Details

sample28.8m (73.3%)

Algorithm
76×intervals
Results
25.4m170157×body10240exit
1.1m36661×body1280valid
27.6s201301×body80valid
27.2s26066×body640valid
20.9s153117×body80nan
15.4s25718×body320valid
12.1s35483×body160valid
11.9s194778×pre80true
3.2s3149×body2560valid
1.8s7952×body160nan
899.0ms4060×pre10240exit
729.0ms244×body5120valid

simplify5.3m (13.6%)

prune3.8m (9.5%)

series52.5s (2.2%)

Calls

428 calls:

1.6s
(* (hypot (* (- (* (cos (* 1/2 phi1)) (cos (* 1/2 phi2))) (* (sin (* 1/2 phi1)) (sin (* 1/2 phi2)))) (- lambda1 lambda2)) (- phi1 phi2)) R)
1.5s
(* (sqrt (fma (* -3 c) a (* b b))) (fma (* -3 c) a (* b b)))
1.3s
(- (* (sqrt (fma (* -3 c) a (* b b))) (fma (* -3 c) a (* b b))) (* (* b b) b))
1.2s
(- (* (fma a (* -3 c) (* b b)) (sqrt (fma a (* -3 c) (* b b)))) (* b (* b b)))
803.0ms
(/ (/ (+ (* (sqrt (fma (* -3 c) a (* b b))) (* (* -3 c) a)) (/ (* (- (* (fma a (* -3 c) (* b b)) (sqrt (fma a (* -3 c) (* b b)))) (* b (* b b))) (* b b)) (+ (* (sqrt (fma (* -3 c) a (* b b))) (sqrt (fma (* -3 c) a (* b b)))) (+ (* b b) (* (sqrt (fma (* -3 c) a (* b b))) b))))) (+ (fma (sqrt (fma (* -3 c) a (* b b))) b (* b b)) (fma (* -3 c) a (* b b)))) (* 3 a))

regimes14.8s (0.6%)

Accuracy

Total 46.5b remaining (23.5%)

Threshold costs 3.4b (1.7%)

7.1b49.1%Quadratic roots, narrow range
6.1b13.3%Quadratic roots, medium range
4.9b53.9%Quotient of products
4.8b82.7%Quadratic roots, full range
4.8b31.8%Cubic critical, medium range

rewrite11.9s (0.5%)

Algorithm
133×rewrite-expression-head
Calls

428 calls:

364.0ms
(/ (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (sqrt (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))))))
350.0ms
(/ (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (sqrt (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))))))
344.0ms
(/ (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x))) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))
335.0ms
(/ (/ (+ (* (sqrt (fma (* -3 c) a (* b b))) (* (* -3 c) a)) (/ (* (- (* (fma a (* -3 c) (* b b)) (sqrt (fma a (* -3 c) (* b b)))) (* b (* b b))) (* b b)) (+ (* (sqrt (fma (* -3 c) a (* b b))) (sqrt (fma (* -3 c) a (* b b)))) (+ (* b b) (* (sqrt (fma (* -3 c) a (* b b))) b))))) (+ (fma (sqrt (fma (* -3 c) a (* b b))) b (* b b)) (fma (* -3 c) a (* b b)))) (* 3 a))
316.0ms
(/ (+ (* (sqrt (fma (* -3 c) a (* b b))) (* (* -3 c) a)) (/ (* (- (* (fma a (* -3 c) (* b b)) (sqrt (fma a (* -3 c) (* b b)))) (* b (* b b))) (* b b)) (+ (* (sqrt (fma (* -3 c) a (* b b))) (sqrt (fma (* -3 c) a (* b b)))) (+ (* b b) (* (sqrt (fma (* -3 c) a (* b b))) b))))) (+ (fma (sqrt (fma (* -3 c) a (* b b))) b (* b b)) (fma (* -3 c) a (* b b))))
Rules
11228×times-frac
10604×*-un-lft-identity
9239×add-sqr-sqrt
6971×add-cube-cbrt
2947×prod-diff
2808×add-exp-log
1486×add-cbrt-cube
1338×cbrt-prod
1105×associate-*l*
1081×distribute-lft-out
1031×prod-exp
1011×pow1
997×div-exp
925×difference-of-squares
867×sqrt-prod
713×div-inv
695×pow-exp
628×add-log-exp
576×associate-/l*
540×associate-*r*
537×associate-/r/
536×associate-/r*
529×distribute-lft-out--
433×expm1-log1p-u
428×log1p-expm1-u insert-posit16
359×cbrt-undiv
347×pow-to-exp
339×cbrt-unprod
309×fma-neg
279×difference-of-sqr-1
272×swap-sqr
262×flip-+
261×flip3-+
193×flip--
192×flip3--
185×log-prod
176×unswap-sqr
172×pow-prod-down
162×associate--l+
144×1-exp rec-exp
128×distribute-lft-in distribute-rgt-in
125×fma-def
114×frac-2neg clear-num
103×unpow-prod-down
94×*-commutative
78×associate-*l/
75×associate-*r/
73×associate-/l/
72×frac-times sub-neg
69×fma-udef diff-log
67×sqrt-pow1
66×pow1/2
61×pow-prod-up log-pow
53×frac-sub
48×sqrt-div
44×cbrt-div
42×sum-log
39×rem-sqrt-square
38×pow-sqr
36×pow-plus tan-quot
34×pow1/3
33×sin-sum exp-prod
32×log-div
31×cos-sum
28×pow-flip rem-log-exp
27×pow2 sqr-pow
26×pow3
24×distribute-rgt-neg-in inv-pow
22×exp-sum
21×div-sub
20×+-commutative
19×difference-cubes
17×cube-unmult
16×frac-add
15×distribute-lft-neg-in
11×associate--r+
acos-asin
distribute-rgt-out-- sin-mult
neg-sub0 cos-mult associate-+l-
pow-div pow-unpow pow-pow distribute-rgt-out log1p-udef
log1p-expm1 log-rec neg-log neg-mul-1
exp-diff sub-div rem-exp-log log1p-def associate--r-
associate--l- distribute-frac-neg acos-neg hypot-def
associate-+l+ distribute-lft-neg-out distribute-rgt1-in sqrt-unprod rem-square-sqrt cos-diff expm1-def
expm1-log1p expm1-udef associate-+r+ tanh-def un-div-inv tanh-undef hypot-udef asin-acos remove-posit16 sin-diff

localize5.1s (0.2%)

bsearch1.5s (0.1%)

end1.0ms (0.0%)