Details

sample7.3m (46.1%)

Algorithm
78×intervals
Results
3.0m25814×body10240exit
1.7m44166×body1280valid
41.3s30015×body640valid
27.7s202470×body80valid
20.5s152484×body80nan
18.5s27642×body320valid
13.1s36258×body160valid
11.2s162500×pre80true
3.6s3133×body2560valid
1.3s4071×pre10240exit
1.3s7984×body160nan
268.0ms246×body5120valid

prune3.9m (24.9%)

simplify3.0m (19.3%)

series55.4s (5.9%)

Calls

456 calls:

1.7s
(- (* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b))) (* b (* b b)))
1.4s
(* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b)))
1.1s
(- (pow (cos delta) 3) (pow (log1p (expm1 (* (sin (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))) (sin phi1)))) 3))
937.0ms
(- (pow (cos delta) 3) (pow (log1p (expm1 (* (sin (asin (fma (sin phi1) (cos delta) (* (cos theta) (* (cos phi1) (sin delta)))))) (sin phi1)))) 3))
870.0ms
(cbrt (fma (pow x 5) 2/15 x))

regimes19.0s (2.0%)

Accuracy

Total 48.1b remaining (25.5%)

Threshold costs 4.4b (2.3%)

7.1b47%Quadratic roots, narrow range
6.2b41.6%Quotient of products
5.2b19.4%Quadratic roots, medium range
5.0b21.9%Cubic critical, medium range
4.3b84.4%Quadratic roots, full range

rewrite10.4s (1.1%)

Algorithm
146×rewrite-expression-head
Calls

456 calls:

387.0ms
(* (/ -27/8 (* 3 (* 9 (* a a)))) (/ (* (/ (* a c) b) (* (/ (* a c) b) (/ (* a c) b))) a))
321.0ms
(cbrt (* (/ -27/8 (* 3 (* 9 (* a a)))) (/ (* (/ (* a c) b) (* (/ (* a c) b) (/ (* a c) b))) a)))
293.0ms
(/ (+ (* (sqrt (fma (* a c) -3 (* b b))) (* (* a c) -3)) (- (* (sqrt (fma (* a c) -3 (* b b))) (* b b)) (* b (* b b)))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (* b b) (fma (* a c) -3 (* b b)))))
255.0ms
(/ (/ (+ (* (sqrt (fma (* a c) -3 (* b b))) (* (* a c) -3)) (- (* (sqrt (fma (* a c) -3 (* b b))) (* b b)) (* b (* b b)))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (* b b) (fma (* a c) -3 (* b b))))) (* 3 a))
193.0ms
(* (* (/ (/ -2 (/ b (* c a))) a) (/ (/ -2 (/ b (* c a))) a)) (/ (/ -2 (/ b (* c a))) a))
Rules
7734×*-un-lft-identity
7298×add-sqr-sqrt
6701×times-frac
5948×add-exp-log
4895×add-cube-cbrt
4311×add-cbrt-cube
2432×div-exp
2384×prod-exp
2278×prod-diff
1653×cbrt-undiv
1511×cbrt-unprod
1465×sqrt-prod
1154×pow1
929×difference-of-squares
835×associate-*r*
756×associate-*l*
724×distribute-lft-out
695×pow-exp
636×add-log-exp
497×distribute-lft-out--
493×cbrt-prod
461×swap-sqr
460×expm1-log1p-u
458×log1p-expm1-u
456×insert-posit16
450×div-inv
441×associate-/r/
394×associate-/l*
347×pow-to-exp
335×associate-/r*
258×fma-neg
253×difference-of-sqr-1
239×flip--
238×flip3--
233×log-prod
220×unpow-prod-down
219×1-exp rec-exp
211×flip-+
210×flip3-+
208×unswap-sqr
205×pow-prod-down
180×cube-prod
170×sqrt-div
140×pow-prod-up
134×frac-times
131×fma-def
116×distribute-rgt-in associate-*r/ distribute-lft-in
112×sqrt-pow1
106×*-commutative
99×associate-*l/
91×frac-2neg clear-num
88×pow1/2
86×associate-/l/
76×pow-flip
75×sub-neg
72×sqr-pow
69×inv-pow
61×diff-log
58×cos-sum
55×pow-sqr
54×pow-plus log-pow fma-udef
52×unpow3 cube-mult
46×div-sub
44×pow1/3
38×rem-sqrt-square
37×sum-log
30×tan-quot
29×pow2 rem-log-exp
28×associate-+r+ log-div
24×associate-+l+ cube-unmult
22×sin-sum distribute-rgt-neg-in exp-prod
21×cbrt-div +-commutative
18×frac-sub sin-diff
15×sin-cos-mult associate--l+
14×frac-add
13×difference-cubes sin-mult log1p-udef
12×pow-unpow distribute-lft-neg-in distribute-rgt-out
11×sqrt-undiv
10×acos-asin
9×associate--r+ cos-diff
8×pow3 pow-pow associate-+l-
7×neg-sub0 un-div-inv expm1-def
6×log1p-expm1 sqrt-unprod distribute-neg-frac asin-acos log1p-def pow-div
5×associate-+r-
4×cos-mult distribute-rgt1-in distribute-frac-neg neg-log neg-mul-1 exp-to-pow rem-exp-log acos-neg
3×expm1-log1p expm1-udef exp-diff log-rec hypot-udef
2×rem-cube-cbrt exp-sum rem-square-sqrt rem-cbrt-cube associate--r- distribute-lft-neg-out
1×remove-posit16 associate--l- unsub-neg tanh-undef tanh-def distribute-rgt-out-- hypot-def

localize6.1s (0.6%)

bsearch1.2s (0.1%)

end1.0ms (0.0%)