Details

rewrite1.2m (32.4%)

Algorithm
108×rewrite-expression-head
Calls

304 calls:

44.7s
(+ (+ (* (* (* (* 2.0 x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (* (cbrt (- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)) (cbrt (- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)))) (cbrt (- (/ (- (+ (* (* 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 (* x1 (- 6.0))))
3.4s
(+ (+ (* (* (* 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 (* x1 (- 6.0))))
2.5s
(+ (+ (* 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)))
1.1s
(+ (+ (+ (* 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))) (/ 77617.0 (* 2.0 33096.0)))
1.1s
(* (* (* 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
7017×times-frac
5704×*-un-lft-identity
5006×add-sqr-sqrt
3338×add-cube-cbrt
1556×add-exp-log
1253×add-cbrt-cube
831×distribute-lft-out
771×add-log-exp
755×difference-of-squares
733×unpow-prod-down
707×associate-*l*
670×pow1
661×associate-*r*
560×associate-/r*
528×sqrt-prod
464×distribute-rgt-neg-in
461×prod-exp
435×distribute-lft-neg-in
416×div-exp
393×associate-/r/
377×sqr-pow
364×cbrt-unprod
349×distribute-lft-out--
342×associate-/l*
334×associate-*r/
324×div-inv
269×cbrt-undiv
266×flip3-- flip--
254×flip-+ flip3-+
197×unpow2
187×sum-log
162×pow-prod-down
145×neg-mul-1
139×unswap-sqr
120×cube-prod
109×sub-neg
105×frac-times
90×associate-/l/
88×diff-log
80×associate-*l/
74×cbrt-prod
73×distribute-rgt-in frac-add swap-sqr distribute-lft-in
71×sqrt-div
68×clear-num frac-2neg
66×*-commutative
56×pow-exp
53×+-commutative
52×pow-to-exp
45×log-prod
37×associate-+l+
35×1-exp rec-exp
34×associate-+r+ frac-sub
31×rem-sqrt-square
25×div-sub
24×pow1/2 sqrt-pow1
20×log-div
19×pow-unpow
17×pow-prod-up associate--l+
15×pow-plus cbrt-div associate--r+
13×pow-sqr log-pow
12×unpow3 cube-mult neg-sub0
11×distribute-rgt-out--
10×difference-cubes associate--l- pow2 sub-div neg-log pow-pow
exp-prod exp-sum
cube-div pow1/3 distribute-rgt-neg-out
inv-pow pow-flip rem-log-exp
pow3 associate-+l-
associate-+r- unsub-neg associate--r- rem-cbrt-cube
distribute-frac-neg exp-to-pow
exp-diff rem-exp-log distribute-lft-neg-out distribute-rgt-out distribute-neg-frac
rem-cube-cbrt un-div-inv distribute-lft1-in

prune1.2m (32.2%)

sample39.4s (17.3%)

Algorithm
73×intervals
Results
14.5s294392×body80valid
5.2s13520×body1280valid
2.7s3867×body2560valid
2.4s9616×body640valid
2.0s16879×body160valid
1.9s2182×body10240exit
1.4s100625×pre80true
1.1s6878×body320valid
628.0ms19722×body80nan
94.0ms229×body5120valid
4.0ms100×pre80false

series23.1s (10.1%)

Calls

304 calls:

909.0ms
(cbrt (* 100.0 (* (/ (+ (+ (* 1.0 i) (* (log 1.0) n)) (* (pow i 2) (- 0.5 (* 0.5 (log 1.0))))) i) n)))
607.0ms
(- (* 9.0 (pow x 4.0)) (pow y 4))
484.0ms
(+ (+ (* (* (* (* 2.0 x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (* (cbrt (- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)) (cbrt (- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)))) (cbrt (- (/ (- (+ (* (* 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 (* x1 (- 6.0))))
402.0ms
(cbrt (pow (- (* 9.0 (pow x 4.0)) (pow y 4)) 3))
400.0ms
(cbrt (pow (- (* 9.0 (pow x 4.0)) (pow y 4.0)) 3))

simplify9.4s (4.1%)

Algorithm
178×egg-herbie

regimes5.7s (2.5%)

Accuracy

Total 34.9b remaining (8.3%)

Threshold costs 4.0b (0.9%)

12.9b44.5%Compound Interest
5.5b73.8%Kahan p9 Example
4.2b85.2%The quadratic formula (r2)
3.2b89%The quadratic formula (r1)
2.8b9%Complex division, real part

bsearch1.6s (0.7%)

localize1.5s (0.6%)

end1.0ms (0.0%)