Details

simplify4.8m (56.5%)

sample1.3m (15.3%)

Algorithm
73×intervals
Results
27.0s285446×body80valid
10.2s25073×body160valid
9.2s13846×body1280valid
3.8s9547×body640valid
3.7s3769×body2560valid
3.1s2273×body10240exit
2.7s100635×pre80true
2.3s6940×body320valid
1.3s19295×body80nan
168.0ms252×body5120valid
7.0ms100×pre80false

prune57.0s (11.2%)

rewrite39.4s (7.7%)

Algorithm
101×rewrite-expression-head
Calls

282 calls:

9.3s
(+ (+ (* (* x x) (- (- (- (* 11.0 (* (* x y) (* x y))) (pow y 6.0)) (* 121.0 (pow y 4.0))) 2.0)) (* (pow y 6.0) 333.75)) (+ (* (pow y 8.0) 5.5) (/ x (* y 2.0))))
3.9s
(+ (+ (* (* (* 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 (* (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) x1))) (* x1 (* (- 6.0) x1)))
1.7s
(+ (+ (* 333.75 (pow 33096.0 6.0)) (* (* 77617.0 77617.0) (+ (+ (+ (* (* 11.0 (* 77617.0 77617.0)) (* 33096.0 33096.0)) (- (pow 33096.0 6.0))) (* -121.0 (pow 33096.0 4.0))) -2.0))) (* 5.5 (pow 33096.0 8.0)))
1.6s
(+ (* (* (* 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)) (+ (* (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (* x1 x1)) (* (- 6.0) (* x1 x1))))
1.3s
(* (* (* 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))
Rules
2911×*-un-lft-identity
2648×add-sqr-sqrt
2547×times-frac
1791×add-cube-cbrt
1585×add-exp-log
1503×add-cbrt-cube
792×pow1
625×add-log-exp
615×associate-*r*
564×associate-*l*
561×prod-exp
525×cbrt-unprod
355×sqrt-prod
354×distribute-lft-out
351×div-exp
330×cbrt-undiv
321×difference-of-squares
293×associate-/r*
289×frac-times
274×flip3-- flip--
265×associate-*r/
244×associate-/l*
242×flip-+ flip3-+
239×distribute-lft-out--
235×pow-prod-down
181×frac-sub
179×associate-*l/
171×div-inv
157×cbrt-prod
152×associate-/r/
120×sum-log
113×sub-neg
101×unswap-sqr
93×unpow-prod-down
89×distribute-rgt-neg-in
84×diff-log
81×sqrt-div distribute-lft-neg-in
79×*-commutative
76×swap-sqr exp-neg
73×cbrt-div associate-/l/
71×frac-add
64×neg-sub0
63×distribute-rgt-in distribute-lft-in
59×exp-diff sqrt-pow1
58×frac-2neg sqr-pow clear-num
39×pow1/2
35×pow-prod-up
31×log-prod
30×associate-+l+ +-commutative
28×associate--l+ rem-sqrt-square
27×neg-mul-1
26×div-sub
25×log-pow
24×associate-+r+
22×pow-plus
21×pow1/3 un-div-inv
19×exp-prod pow-sqr
14×pow-exp pow2 pow-to-exp
13×exp-sum
12×associate--r+
9×distribute-lft-neg-out associate--l- 1-exp rec-exp distribute-frac-neg
7×log-div
6×associate-+r-
5×rem-log-exp associate-+l-
4×distribute-rgt-out-- pow3 neg-log rem-exp-log
3×pow-unpow rem-cbrt-cube unsub-neg
2×pow-flip cube-unmult distribute-rgt-neg-out inv-pow
1×distribute-lft1-in sqrt-undiv sqrt-unprod sub-div pow-pow +-inverses rem-square-sqrt associate--r-

series35.5s (7.0%)

Calls

282 calls:

753.0ms
(+ (+ (* (* x x) (- (- (- (* 11.0 (* (* x y) (* x y))) (pow y 6.0)) (* 121.0 (pow y 4.0))) 2.0)) (* (pow y 6.0) 333.75)) (+ (* (pow y 8.0) 5.5) (/ x (* y 2.0))))
665.0ms
(cbrt (* (* (- (* 9.0 (pow x 4.0)) (* (* y y) (* y y))) (- (* 9.0 (pow x 4.0)) (* (* y y) (* y y)))) (- (* 9.0 (pow x 4.0)) (* (* y y) (* y y)))))
653.0ms
(- (* 9.0 (pow x 4.0)) (* (* y y) (* y y)))
643.0ms
(- (* 9.0 (pow x 4.0)) (* (* y y) (* y y)))
627.0ms
(cbrt (* (* (- (* 9.0 (pow x 4.0)) (pow y 4.0)) (- (* 9.0 (pow x 4.0)) (pow y 4.0))) (- (* 9.0 (pow x 4.0)) (pow y 4.0))))

regimes5.9s (1.2%)

Accuracy

Total 33.9b remaining (8.6%)

Threshold costs 3.0b (0.7%)

13.1b42.1%Compound Interest
4.7b76%Kahan p9 Example
4.5b84.3%The quadratic formula (r1)
3.4b-13.7%Complex division, real part
3.1b0%Complex division, imag part

localize4.2s (0.8%)

bsearch1.3s (0.3%)

end1.0ms (0.0%)