Details

simplify5.9m (62.2%)

sample1.5m (16.0%)

Algorithm
67×intervals
Results
37.2s268138×body80valid
12.5s13793×body1280valid
7.0s16922×body160valid
6.5s9299×body640valid
5.1s3874×body2560valid
4.6s2254×body10240exit
4.1s75916×pre80true
2.7s19001×body80nan
2.5s6979×body320valid
506.0ms210×body5120valid
6.0ms100×pre80false

prune1.2m (12.7%)

series26.2s (4.6%)

Calls

272 calls:

632.0ms
(+ (* (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (fma (/ 1 (sqrt (+ (* x1 x1) 1))) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (sqrt (+ (* x1 x1) 1))) -3)) (+ (* (* 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (* x1 x1)) (* -6 (* x1 x1))))
581.0ms
(+ (* (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (- (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) 3)) (+ (* (* x1 x1) (fma 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) (- (* (sqrt 6) (sqrt 6))))) 0))
462.0ms
(sqrt (fma b b (* (* a -4) c)))
436.0ms
(sqrt (fma d d (* c c)))
419.0ms
(+ (* (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (- (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) 3)) (* (* x1 x1) (- (* 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) 6)))

rewrite17.1s (3.0%)

Algorithm
94×rewrite-expression-head
Calls

272 calls:

1.5s
(+ (* (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (- (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) 3)) (+ (* (* 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (* x1 x1)) (* -6 (* x1 x1))))
1.1s
(+ (+ (+ (* 333.75 (pow 33096 6)) (* (* 77617 77617) (+ (+ (+ (* (* 11 (* 77617 77617)) (* 33096 33096)) (- (pow 33096 6))) (* -121 (pow 33096 4))) -2))) (* 5.5 (pow 33096 8))) (/ 77617 (* 2 33096)))
981.0ms
(+ (* (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (fma (/ 1 (sqrt (+ (* x1 x1) 1))) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (sqrt (+ (* x1 x1) 1))) -3)) (+ (* (* 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (* x1 x1)) (* -6 (* x1 x1))))
910.0ms
(+ (+ (* 333.75 (pow 33096 6)) (* (* 77617 77617) (+ (+ (+ (* (* 11 (* 77617 77617)) (* 33096 33096)) (- (pow 33096 6))) (* -121 (pow 33096 4))) -2))) (* 5.5 (pow 33096 8)))
772.0ms
(+ (* (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (- (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) 3)) (+ (* (* x1 x1) (fma 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) (- (* (sqrt 6) (sqrt 6))))) 0))
Rules
7972×times-frac
7741×*-un-lft-identity
6764×add-sqr-sqrt
4716×add-cube-cbrt
2118×sqrt-prod
1688×add-exp-log
1438×prod-diff
1389×add-cbrt-cube
925×difference-of-squares
887×pow1
852×associate-*r*
774×distribute-lft-out
640×prod-exp
606×distribute-lft-out--
519×add-log-exp
514×cbrt-unprod
496×associate-*l*
460×associate-/l*
420×associate-/r*
415×associate-+l+
384×div-exp
360×sqrt-div
357×associate-/r/
351×div-inv
343×flip-+ flip3-+
342×pow-prod-down
272×expm1-log1p-u log1p-expm1-u insert-posit16
253×cbrt-undiv
248×frac-times
223×distribute-rgt-neg-in
220×distribute-rgt-in distribute-lft-in
213×associate-*l/
170×fma-neg
155×associate-*r/
150×distribute-lft-neg-in
146×cbrt-div
128×unswap-sqr
123×flip3-- flip--
111×sum-log
95×fma-udef
83×fma-def
81×exp-sum
71×*-commutative
68×frac-2neg clear-num
63×1-exp rec-exp
51×difference-of-sqr-1
50×neg-mul-1 frac-add
49×associate-/l/
48×unpow-prod-down exp-prod
47×sub-neg
44×cbrt-prod
39×sqrt-pow1 pow1/2 diff-log
36×swap-sqr pow-prod-up
30×rem-sqrt-square
28×log-prod
27×pow1/3
21×sqr-pow un-div-inv
20×associate-+r+ +-commutative div-sub log-pow
16×pow-flip pow-sqr
14×inv-pow
13×pow-plus
12×pow-exp pow-to-exp hypot-def
10×rem-exp-log
pow2 distribute-frac-neg
associate--l- associate--l+
neg-sub0 pow-div
distribute-lft-neg-out
exp-diff cube-prod neg-log log-div
remove-posit16 frac-sub pow-unpow
pow3 sqrt-unprod sub-div rem-log-exp hypot-udef rem-square-sqrt
expm1-udef cube-unmult unpow3 hypot-1-def pow-pow distribute-rgt-out-- associate-+l- rem-cbrt-cube cube-mult associate--r- distribute-rgt-out

regimes3.6s (0.6%)

Accuracy

Total 33.3b remaining (23.4%)

Threshold costs 2.2b (1.5%)

10.8b60.5%Compound Interest
6.8b33.4%Complex division, real part
5.2b80.9%The quadratic formula (r1)
4.7b82.9%The quadratic formula (r2)
2.4b0%Complex division, imag part

localize3.3s (0.6%)

bsearch1.4s (0.2%)

end1.0ms (0.0%)