Details

simplify5.4m (57.3%)

sample1.2m (13.3%)

Algorithm
73×intervals
Results
28.0s293756×body80valid
10.3s13892×body1280valid
5.3s16772×body160valid
4.9s9318×body640valid
4.5s3867×body2560valid
3.2s2226×body10240exit
2.9s19601×body80nan
2.8s100598×pre80true
2.1s6939×body320valid
181.0ms238×body5120valid
4.0ms100×pre80false

rewrite1.1m (11.9%)

Algorithm
115×rewrite-expression-head
Calls

334 calls:

11.8s
(* (pow (+ (* (* 77617.0 77617.0) (+ (+ (* -121.0 (pow 33096.0 4.0)) (- (* (* 11.0 (* 77617.0 77617.0)) (* 33096.0 33096.0)) (pow 33096.0 6.0))) -2.0)) (* 333.75 (pow 33096.0 6.0))) 2) (+ (* (* 77617.0 77617.0) (+ (+ (* -121.0 (pow 33096.0 4.0)) (- (* (* 11.0 (* 77617.0 77617.0)) (* 33096.0 33096.0)) (pow 33096.0 6.0))) -2.0)) (* 333.75 (pow 33096.0 6.0))))
5.9s
(+ (pow (* 5.5 (pow 33096.0 8.0)) 3) (pow (+ (* (* 77617.0 77617.0) (+ (+ (* -121.0 (pow 33096.0 4.0)) (- (* (* 11.0 (* 77617.0 77617.0)) (* 33096.0 33096.0)) (pow 33096.0 6.0))) -2.0)) (* 333.75 (pow 33096.0 6.0))) 3))
4.2s
(+ (pow (* 5.5 (pow 33096.0 8.0)) 3) (* (pow (+ (* (* 77617.0 77617.0) (+ (+ (* -121.0 (pow 33096.0 4.0)) (- (* (* 11.0 (* 77617.0 77617.0)) (* 33096.0 33096.0)) (pow 33096.0 6.0))) -2.0)) (* 333.75 (pow 33096.0 6.0))) 2) (+ (* (* 77617.0 77617.0) (+ (+ (* -121.0 (pow 33096.0 4.0)) (- (* (* 11.0 (* 77617.0 77617.0)) (* 33096.0 33096.0)) (pow 33096.0 6.0))) -2.0)) (* 333.75 (pow 33096.0 6.0)))))
4.0s
(+ (+ (* 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)))
3.9s
(+ (pow (* 5.5 (pow 33096.0 8.0)) 3) (* (pow (+ (* (* 77617.0 77617.0) (+ (+ (* -121.0 (pow 33096.0 4.0)) (- (* (* 11.0 (* 77617.0 77617.0)) (* 33096.0 33096.0)) (pow 33096.0 6.0))) -2.0)) (* 333.75 (pow 33096.0 6.0))) 2) (+ (* (* 77617.0 77617.0) (+ (+ (* -121.0 (pow 33096.0 4.0)) (- (* (* 11.0 (* 77617.0 77617.0)) (* 33096.0 33096.0)) (pow 33096.0 6.0))) -2.0)) (* 333.75 (pow 33096.0 6.0)))))
Rules
4693×add-sqr-sqrt
4517×times-frac
4213×*-un-lft-identity
2364×add-cube-cbrt
1930×add-exp-log
1673×add-cbrt-cube
1168×difference-of-squares
800×associate-*r*
784×add-log-exp
761×pow1
757×unpow-prod-down
629×prod-exp
547×distribute-lft-out--
542×associate-*l*
526×cbrt-unprod
505×associate-/r*
468×div-exp
433×sqr-pow
431×distribute-lft-out
395×associate-/l*
393×cbrt-undiv
365×sqrt-prod
340×flip-+ flip3-+
306×associate-/r/
300×cube-prod
272×div-inv
259×associate-*r/
248×flip3-- flip--
224×frac-times
190×cbrt-prod
186×pow-prod-down
159×associate-*l/
151×sum-log
137×unswap-sqr
124×sub-neg
114×diff-log
108×associate-/l/
98×frac-sub
87×swap-sqr
83×frac-add
79×*-commutative
78×cbrt-div
73×clear-num frac-2neg
72×exp-neg
69×sqrt-div
59×neg-sub0
57×pow-exp
55×distribute-rgt-in unpow2 distribute-lft-in
54×exp-diff
46×distribute-rgt-out--
42×pow-unpow pow-to-exp +-commutative
38×cube-mult
37×unpow3
36×distribute-rgt-neg-in
33×distribute-lft-neg-in
29×associate-+r+ pow-pow
28×div-sub sqrt-pow1
27×un-div-inv pow1/3 associate--l+
26×1-exp rec-exp
25×pow1/2
23×rem-sqrt-square pow-prod-up
22×exp-sum
21×associate-+l+
20×distribute-rgt-out
19×distribute-lft1-in pow-plus
18×pow-sqr
17×cube-div
14×difference-cubes associate--l-
13×pow2
12×rem-cube-cbrt
11×neg-mul-1
inv-pow distribute-lft-neg-out pow-flip associate--r+
associate-+r- rem-cbrt-cube
pow3 neg-log log-prod
unsub-neg distribute-frac-neg exp-prod sum-cubes
log-div
sqrt-pow2 sub-div log-pow rem-log-exp

prune50.4s (8.9%)

series39.7s (7.0%)

Calls

334 calls:

818.0ms
(+ (* (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) (+ (* (* 3.0 x1) x1) (* (* (- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0) (* 2.0 x1)) (+ (* x1 x1) 1.0)))) (* (+ (* x1 x1) 1.0) (* (* x1 x1) (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0))))
696.0ms
(- (* 9.0 (pow x 4.0)) (pow y 4.0))
683.0ms
(cbrt (pow (- (* 9.0 (pow x 4.0)) (pow y 4.0)) 3))
641.0ms
(* (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) (+ (* (* 3.0 x1) x1) (* (* (- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0) (* 2.0 x1)) (+ (* x1 x1) 1.0))))
634.0ms
(- (* 9.0 (pow x 4.0)) (pow y 4))

regimes4.3s (0.8%)

Accuracy

Total 40.7b remaining (9.1%)

Threshold costs 3.9b (0.9%)

12.6b52.8%Compound Interest
12.1b41.9%Kahan p9 Example
4.6b84.2%The quadratic formula (r1)
2.7b0%Complex division, real part
2.5b0%Complex division, imag part

localize2.9s (0.5%)

bsearch1.9s (0.3%)

end1.0ms (0.0%)