Details

simplify6.4m (65.7%)

sample1.6m (15.9%)

Algorithm
67×intervals
Results
36.9s268827×body80valid
13.5s13526×body1280valid
7.7s16887×body160valid
6.0s3738×body2560valid
5.8s9684×body640valid
4.0s2305×body10240exit
3.5s75793×pre80true
3.4s6891×body320valid
2.7s19740×body80nan
243.0ms206×body5120valid
11.0ms100×pre80false

prune56.7s (9.7%)

series29.4s (5.0%)

Calls

263 calls:

2.6s
(* (* 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)))))))
937.0ms
(* (cbrt (/ PI (* (+ a b) 2))) (cbrt (/ PI (* (+ a b) 2))))
904.0ms
(cbrt (+ (* (* (fma x (* x x) (* x x)) (fma x (* x x) (* x x))) (* x (* x x))) (* (* (fma x (* x x) (* x x)) (fma x (* x x) (* x x))) (* x x))))
656.0ms
(+ (* (* (* 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)) (* (* x1 x1) (- (* 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) 6)))
656.0ms
(+ (* (* (* 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)) (+ (* (* (* 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))

rewrite13.5s (2.3%)

Algorithm
94×rewrite-expression-head
Calls

263 calls:

1.3s
(+ (+ (+ (* 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)))
1.2s
(+ (* (* (* 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)))
994.0ms
(+ (+ (* 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)))
881.0ms
(* (* (exp a) (exp e)) (* (sqrt (* (exp b) (* (exp d) (exp c)))) (sqrt (* (exp b) (* (exp d) (exp c))))))
708.0ms
(- (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) 3)
Rules
4216×times-frac
4042×*-un-lft-identity
3678×add-sqr-sqrt
3048×add-cube-cbrt
1366×prod-diff
1025×add-exp-log
953×add-cbrt-cube
886×pow1
465×add-log-exp
401×sqrt-prod
381×associate-*r*
320×associate-/r*
313×associate-/l*
299×distribute-lft-out
298×div-inv
296×prod-exp
280×associate-*l*
273×pow-prod-down
272×cbrt-unprod
264×expm1-log1p-u
263×log1p-expm1-u insert-posit16
262×difference-of-squares
250×associate-+r+
216×div-exp
203×flip-+ flip3-+
197×associate-/r/
171×cbrt-undiv
158×distribute-lft-out--
154×frac-times
145×associate-+l+ cbrt-prod
133×associate-*r/
124×distribute-rgt-neg-in
121×associate-*l/
117×distribute-lft-neg-in
112×fma-neg
107×distribute-rgt-in distribute-lft-in
105×pow-prod-up
104×exp-prod
100×flip-- flip3--
99×unpow-prod-down
98×sqrt-pow1
94×sum-log
83×frac-sub
82×fma-def
81×exp-neg
70×unswap-sqr
68×fma-udef
67×*-commutative
66×neg-sub0
61×exp-diff
58×frac-2neg clear-num
51×associate-/l/
46×swap-sqr
41×pow-plus frac-add
40×pow1/2 pow-sqr
39×neg-mul-1
37×sub-neg
34×sqr-pow
32×log-pow
27×un-div-inv diff-log
23×pow1/3 cbrt-div
22×1-exp rec-exp pow2
21×+-commutative rem-sqrt-square
18×div-sub
16×log-prod
11×distribute-lft-neg-out rem-exp-log
10×pow-flip pow-exp inv-pow
distribute-rgt-neg-out pow-div hypot-def
distribute-frac-neg pow-to-exp
pow-unpow
exp-sum pow3
pow-pow rem-log-exp
neg-log difference-of-sqr-1 associate--l-
remove-posit16 cube-unmult sqrt-unprod distribute-neg-frac rem-square-sqrt rem-cbrt-cube unsub-neg distribute-rgt-out
expm1-log1p expm1-udef associate-+r- associate--l+ sqrt-div log1p-expm1 log1p-udef

regimes3.8s (0.6%)

Accuracy

Total 37.9b remaining (26.5%)

Threshold costs 3.1b (2.1%)

10.3b63%Compound Interest
7.8b31.5%Complex division, real part
5.0b81.7%The quadratic formula (r2)
4.8b75.8%Kahan p9 Example
4.3b84.2%The quadratic formula (r1)

localize3.7s (0.6%)

bsearch1.3s (0.2%)

end1.0ms (0.0%)