Details

simplify8.3m (66.8%)

prune1.6m (12.6%)

sample1.3m (10.2%)

Algorithm
73×intervals
Results
27.6s285851×body80valid
9.2s13794×body1280valid
9.1s25173×body160valid
4.2s3848×body2560valid
4.0s9461×body640valid
3.5s100685×pre80true
3.3s2175×body10240exit
2.4s6968×body320valid
1.5s19331×body80nan
146.0ms227×body5120valid
7.0ms100×pre80false

series41.1s (5.5%)

Calls

284 calls:

1.7s
(+ (* (* (* 2.0 x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (fma (/ (* (cbrt (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1)) (cbrt (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1))) (sqrt (+ (* x1 x1) 1.0))) (/ (cbrt (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1)) (sqrt (+ (* x1 x1) 1.0))) (- 3.0))) (* (* x1 x1) (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0)))
1.0s
(log (* (cbrt (exp (* (* x x) x))) (cbrt (exp (* (* x x) x)))))
1.0s
(/ (fma (pow (* (cbrt (+ 1.0 (/ i n))) (cbrt (+ 1.0 (/ i n)))) n) (pow (cbrt (+ 1.0 (/ i n))) n) (- 1.0)) (/ i n))
989.0ms
(log (cbrt (exp (* (* x x) x))))
944.0ms
(+ (* (* (* 2.0 x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)) (+ (* (fma 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) (- (* (sqrt 6.0) (sqrt 6.0)))) (* x1 x1)) (* (fma 6.0 -1 6.0) (* x1 x1))))

rewrite25.7s (3.4%)

Algorithm
105×rewrite-expression-head
Calls

284 calls:

3.1s
(+ (+ (+ (* 333.75 (pow y 6.0)) (* (* x x) (- (- (- (* (* (* (* 11.0 x) x) y) y) (pow y 6.0)) (* 121.0 (pow y 4.0))) 2.0))) (* 5.5 (pow y 8.0))) (/ x (* 2.0 y)))
3.0s
(+ (+ (* 333.75 (pow y 6.0)) (* (* x x) (- (- (- (* (* (* (* 11.0 x) x) y) y) (pow y 6.0)) (* 121.0 (pow y 4.0))) 2.0))) (* 5.5 (pow y 8.0)))
1.4s
(- (- (+ 3.0 (/ (/ 2.0 r) r)) (* (* (* w r) (* w r)) (/ (* 0.125 (- 3.0 (* 2.0 v))) (- 1.0 v)))) 4.5)
939.0ms
(+ (* (* (* 2.0 x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)) (* (fma 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) (- (* (cbrt 6.0) (* (cbrt 6.0) (cbrt 6.0))))) (* x1 x1)))
936.0ms
(+ (* (* (* 2.0 x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)) (+ (* (fma 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) (- (* (sqrt 6.0) (sqrt 6.0)))) (* x1 x1)) (* (fma 6.0 -1 6.0) (* x1 x1))))
Rules
6980×times-frac
6720×*-un-lft-identity
6705×add-sqr-sqrt
5540×add-cube-cbrt
3976×prod-diff
1201×add-exp-log
1153×pow1
1116×add-cbrt-cube
782×distribute-rgt-in distribute-lft-in
661×div-inv
604×associate-*r*
597×add-log-exp
427×difference-of-squares
411×associate-*l*
402×associate-+l+
401×unpow-prod-down
381×sqrt-prod
371×prod-exp
348×cbrt-unprod
323×distribute-lft-out--
307×distribute-lft-out
290×fma-neg
287×pow-prod-down
285×log1p-expm1-u
284×expm1-log1p-u
239×associate-/r*
237×div-exp
220×associate-/l*
211×cbrt-undiv
176×pow-prod-up
165×cbrt-prod
158×sqr-pow
153×flip-- flip3--
152×associate-*r/
138×flip-+ flip3-+
136×associate-/r/
123×frac-times
119×distribute-rgt-neg-in
111×unswap-sqr
110×sum-log
108×distribute-lft-neg-in
99×associate-*l/
93×sqrt-pow1
90×pow-plus pow-sqr
88×sub-neg
69×associate-/l/ log-pow
67×diff-log
65×swap-sqr
63×*-commutative fma-def
57×pow1/2
55×log-prod cbrt-div
52×frac-2neg clear-num
50×pow2
46×pow1/3
38×fma-udef exp-prod
36×frac-sub neg-mul-1
33×frac-add
28×associate-+r+
27×sqrt-div
25×exp-sum
19×+-commutative
18×rem-sqrt-square
15×exp-to-pow div-sub log-div
14×rem-log-exp
13×1-exp rec-exp
11×pow3 sub-div
10×associate--l+
pow-unpow
associate--l-
pow-exp pow-to-exp
pow-flip distribute-frac-neg distribute-rgt-out
neg-sub0 distribute-lft-neg-out cube-prod neg-log sqrt-unprod hypot-def
pow-pow inv-pow rem-exp-log
pow-div associate--r+ rem-square-sqrt
expm1-log1p expm1-udef distribute-rgt-out-- unpow3 un-div-inv cube-mult rem-cbrt-cube

regimes5.8s (0.8%)

Accuracy

Total 53.2b remaining (21%)

Threshold costs 2.3b (0.9%)

15.3b39.5%Compound Interest
9.5b18.3%Complex division, real part
7.7b30.9%Complex division, imag part
7.5b61.7%Kahan p9 Example
4.8b85.5%The quadratic formula (r1)

localize4.3s (0.6%)

bsearch1.6s (0.2%)

end1.0ms (0.0%)