Details

simplify6.6m (52.2%)

prune3.6m (28.2%)

sample1.5m (12.1%)

Algorithm
67×intervals
Results
36.8s269493×body80valid
13.2s13782×body1280valid
7.7s16966×body160valid
5.6s9515×body640valid
4.6s3698×body2560valid
4.5s2183×body10240exit
4.0s75895×pre80true
3.1s6686×body320valid
2.7s19301×body80nan
347.0ms240×body5120valid
12.0ms100×pre80false

series27.9s (3.7%)

Calls

307 calls:

555.0ms
(/ (sqrt (/ (- 1 v) (* (- 3 (* 2 v)) 0.125))) r)
494.0ms
(/ (sqrt (/ (- 1 v) (* (- 3 (* 2 v)) 0.125))) r)
493.0ms
(+ (* (* (* 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)))
417.0ms
(- 2 (/ 2 (+ 1 t)))
404.0ms
(+ (- 2 (* x x)) (* (* x 2/3) (* x x)))

rewrite19.2s (2.5%)

Algorithm
100×rewrite-expression-head
Calls

307 calls:

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)))
954.0ms
(+ (+ (* 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)))
726.0ms
(- (+ (exp (+ (- x) (* x eps))) (/ (exp (+ (- x) (* x eps))) eps)) (- (/ (exp (- (- x) (* x eps))) eps) (exp (- (- x) (* x eps)))))
701.0ms
(* (/ x (+ (* (* (* x x) x) (* (* x x) x)) 1)) (+ (* (* x x) (* x x)) (- (* 1 1) (* (* x x) 1))))
582.0ms
(+ (* (* (* 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
31696×times-frac
20416×*-un-lft-identity
19495×add-sqr-sqrt
10252×add-cube-cbrt
3623×difference-of-squares
3542×distribute-lft-out--
1759×div-inv
1741×distribute-lft-out
1440×add-exp-log
1432×associate-/l*
1318×add-cbrt-cube
1191×associate-*r*
1064×pow1
811×sqrt-prod
684×add-log-exp
599×associate-/r/
446×associate-*l*
413×prod-exp
374×div-exp
366×unpow-prod-down
362×associate-/r*
361×cbrt-unprod
346×sqr-pow
339×cbrt-prod
335×difference-of-sqr-1
318×cbrt-undiv
307×insert-posit16
278×flip-+ flip3-+
263×flip3-- flip--
262×pow-prod-down associate-*l/
154×pow-prod-up
147×sqrt-div
138×sum-log
122×unswap-sqr
121×swap-sqr
120×frac-sub
105×frac-times
100×associate-*r/
87×exp-prod
86×sub-neg
81×diff-log
77×pow-plus
72×*-commutative associate-/l/
67×frac-2neg clear-num
66×pow-sqr
65×sqrt-pow1
61×log-prod
55×pow1/2
51×cbrt-div
48×pow-flip
47×pow2
46×exp-sum
45×distribute-rgt-neg-in
40×+-commutative
39×log-pow rem-sqrt-square
32×distribute-rgt-in distribute-lft-in distribute-lft-neg-in
29×pow1/3 frac-add
28×div-sub
26×rem-exp-log
23×associate-+l+
22×1-exp
19×distribute-rgt-out--
18×rec-exp difference-of-sqr--1
16×exp-diff associate-+r+ log-div
11×neg-sub0 associate--l-
10×associate--l+ neg-log neg-mul-1 associate-+l-
pow-exp pow-to-exp
pow-div rem-log-exp distribute-rgt-out
pow-unpow pow3 associate--r+ inv-pow
remove-posit16
distribute-frac-neg distribute-lft-neg-out
associate-+r- sub-div pow-pow
distribute-lft1-in cube-unmult sqrt-unprod rem-square-sqrt associate--r-

regimes4.2s (0.6%)

Accuracy

Total 30.5b remaining (13.8%)

Threshold costs 2.9b (1.3%)

10.6b52.8%Compound Interest
4.9b82.5%The quadratic formula (r1)
4.3b77.7%Kahan p9 Example
4.2b83.5%The quadratic formula (r2)
2.4b8.1%Complex division, real part

localize4.1s (0.5%)

bsearch1.1s (0.1%)

end1.0ms (0.0%)