Details

simplify6.9m (58.7%)

rewrite2.1m (17.7%)

Algorithm
108×rewrite-expression-head
Calls

312 calls:

32.7s
(+ (/ (+ (pow (* 5.5 (pow 33096.0 8.0)) 3) (* (+ (* (* 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))) (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))) (+ (* (* 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)))) (* (* 5.5 (pow 33096.0 8.0)) (- (* 5.5 (pow 33096.0 8.0)) (+ (* (* 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))))))) (/ 77617.0 (* 2.0 33096.0)))
30.4s
(+ (/ (+ (pow (* 5.5 (pow 33096.0 8.0)) 3) (* (+ (* (* 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))) (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))) (+ (* (* 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)))) (* (* 5.5 (pow 33096.0 8.0)) (- (* (* 5.5 (pow (* (cbrt 33096.0) (cbrt 33096.0)) 8.0)) (pow (cbrt 33096.0) 8.0)) (+ (* (* 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))))))) (/ 77617.0 (* 2.0 33096.0)))
5.7s
(+ (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))
4.3s
(+ (+ (* 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)))
4.2s
(* x1 (+ (* 2.0 (* (/ (- (+ (* (* 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))) 6.0))))
Rules
2973×add-sqr-sqrt *-un-lft-identity
2671×times-frac
1912×add-cube-cbrt
1805×add-exp-log
1573×add-cbrt-cube
1079×associate-*r*
848×pow1
734×add-log-exp
673×prod-exp
587×cbrt-unprod
546×associate-*r/
451×associate-*l*
439×unpow-prod-down
436×cbrt-prod
423×flip-- flip3--
406×frac-times
389×div-exp
387×distribute-lft-out
368×cbrt-div
356×sqrt-prod
343×cbrt-undiv
302×difference-of-squares
282×associate-*l/
261×pow-prod-down
251×associate-/r*
247×associate-/l*
245×flip-+ flip3-+
210×cube-prod
204×unswap-sqr
194×frac-add
187×distribute-lft-out--
178×sqr-pow
177×associate-/r/
175×sum-log
174×div-inv
106×sqrt-div
101×frac-sub
93×sub-neg
85×*-commutative
83×associate-/l/
80×exp-neg sqrt-pow1
79×diff-log
72×distribute-rgt-neg-in
68×unpow2
67×swap-sqr pow-exp
66×distribute-lft-neg-in
65×neg-sub0
60×exp-diff
57×distribute-rgt-in distribute-lft-in
54×pow1/2 clear-num pow-to-exp frac-2neg
53×cube-mult
52×unpow3
50×+-commutative
40×log-prod
34×associate-+l+
31×pow-prod-up
28×pow-unpow rem-sqrt-square
26×pow1/3
25×un-div-inv
22×pow-sqr neg-mul-1 div-sub
19×associate-+r+
18×cube-div
15×associate--r+
14×pow-plus
12×associate--l+
11×rem-cube-cbrt pow2
10×log-pow pow-pow log-div
rec-exp rem-cbrt-cube 1-exp
associate--l-
sqrt-unprod
distribute-lft-neg-out associate-+r- distribute-frac-neg associate--r-
sub-div neg-log sum-cubes rem-log-exp
inv-pow cube-unmult distribute-rgt-out-- pow-flip rem-square-sqrt distribute-rgt-out associate-+l-
unsub-neg distribute-lft1-in distribute-rgt1-in unpow-prod-up

sample1.3m (10.8%)

Algorithm
73×intervals
Results
28.5s294377×body80valid
9.0s13724×body1280valid
5.4s16808×body160valid
5.2s3775×body2560valid
3.9s100609×pre80true
3.7s9384×body640valid
2.4s2183×body10240exit
1.7s7009×body320valid
1.4s19545×body80nan
206.0ms223×body5120valid
6.0ms100×pre80false

prune43.7s (6.2%)

series37.6s (5.4%)

Calls

312 calls:

828.0ms
(/ (* (* a c) 4.0) (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
689.0ms
(cbrt (pow (- (* 9.0 (pow x 4.0)) (pow y 4.0)) 3))
656.0ms
(- (* 9.0 (pow x 4.0)) (pow y 4.0))
623.0ms
(* 5.5 (pow y 8.0))
620.0ms
(- (* 9.0 (pow x 4.0)) (pow y 4))

regimes4.4s (0.6%)

Accuracy

Total 34.6b remaining (8%)

Threshold costs 2.7b (0.6%)

10.6b52.2%Compound Interest
4.8b82.2%The quadratic formula (r2)
4.5b76.5%Kahan p9 Example
3.5b87.9%The quadratic formula (r1)
2.8b3.9%Complex division, real part

localize2.7s (0.4%)

bsearch1.8s (0.3%)

end2.0ms (0.0%)