Details

sample32.4s (25.0%)

Algorithm
73×intervals
Results
9.6s294330×body80valid
4.5s13411×body1280valid
2.1s3638×body2560valid
1.9s9573×body640valid
1.8s16923×body160valid
1.4s100627×pre80true
721.0ms6780×body320valid
551.0ms19510×body80nan
209.0ms200×body10240exit
159.0ms2975×body80overflowed
88.0ms231×body5120valid
3.0ms100×pre80false

rewrite30.9s (23.8%)

Algorithm
109×rewrite-expression-head
Calls

298 calls:

3.2s
(+ (+ (* (* (* 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))) (* (* x1 x1) (- 6.0)))
2.4s
(+ (+ (* 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)))
1.8s
(cbrt (+ (+ (* (* (* 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))) (* (* x1 x1) (- 6.0))))
1.8s
(cbrt (+ (+ (* (* (* 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))) (* (* x1 x1) (- 6.0))))
1.8s
(cbrt (+ (+ (* (* (* 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))) (* (* x1 x1) (- 6.0))))
Rules
6367×times-frac
5148×*-un-lft-identity
4844×add-sqr-sqrt
3013×add-cube-cbrt
1978×add-exp-log
1382×add-cbrt-cube
987×associate-*r*
944×unpow-prod-down
734×add-log-exp
679×div-exp
673×difference-of-squares
663×pow1
652×distribute-lft-out
574×sqrt-prod prod-exp
535×associate-/r*
472×associate-*l*
450×associate-/r/
413×distribute-lft-out--
409×cbrt-unprod
345×div-inv
344×sqr-pow
336×associate-*r/
327×cbrt-undiv
282×associate-/l*
272×flip-- flip3--
265×flip-+ flip3-+
256×cube-prod
249×cbrt-prod
193×unpow2
186×unswap-sqr
171×sum-log
156×pow-prod-down
150×frac-times
100×1-exp
98×associate-*l/
95×swap-sqr
94×sub-neg
91×associate-/l/
77×diff-log
76×distribute-rgt-neg-in pow-exp
75×rec-exp
73×distribute-rgt-in distribute-lft-in *-commutative
68×pow-to-exp
58×clear-num frac-2neg
54×distribute-lft-neg-in sqrt-div
49×frac-add
48×log-prod
46×+-commutative
32×associate-+l+
31×cbrt-div
27×div-sub
25×pow-unpow rem-sqrt-square
24×pow1/2 associate-+r+ unpow3 cube-mult sqrt-pow1
23×frac-sub
18×neg-mul-1
17×cube-div
16×pow-plus pow-prod-up exp-prod
15×pow1/3
14×exp-to-pow
13×distribute-rgt-out-- log-pow
12×neg-sub0 exp-sum
11×pow2 pow-sqr pow-flip pow-pow
10×neg-log associate--l+
rem-exp-log associate--l- inv-pow
associate--r+ log-div
rem-cbrt-cube
distribute-frac-neg
rem-cube-cbrt sum-cubes rem-log-exp
un-div-inv unsub-neg distribute-lft-neg-out sub-div associate-+r- associate--r-
exp-diff distribute-rgt-neg-out associate-+l-
sqrt-pow2 distribute-lft1-in pow3 distribute-rgt-out +-inverses remove-double-div

prune28.5s (22.0%)

series22.4s (17.3%)

Calls

298 calls:

653.0ms
(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
398.0ms
(cbrt (+ (+ (* (* (* 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))) (* (* x1 x1) (- 6.0))))
395.0ms
(cbrt (pow (- (* 9.0 (pow x 4.0)) (pow y 4)) 3))
394.0ms
(+ (* 9.0 (pow x 4.0)) (- (pow y 4)))
392.0ms
(cbrt (+ (+ (* (* (* 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))) (* (* x1 x1) (- 6.0))))

simplify9.6s (7.4%)

Algorithm
179×egg-herbie

regimes3.3s (2.6%)

Accuracy

Total 29.9b remaining (6.9%)

Threshold costs 4.2b (1%)

12.2b50.7%Compound Interest
4.4b77.1%Kahan p9 Example
3.0b0%Complex division, imag part
1.9b37.9%Complex division, real part
1.4b0%Rosa's DopplerBench

localize1.4s (1.1%)

bsearch1.0s (0.8%)

end1.0ms (0.0%)