Details

simplify6.0m (64.8%)

sample1.1m (12.2%)

Algorithm
67×intervals
Results
24.8s269828×body80valid
10.6s13759×body1280valid
5.6s9295×body640valid
4.8s16809×body160valid
4.1s3938×body2560valid
3.3s2216×body10240exit
2.7s75892×pre80true
2.1s6881×body320valid
1.4s19428×body80nan
201.0ms245×body5120valid
8.0ms100×pre80false

prune1.1m (11.7%)

series28.8s (5.2%)

Calls

268 calls:

708.0ms
(sqrt (* (/ (fma -2 v 3) (- 1 v)) (* (* w r) (* 0.125 (* w r)))))
664.0ms
(sqrt (* (/ (fma -2 v 3) (- 1 v)) (* (* w r) (* 0.125 (* w r)))))
621.0ms
(+ (* (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (fma (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (- (* (* x1 x1) (* x1 x1)) (* 1 1))) (- (* x1 x1) 1) -3)) (+ (* (fma 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) (- (* (sqrt 6) (sqrt 6)))) (* x1 x1)) 0))
588.0ms
(+ (* (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (fma (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (- (* (* x1 x1) (* x1 x1)) (* 1 1))) (- (* x1 x1) 1) -3)) (* (* x1 x1) (- (* 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) 6)))
576.0ms
(+ (* (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (- (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) 3)) (+ (* (fma 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) (- (* (cbrt 6) (* (cbrt 6) (cbrt 6))))) (* x1 x1)) (* (+ (- 6) 6) (* x1 x1))))

rewrite23.8s (4.3%)

Algorithm
95×rewrite-expression-head
Calls

268 calls:

1.5s
(+ (+ (+ (* 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)))
1.5s
(* (sqrt (* (/ (fma -2 v 3) (- 1 v)) (* (* w r) (* 0.125 (* w r))))) (sqrt (* (/ (fma -2 v 3) (- 1 v)) (* (* w r) (* 0.125 (* w r))))))
1.4s
(+ (+ (* 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)))
1.2s
(+ (* (* (* 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)))
1.1s
(+ (* (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (- (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) 3)) (+ (* (fma 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) (- (* (cbrt 6) (* (cbrt 6) (cbrt 6))))) (* x1 x1)) (* (+ (- 6) 6) (* x1 x1))))
Rules
4532×*-un-lft-identity
4220×add-sqr-sqrt
4173×times-frac
3139×add-cube-cbrt
2364×pow1
1482×pow-prod-down
1333×prod-diff
1232×add-exp-log
1070×add-cbrt-cube
659×associate-*r*
555×add-log-exp
462×sqrt-pow1
457×difference-of-squares
425×distribute-lft-out
404×prod-exp
358×sqrt-prod
351×associate-*l*
348×cbrt-unprod
302×associate-/r*
296×associate-+l+
295×associate-/l*
270×expm1-log1p-u
269×log1p-expm1-u
268×insert-posit16
264×div-inv
246×div-exp
222×distribute-lft-out--
198×associate-/r/
184×cbrt-undiv
176×flip-+ flip3-+
175×distribute-rgt-in distribute-lft-in
168×fma-neg
144×unpow-prod-down
141×cbrt-prod
121×sum-log
120×difference-of-sqr-1
113×pow-prod-up associate-*r/
112×distribute-rgt-neg-in
109×fma-def
107×sqr-pow
105×distribute-lft-neg-in
101×unswap-sqr
97×flip3-- flip--
87×fma-udef
79×pow-sqr
76×associate-*l/
68×frac-times exp-sum *-commutative
59×sub-neg
58×pow1/2
56×frac-2neg clear-num
54×frac-add
51×diff-log
50×associate-/l/
35×neg-mul-1
31×associate-+r+ swap-sqr
29×+-commutative
28×log-prod 1-exp rec-exp
27×cbrt-div
24×rem-sqrt-square
23×associate--r+
22×div-sub
20×sqrt-div exp-prod
18×associate--l+
13×frac-sub
12×pow-exp pow-to-exp log-pow
10×pow-flip pow-plus inv-pow
pow2
hypot-def
distribute-rgt-out
pow-div log-div
associate--l- rem-exp-log
expm1-udef exp-diff pow1/3 cube-unmult distribute-frac-neg
neg-sub0 remove-posit16 pow-unpow log1p-expm1 associate--r- expm1-def log1p-udef
neg-log sqrt-unprod distribute-lft-neg-out un-div-inv rem-log-exp exp-to-pow sub-div associate-+l- rem-square-sqrt
expm1-log1p sub0-neg pow-pow log1p-def

regimes5.0s (0.9%)

Accuracy

Total 37.3b remaining (28%)

Threshold costs 2.6b (1.9%)

8.9b18.6%Complex division, real part
8.0b25.4%Compound Interest
7.6b35.9%Complex division, imag part
5.0b82.3%The quadratic formula (r2)
3.8b86.1%The quadratic formula (r1)

localize3.5s (0.6%)

bsearch1.2s (0.2%)

end1.0ms (0.0%)