Details

simplify6.8m (61.1%)

rewrite1.3m (11.6%)

Algorithm
112×rewrite-expression-head
Calls

337 calls:

9.6s
(+ (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))) (+ (* (* 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)))))
9.1s
(+ (* (* (* 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 x1) (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0)))
8.4s
(+ (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))) (+ (* (* 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)))))
5.7s
(+ (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))
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
5288×add-sqr-sqrt
5167×times-frac
4903×*-un-lft-identity
2867×add-cube-cbrt
1796×add-exp-log
1578×associate-*r*
1513×add-cbrt-cube
1215×sqrt-prod
1088×difference-of-squares
990×unpow-prod-down
872×pow1
779×add-log-exp
707×associate-*l*
697×cube-prod
657×distribute-lft-out
621×associate-*r/
605×prod-exp
495×cbrt-unprod
420×flip-- flip3--
412×distribute-lft-out--
400×div-exp
379×sqr-pow
378×cbrt-div
376×frac-times
340×associate-/l*
313×flip-+ flip3-+
300×cbrt-undiv
288×associate-/r*
250×pow-prod-down div-inv
237×associate-/r/
228×sqrt-div
215×frac-add
193×unswap-sqr
189×cbrt-prod
178×associate-*l/
160×sum-log
116×sub-neg
101×diff-log
91×*-commutative
88×swap-sqr
76×associate-/l/
68×distribute-rgt-in distribute-lft-in exp-prod
65×pow-unpow
63×pow-exp
59×clear-num frac-2neg
55×cube-mult
51×sqrt-pow1
50×frac-sub
48×pow-to-exp
47×pow-pow
46×log-prod
45×+-commutative
44×pow1/3
43×distribute-rgt-neg-in
42×pow1/2
40×rem-sqrt-square log-pow unpow3
39×1-exp
37×unpow2
33×distribute-lft-neg-in rec-exp
32×associate-+r+
29×pow-prod-up
27×associate--l+
26×pow-sqr
23×div-sub
21×associate-+l+
19×distribute-rgt-out
18×difference-cubes
15×distribute-lft1-in
14×pow-plus sum-cubes
12×rem-cube-cbrt associate--l- pow2
11×neg-mul-1
10×cube-div rem-log-exp
8×log-div
6×distribute-lft-neg-out associate-+r- associate--r+
5×un-div-inv inv-pow unpow-prod-up pow-flip distribute-frac-neg neg-sub0
4×rem-exp-log neg-log exp-sum rem-cbrt-cube exp-to-pow
2×sqrt-pow2 pow3
1×unsub-neg sqrt-unprod rem-square-sqrt associate--r- associate-+l-

sample1.2m (11.1%)

Algorithm
73×intervals
Results
27.7s293544×body80valid
9.6s13804×body1280valid
5.6s16942×body160valid
3.9s3830×body2560valid
3.4s9450×body640valid
3.1s2195×body10240exit
2.9s6699×body320valid
2.6s100652×pre80true
1.5s19194×body80nan
218.0ms217×body5120valid
6.0ms100×pre80false

series51.8s (7.7%)

Calls

337 calls:

2.1s
(log (pow (exp (pow (* (cbrt (sqrt (/ (* 2.0 t) (+ 1.0 t)))) (cbrt (sqrt (/ (* 2.0 t) (+ 1.0 t))))) 4)) (pow (cbrt (sqrt (/ (* 2.0 t) (+ 1.0 t)))) (+ 3 1))))
1.9s
(pow (exp (pow (* (cbrt (sqrt (/ (* 2.0 t) (+ 1.0 t)))) (cbrt (sqrt (/ (* 2.0 t) (+ 1.0 t))))) 4)) (pow (cbrt (sqrt (/ (* 2.0 t) (+ 1.0 t)))) (+ 3 1)))
1.1s
(* (+ (sqrt (exp x)) (sqrt 1.0)) (/ (/ (- (pow (sqrt (exp x)) 3) (pow (sqrt 1.0) 3)) (+ (exp x) (+ 1.0 (* (sqrt (exp x)) (sqrt 1.0))))) x))
958.0ms
(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)) (* (* x1 x1) (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0))))
721.0ms
(- (* 9.0 (pow x 4.0)) (pow y 4))

prune48.6s (7.2%)

regimes4.1s (0.6%)

Accuracy

Total 35.9b remaining (8.3%)

Threshold costs 3.3b (0.8%)

12.2b45.9%Compound Interest
4.6b77.1%Kahan p9 Example
4.3b84.6%The quadratic formula (r1)
4.0b85.9%The quadratic formula (r2)
3.1b0%Complex division, imag part

localize3.0s (0.4%)

bsearch1.9s (0.3%)

end1.0ms (0.0%)