Details

simplify10.2m (67.1%)

prune2.6m (16.9%)

sample1.6m (10.3%)

Algorithm
67×intervals
Results
36.7s269448×body80valid
13.3s13771×body1280valid
8.1s16830×body160valid
6.4s9477×body640valid
6.3s3895×body2560valid
4.1s75932×pre80true
3.8s2170×body10240exit
3.0s6903×body320valid
2.6s19333×body80nan
402.0ms232×body5120valid
6.0ms100×pre80false

series28.2s (3.1%)

Calls

276 calls:

881.0ms
(+ (* (fma (* (cbrt (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (cbrt (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)))) (cbrt (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (- (* 3 1))) (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)))) (fma 0 (/ (- (fma 3 (* x1 x1) (* 2 x2)) x1) (fma x1 x1 1)) (fma (fma 4 (/ (- (fma 3 (* x1 x1) (* 2 x2)) x1) (fma x1 x1 1)) -6) (* x1 x1) 0)))
806.0ms
(+ (* (fma (/ 1 (* (cbrt (+ (* x1 x1) 1)) (cbrt (+ (* x1 x1) 1)))) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (cbrt (+ (* x1 x1) 1))) (- (* 3 1))) (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)))) (fma 0 (/ (- (fma 3 (* x1 x1) (* 2 x2)) x1) (fma x1 x1 1)) (fma (fma 4 (/ (- (fma 3 (* x1 x1) (* 2 x2)) x1) (fma x1 x1 1)) -6) (* x1 x1) 0)))
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))))) (* (* x1 0) x1)))
526.0ms
(/ (fma (exp (* n (log1p (/ i n)))) 100 -100) (/ i n))
505.0ms
(cbrt (/ PI (* a (* (+ a b) 2))))

rewrite14.1s (1.5%)

Algorithm
97×rewrite-expression-head
Calls

276 calls:

1.1s
(- (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) 3)
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)))
844.0ms
(+ (* (* (* 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)))
749.0ms
(+ (+ (* 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)))
694.0ms
(+ (* (* (* 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))))) (* (* x1 0) x1)))
Rules
6011×times-frac
5382×*-un-lft-identity
5098×add-sqr-sqrt
3808×add-cube-cbrt
2249×sqrt-prod
1501×prod-diff
1093×add-exp-log
984×add-cbrt-cube
864×pow1
611×difference-of-squares
550×add-log-exp
449×associate-*r*
394×associate-/r*
378×associate-*l*
367×distribute-lft-out
348×distribute-lft-out--
320×div-inv
319×associate-/l*
294×prod-exp
280×expm1-log1p-u
276×log1p-expm1-u insert-posit16
266×associate-+l+
261×sqrt-pow1
258×cbrt-unprod
252×div-exp
250×unpow-prod-down
241×pow-prod-down
224×associate-/r/
221×distribute-rgt-in distribute-lft-in
192×cbrt-undiv
185×flip-+ flip3-+
173×sqrt-div distribute-rgt-neg-in
169×fma-neg
165×distribute-lft-neg-in
161×associate-*l/
130×sum-log
128×pow1/2
126×pow-prod-up
99×sqr-pow
97×unswap-sqr
93×exp-prod
92×associate-*r/
75×frac-times
70×flip-- flip3--
66×frac-2neg clear-num
65×cbrt-prod
61×*-commutative
55×neg-mul-1
52×fma-udef
51×rem-sqrt-square
50×swap-sqr
47×fma-def
44×associate-/l/ sub-neg
36×diff-log
34×rem-exp-log
28×1-exp rec-exp
26×log-pow frac-add
22×pow-sqr
20×pow-plus
18×associate-+r+
17×+-commutative
16×div-sub
15×exp-sum
12×pow1/3
11×log-prod hypot-def
10×distribute-frac-neg
pow2 distribute-lft-neg-out
pow-flip sqrt-unprod inv-pow
neg-sub0
pow-exp pow-unpow associate--l-
pow-to-exp
cube-prod log1p-expm1 neg-log un-div-inv log1p-udef
expm1-udef cbrt-div pow3 rem-log-exp rem-square-sqrt
cube-unmult associate--r+ pow-pow
unpow-prod-up expm1-log1p remove-posit16 unpow3 hypot-udef cube-mult e-exp-1 distribute-rgt-out

regimes4.7s (0.5%)

Accuracy

Total 34.7b remaining (23.9%)

Threshold costs 2.2b (1.5%)

13.8b42.5%Compound Interest
7.4b37.3%Complex division, real part
5.5b80%The quadratic formula (r2)
4.3b84.7%The quadratic formula (r1)
1.3b0%Rosa's DopplerBench

localize3.4s (0.4%)

bsearch1.9s (0.2%)

end1.0ms (0.0%)