Details

simplify2.3m (34.4%)

prune2.0m (29.0%)

sample1.5m (22.5%)

Algorithm
67×intervals
Results
37.1s268656×body80valid
13.1s13736×body1280valid
7.7s16987×body160valid
5.5s9595×body640valid
5.4s3850×body2560valid
5.0s2183×body10240exit
3.4s75854×pre80true
2.8s6737×body320valid
2.0s19130×body80nan
338.0ms247×body5120valid
11.0ms100×pre80false

series30.8s (7.6%)

Calls

265 calls:

3.1s
(* (* x1 x1) (* (cbrt (fma 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) (- (* (sqrt 6) (sqrt 6))))) (cbrt (fma 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) (- (* (sqrt 6) (sqrt 6)))))))
877.0ms
(expm1 (log1p (cbrt (- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x))))))))
676.0ms
(cbrt x)
616.0ms
(+ (* (* (* 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) (fma 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) (- (* (sqrt 6) (sqrt 6))))) 0))
563.0ms
(+ (* (* (* 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) (* (cbrt (fma 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) (- (* (sqrt 6) (sqrt 6))))) (cbrt (fma 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) (- (* (sqrt 6) (sqrt 6))))))) (cbrt (fma 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) (- (* (sqrt 6) (sqrt 6)))))) 0))

rewrite17.1s (4.2%)

Algorithm
92×rewrite-expression-head
Calls

265 calls:

939.0ms
(+ (+ (* 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)))
918.0ms
(+ (+ (+ (* 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))) (/ 77617 (* 2 33096)))
790.0ms
(* (/ 1 (sqrt (/ (- 1 v) (fma -2 v 3)))) (* (/ 0.125 (sqrt (/ (- 1 v) (fma -2 v 3)))) (* (* w r) (* w r))))
701.0ms
(- (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) 3)
687.0ms
(+ (* (* (* 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)))
Rules
33449×times-frac
21096×*-un-lft-identity
17311×add-sqr-sqrt
13597×add-cube-cbrt
5069×frac-times
3457×flip-+ flip3-+
2185×distribute-lft-out
1953×associate-*l/
1762×difference-of-squares
1514×pow1
1500×distribute-lft-out--
1478×add-exp-log
1401×prod-diff
1326×associate-/l*
1316×associate-*r/
1253×add-cbrt-cube
1245×div-inv
902×associate-/r/
841×cbrt-div
760×associate-*r*
738×sqrt-prod
650×frac-sub
585×exp-neg
514×prod-exp
509×associate-*l*
506×add-log-exp
504×flip3-- flip--
444×neg-sub0
443×exp-diff
408×cbrt-unprod associate-/r*
407×pow-prod-down
365×associate-+l+
361×pow-prod-up
357×div-exp
271×cbrt-undiv
267×expm1-log1p-u
266×log1p-expm1-u
265×insert-posit16
236×pow-plus
180×cbrt-prod
168×distribute-rgt-neg-in
156×fma-neg
151×distribute-lft-neg-in
148×un-div-inv unpow-prod-down
133×pow-sqr
129×unswap-sqr
118×distribute-rgt-in distribute-lft-in
109×sqr-pow
91×sum-log sqrt-pow1
87×difference-of-sqr-1
86×fma-def
75×pow2
70×*-commutative pow1/2
59×frac-2neg clear-num
57×sub-neg
52×diff-log
51×neg-mul-1 exp-prod
50×associate-/l/
44×sqrt-div fma-udef
36×swap-sqr
32×log-prod 1-exp rec-exp
30×pow3
28×rem-sqrt-square
27×associate-+r+
26×frac-add
23×exp-sum
22×log-pow
19×pow1/3 associate--l+
17×+-commutative div-sub
13×pow-exp pow-to-exp
11×rem-exp-log hypot-def
10×pow-flip
sqrt-unprod
inv-pow pow-div
associate--l- log-div
expm1-udef neg-log
cube-prod distribute-frac-neg distribute-lft-neg-out
pow-unpow rem-log-exp rem-square-sqrt expm1-def
expm1-log1p log1p-expm1 associate--r+ rem-cbrt-cube log1p-udef
remove-posit16 unpow3 pow-pow associate-+l- log1p-def cube-mult distribute-rgt-out

regimes4.4s (1.1%)

Accuracy

Total 30.2b remaining (19.1%)

Threshold costs 2.0b (1.3%)

8.9b16.6%Compound Interest
5.3b73.4%Kahan p9 Example
4.7b82.9%The quadratic formula (r2)
3.2b85.3%The quadratic formula (r1)
2.5b0%Complex division, real part

localize3.4s (0.8%)

bsearch1.5s (0.4%)

end1.0ms (0.0%)