
543×flip--
542×flip3--
540×distribute-lft-out--
506×associate-*r*
482×cbrt-div
462×frac-times
460×expm1-log1p-u
458×log1p-expm1-u
446×associate-*l*
445×associate-/l*
435×pow-prod-down
393×associate-/r* div-inv
384×distribute-rgt-neg-in
380×distribute-lft-neg-in
356×associate-/r/
345×fma-neg
334×sqrt-div
274×cbrt-prod
265×pow-exp
264×pow-prod-up
262×distribute-rgt-in distribute-lft-in
246×associate-*l/ associate-*r/
187×flip-+
186×flip3-+
185×pow-to-exp
170×exp-prod
150×pow-sqr unswap-sqr
146×log-prod
141×pow-plus
116×fma-def
112×*-commutative
111×sub-neg
101×clear-num frac-2neg
92×pow1/3
91×associate-/l/ swap-sqr
87×neg-mul-1
84×tan-quot
80×log-pow
73×pow2
67×diff-log
60×cos-sum
52×div-sub
48×unpow-prod-down
46×fma-udef
44×sin-sum
39×log-div
38×pow1/2 sqrt-pow1
37×associate--l+
32×cos-mult
29×pow-flip
26×rem-sqrt-square
25×1-exp rec-exp
24×rem-log-exp
23×sum-log
21×+-commutative sin-mult frac-sub
18×sin-diff
17×pow3 cos-diff
16×exp-sum
15×neg-sub0
14×associate-+r+
12×associate--r+
10×exp-diff sin-cos-mult distribute-frac-neg acos-asin
log1p-udef inv-pow exp-neg log1p-expm1 frac-add expm1-log1p expm1-udef distribute-rgt-neg-out
pow-unpow difference-cubes sqr-pow
sin-neg
rem-exp-log acos-neg sub-div associate--l-
un-div-inv
pow-pow sqrt-unprod hypot-udef hypot-def associate--r- associate-+l- tanh-def
rem-square-sqrt distribute-rgt-out tanh-undef asin-acos rem-cbrt-cube

localize9.5s (0.6%)

bsearch1.6s (0.1%)

end5.0ms (0.0%)