Details

simplify5.5m (54.4%)

rewrite1.6m (16.0%)

Algorithm
115×rewrite-expression-head
Calls

338 calls:

39.0s
(/ (+ (* (* (+ (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))) 2.0) 33096.0) (* (+ (* (+ (* (* 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 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)) (* (+ (* (+ (* (* 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 (* (cbrt 33096.0) (cbrt 33096.0)) 8.0)) (pow (cbrt 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)))))) (* 2.0 33096.0)))
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))
4.6s
(+ (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)))
4.2s
(+ (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)))
3.9s
(+ (+ (* 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)))
Rules
4496×add-sqr-sqrt
4480×times-frac
4240×*-un-lft-identity
2414×add-cube-cbrt
2020×add-exp-log
1739×add-cbrt-cube
929×pow1
922×difference-of-squares
747×add-log-exp
738×associate-*r*
670×prod-exp
656×unpow-prod-down
564×associate-*l*
554×cbrt-unprod
522×associate-/r*
519×distribute-lft-out--
487×div-exp
433×distribute-lft-out
403×cbrt-undiv
399×flip-+ flip3-+
384×associate-/l*
373×sqrt-prod
331×associate-/r/
322×associate-*r/
305×cube-prod
298×associate-*l/
285×sqr-pow
279×div-inv
264×flip3-- flip--
247×frac-times
234×pow-prod-down
190×cbrt-prod
167×frac-add
151×sum-log
146×associate-/l/
141×unswap-sqr
113×sub-neg
94×frac-sub
89×swap-sqr diff-log
86×pow-prod-up
85×*-commutative
78×cbrt-div
77×clear-num frac-2neg
72×exp-neg
68×sqrt-div
67×pow-exp
64×sqrt-pow1
61×pow1/2
58×pow-plus
57×distribute-rgt-in neg-sub0 distribute-lft-in
54×exp-diff
52×unpow2
51×pow-to-exp
45×pow-unpow
41×+-commutative
36×distribute-rgt-neg-in
34×pow-sqr
33×distribute-lft-neg-in
28×distribute-lft1-in distribute-rgt-out div-sub
25×un-div-inv
24×1-exp rec-exp
23×associate-+l+ rem-sqrt-square associate-+r+
22×unpow3 cube-mult exp-sum pow-pow
21×pow1/3
18×cube-div
15×pow2
14×rem-cube-cbrt difference-cubes
11×cube-unmult neg-mul-1
8×associate--l+
7×associate--l- associate--r+
6×inv-pow distribute-lft-neg-out pow-flip
5×rem-cbrt-cube
4×log-prod
3×distribute-rgt-out-- associate-+r- distribute-frac-neg exp-prod sum-cubes
2×neg-log log-div
1×sqrt-pow2 unsub-neg pow3 sub-div log-pow associate--r- associate-+l- rem-log-exp

sample1.3m (12.9%)

Algorithm
73×intervals
Results
29.4s293756×body80valid
10.7s13892×body1280valid
5.0s3867×body2560valid
4.8s16772×body160valid
3.9s9318×body640valid
3.4s2226×body10240exit
2.8s100598×pre80true
1.7s6939×body320valid
1.4s19601×body80nan
195.0ms238×body5120valid
4.0ms100×pre80false

prune51.7s (8.5%)

series40.8s (6.7%)

Calls

338 calls:

807.0ms
(+ (* (/ (- (+ (* (* 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
(cbrt (pow (- (* 9.0 (pow x 4.0)) (pow y 4.0)) 3))
696.0ms
(- (* 9.0 (pow x 4.0)) (pow y 4.0))
678.0ms
(cbrt (pow (- (* 9.0 (pow x 4.0)) (pow y 4)) 3))
646.0ms
(* (/ (- (+ (* (* 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))))

regimes4.4s (0.7%)

Accuracy

Total 42.0b remaining (9.7%)

Threshold costs 3.2b (0.7%)

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

localize2.7s (0.5%)

bsearch2.3s (0.4%)

end0.0ms (0.0%)