Details

simplify8.3m (68.0%)

prune1.5m (12.3%)

sample1.2m (10.2%)

Algorithm
73×intervals
Results
25.1s285446×body80valid
9.6s25073×body160valid
9.4s13846×body1280valid
6.0s9547×body640valid
3.8s100635×pre80true
3.5s3769×body2560valid
2.8s2273×body10240exit
2.0s19295×body80nan
1.7s6940×body320valid
203.0ms252×body5120valid
5.0ms100×pre80false

series35.4s (4.8%)

Calls

254 calls:

1.0s
(+ (* (* (* 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)) (+ (* (* x1 x1) (fma 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) (- (* (sqrt 6.0) (sqrt 6.0))))) (* (fma 6.0 -1 6.0) (* x1 x1))))
973.0ms
(log (cbrt (exp (* x (* x x)))))
944.0ms
(log (* (cbrt (exp (* x (* x x)))) (cbrt (exp (* x (* x x))))))
941.0ms
(- (* (pow x 4.0) 9.0) (pow y 4.0))
625.0ms
(* 333.75 (pow y 6.0))

rewrite22.8s (3.1%)

Algorithm
95×rewrite-expression-head
Calls

254 calls:

3.3s
(+ (+ (+ (* 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)))
3.3s
(+ (+ (* 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)))
956.0ms
(+ (* (* (* 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)) (* (* (cbrt (* (* x1 x1) (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0))) (cbrt (* (* x1 x1) (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0)))) (cbrt (* (* x1 x1) (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0)))))
884.0ms
(+ (* (* (* 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)) (* (* x1 x1) (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0)))
863.0ms
(+ (* (* (* 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)) (+ (* (* x1 x1) (fma 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) (- (* (sqrt 6.0) (sqrt 6.0))))) (* (fma 6.0 -1 6.0) (* x1 x1))))
Rules
6958×times-frac
6596×*-un-lft-identity
6280×add-sqr-sqrt
5096×add-cube-cbrt
3502×prod-diff
1073×add-exp-log
995×add-cbrt-cube
772×distribute-rgt-in distribute-lft-in
729×pow1
615×div-inv
582×associate-*r/
506×sqrt-prod
493×add-log-exp
453×associate-*r*
438×difference-of-squares
436×distribute-lft-out
427×associate-*l*
400×associate-+l+
357×distribute-lft-out--
351×flip3-- flip--
317×cbrt-div
316×unpow-prod-down
313×prod-exp
312×associate-/r*
305×frac-times
282×cbrt-unprod
278×associate-/l*
254×expm1-log1p-u log1p-expm1-u
224×fma-neg div-exp
223×associate-/r/
211×pow-prod-down
199×cbrt-undiv
188×associate-*l/
163×flip-+ flip3-+
160×frac-add
152×distribute-rgt-neg-in
144×distribute-lft-neg-in
125×sqr-pow
92×sum-log
80×unswap-sqr
74×sub-neg
59×frac-2neg clear-num
58×associate-/l/
57×*-commutative fma-def
55×sqrt-div
48×neg-mul-1 diff-log
42×log-pow
36×log-prod
35×pow-prod-up fma-udef
30×cbrt-prod
28×sqrt-pow1 pow1/2
27×rem-sqrt-square
24×div-sub
23×pow-sqr
22×pow1/3
19×frac-sub
17×+-commutative
16×associate-+r+ swap-sqr hypot-def
15×exp-sum
14×pow-plus
13×1-exp rec-exp
12×exp-prod
10×pow2
distribute-frac-neg rem-log-exp
log-div
neg-sub0
distribute-lft-neg-out associate--l- un-div-inv exp-to-pow
distribute-rgt-out--
pow-exp pow-unpow cube-unmult neg-log pow-to-exp
pow-flip pow3 inv-pow rem-cbrt-cube
expm1-log1p expm1-udef sqrt-undiv associate--l+ sub-div associate--r+ pow-pow +-inverses associate-+l- distribute-rgt-out

regimes5.6s (0.8%)

Accuracy

Total 37.9b remaining (14.7%)

Threshold costs 2.6b (1%)

13.1b42.1%Compound Interest
7.3b34%Complex division, imag part
4.7b76%Kahan p9 Example
4.7b83.9%The quadratic formula (r1)
3.3b-14.4%Complex division, real part

localize3.9s (0.5%)

bsearch1.4s (0.2%)

end2.0ms (0.0%)