Details

series10.6m (56.0%)

Calls

275 calls:

2.5s
(+ (pow y 6.0) (fma (pow y 4.0) 121.0 2.0))
1.8s
(fma (sqrt (pow x 4.0)) (sqrt (pow x 4.0)) (- (pow y 4.0)))
1.7s
(+ (* (* (* 2.0 x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (fma (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (pow (* x1 x1) 3) (pow 1.0 3))) (+ (* (* x1 x1) (* x1 x1)) (- (* 1.0 1.0) (* (* x1 x1) 1.0))) (- 3.0))) (* (* (* (* x1 x1) (cbrt (- (* (/ (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0)) 4.0) 6.0))) (cbrt (- (* (/ (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0)) 4.0) 6.0))) (cbrt (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0))))
1.0s
(expm1 (log1p (* (pow y 6.0) 333.75)))
926.0ms
(+ (* (* (* 2.0 x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (fma (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (pow (* x1 x1) 3) (pow 1.0 3))) (+ (* (* x1 x1) (* x1 x1)) (- (* 1.0 1.0) (* (* x1 x1) 1.0))) (- 3.0))) (* (* x1 x1) (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0)))

simplify4.5m (23.7%)

prune1.7m (9.0%)

sample1.3m (6.9%)

Algorithm
70×intervals
Results
32.2s276316×body80valid
8.6s12008×body1280valid
5.1s3890×body2560valid
4.3s8169×body640valid
3.8s100675×pre80true
2.3s6237×body320valid
1.8s19623×body80nan
1.2s8289×body160valid
760.0ms233×body5120valid
593.0ms267×body10240exit
5.0ms100×pre80false

rewrite34.0s (3.0%)

Algorithm
100×rewrite-expression-head
Calls

276 calls:

1.5s
(+ 2.0 (/ (- (/ (pow (/ (cbrt 2.0) (cbrt t)) 3) (cbrt (+ 1.0 (/ 1.0 t))))) (* (cbrt (+ 1.0 (/ 1.0 t))) (cbrt (+ 1.0 (/ 1.0 t))))))
1.5s
(+ (* (* (* 2.0 x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)) (* (* x1 x1) (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0)))
1.2s
(- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)
1.1s
(+ (/ (exp (* (- eps 1.0) x)) eps) (- (+ (exp (- (* x (+ eps 1.0)))) (exp (* x (- eps 1.0)))) (/ (exp (- (* x (+ eps 1.0)))) eps)))
1.0s
(+ (/ (exp (* (- eps 1.0) x)) eps) (- (+ (exp (- (* x (+ eps 1.0)))) (exp (* x (- eps 1.0)))) (/ (exp (- (* x (+ eps 1.0)))) eps)))
Rules
10892×times-frac
9484×*-un-lft-identity
8728×add-sqr-sqrt
7442×add-cube-cbrt
4475×prod-diff
1442×add-exp-log
1145×add-cbrt-cube
764×distribute-rgt-in distribute-lft-in
755×distribute-lft-out
741×associate-*r*
700×div-inv
669×associate-+l+
647×associate-*l*
598×add-log-exp
585×pow1
570×sqrt-prod
532×unpow-prod-down
412×prod-exp
402×div-exp
392×difference-of-squares
334×associate-/r*
326×cube-prod
322×associate-/l*
309×cbrt-unprod
289×distribute-lft-out--
279×cbrt-undiv
278×log1p-expm1-u
276×expm1-log1p-u
268×associate-+r+
254×associate-*r/
229×frac-times
208×flip-- flip3--
206×distribute-rgt-neg-in
196×sqr-pow
188×flip-+ flip3-+
187×associate-/r/
179×distribute-lft-neg-in fma-neg
171×unswap-sqr
169×fma-def
165×associate-*l/
139×sum-log
135×cbrt-prod
134×pow-prod-down
125×exp-sum
108×frac-sub
93×unpow3 cube-mult
88×associate-/l/
82×exp-neg
80×distribute-neg-in
74×sub-neg
73×neg-sub0
72×cbrt-div
65×frac-add
64×*-commutative
62×exp-diff
61×clear-num frac-2neg
58×neg-mul-1
53×diff-log log-prod
49×fma-udef
43×1-exp
38×sqrt-div
34×rec-exp
33×+-commutative pow-exp
30×pow-to-exp
26×log-pow swap-sqr
25×un-div-inv
24×unpow2 exp-prod
20×div-sub
19×rem-sqrt-square
16×sqrt-pow1 log-div
15×pow1/2 pow-prod-up
13×pow-plus
12×pow-unpow
11×distribute-lft-neg-out pow-sqr distribute-frac-neg sum-cubes
rem-log-exp
cube-div pow2 pow1/3 neg-log associate--l+
associate--l-
rem-exp-log associate-+l- pow-pow
associate-+r- expm1-udef
rem-cube-cbrt expm1-log1p
inv-pow unsub-neg pow-flip hypot-def rem-cbrt-cube distribute-rgt-neg-out exp-to-pow associate--r+
log1p-udef pow3 log1p-expm1

regimes10.2s (0.9%)

Accuracy

Total 45.2b remaining (24%)

Threshold costs 2.1b (1.1%)

12.2b47.8%Compound Interest
10.4b29.4%Complex division, imag part
9.4b15.9%Complex division, real part
4.6b83.2%The quadratic formula (r1)
4.4b84.4%The quadratic formula (r2)

localize4.7s (0.4%)

bsearch2.0s (0.2%)

end1.0ms (0.0%)