Details

simplify8.3m (69.7%)

sample1.2m (10.4%)

Algorithm
73×intervals
Results
28.0s294377×body80valid
10.1s13724×body1280valid
5.4s16808×body160valid
3.9s9384×body640valid
3.6s3775×body2560valid
3.0s2183×body10240exit
2.6s100609×pre80true
1.8s7009×body320valid
1.3s19545×body80nan
138.0ms223×body5120valid
6.0ms100×pre80false

prune1.2m (9.7%)

series38.4s (5.4%)

Calls

284 calls:

2.0s
(+ (pow y 6.0) (fma (pow y 4.0) 121.0 2.0))
1.2s
(+ (* (* (* 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)) (* (* (* (cbrt (- (* 4.0 (/ (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0))) 6.0)) (cbrt (- (* 4.0 (/ (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0))) 6.0))) (* x1 x1)) (cbrt (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0))))
804.0ms
(expm1 (log1p (* (pow y 6.0) 333.75)))
636.0ms
(* (pow y 6.0) 333.75)
630.0ms
(- (* 9.0 (pow x 4.0)) (pow y 4.0))

rewrite26.3s (3.7%)

Algorithm
104×rewrite-expression-head
Calls

284 calls:

1.7s
(+ (+ (+ (* 333.75 (pow 33096.0 6.0)) (* (* 77617.0 77617.0) (+ (+ (+ (* (* 11.0 (* 77617.0 77617.0)) (* 33096.0 33096.0)) (- (pow 33096.0 6.0))) (* -121.0 (pow 33096.0 4.0))) -2.0))) (* 5.5 (pow 33096.0 8.0))) (/ 77617.0 (* 2.0 33096.0)))
1.6s
(+ (+ (* 333.75 (pow 33096.0 6.0)) (* (* 77617.0 77617.0) (+ (+ (+ (* (* 11.0 (* 77617.0 77617.0)) (* 33096.0 33096.0)) (- (pow 33096.0 6.0))) (* -121.0 (pow 33096.0 4.0))) -2.0))) (* 5.5 (pow 33096.0 8.0)))
1.2s
(+ (* (* (* 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)) (* (* (* (cbrt (- (* 4.0 (/ (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0))) 6.0)) (cbrt (- (* 4.0 (/ (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0))) 6.0))) (* x1 x1)) (cbrt (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0))))
1.1s
(+ (* (* (* 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)))
977.0ms
(- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)
Rules
9982×times-frac
9794×*-un-lft-identity
8607×add-sqr-sqrt
7291×add-cube-cbrt
4996×prod-diff
1303×add-exp-log
1082×distribute-rgt-in distribute-lft-in
1075×add-cbrt-cube
912×distribute-lft-out
798×div-inv
778×associate-*r*
661×pow1
607×add-log-exp
493×unpow-prod-down
456×associate-*l*
449×difference-of-squares
391×associate-+l+
387×prod-exp
372×associate-*l/
371×frac-times
358×distribute-lft-out--
350×flip3-- flip--
329×cube-prod
325×cbrt-prod
315×cbrt-div
314×associate-/l*
313×associate-*r/
303×div-exp
291×cbrt-unprod
284×log1p-expm1-u expm1-log1p-u
278×sqrt-prod
271×associate-/r/
269×fma-neg
255×associate-/r*
231×flip-+ flip3-+
227×cbrt-undiv
162×unswap-sqr
159×pow-prod-down
148×frac-add
137×sum-log
125×fma-def
123×sqr-pow
112×distribute-rgt-neg-in
107×distribute-lft-neg-in frac-sub
80×exp-neg
79×swap-sqr
75×sub-neg
68×*-commutative
67×neg-sub0
60×exp-diff
58×clear-num frac-2neg
56×diff-log
55×associate-/l/
50×sqrt-pow1
45×fma-udef
40×log-prod
37×cube-mult +-commutative
36×unpow2 unpow3
35×neg-mul-1
34×sqrt-div
31×pow-exp
30×pow1/2 rec-exp 1-exp
28×pow-prod-up
25×pow-to-exp
24×un-div-inv
23×associate-+r+
20×pow-sqr
19×log-pow div-sub
16×pow1/3
14×pow-plus
12×pow-unpow pow2
10×rem-sqrt-square log-div
rem-cube-cbrt associate--l+
cube-div associate--l- distribute-frac-neg
distribute-lft-neg-out associate--r+
inv-pow hypot-udef pow-flip sum-cubes rem-cbrt-cube
neg-log pow-pow
unsub-neg rem-log-exp
associate-+r- sqrt-unprod sub-div rem-square-sqrt associate--r- distribute-rgt-out-- distribute-rgt-neg-out expm1-udef distribute-neg-frac
distribute-rgt1-in expm1-log1p distribute-rgt-out associate-+l-

regimes4.4s (0.6%)

Accuracy

Total 41.5b remaining (17.1%)

Threshold costs 3.7b (1.5%)

10.6b52.2%Compound Interest
10.6b27.7%Complex division, real part
7.0b34.7%Complex division, imag part
4.2b85.3%The quadratic formula (r1)
4.1b84.9%The quadratic formula (r2)

localize2.5s (0.4%)

bsearch1.3s (0.2%)

end1.0ms (0.0%)