Details

simplify3.2m (45.6%)

sample1.2m (17.6%)

Algorithm
73×intervals
Results
26.8s294435×body80valid
9.5s13744×body1280valid
5.5s16992×body160valid
4.7s3942×body2560valid
4.4s9404×body640valid
2.7s2246×body10240exit
2.3s100627×pre80true
2.1s6772×body320valid
1.3s19671×body80nan
176.0ms258×body5120valid
7.0ms100×pre80false

rewrite56.9s (13.5%)

Algorithm
110×rewrite-expression-head
Calls

316 calls:

10.0s
(+ (* (* (* 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)))) (* (* x1 x1) (- 6.0))))
6.8s
(* (cbrt (+ (* 2.0 2.0) (- (* (* (/ (* 2.0 t) (+ 1.0 t)) (/ (* 2.0 t) (+ 1.0 t))) (* (/ (* 2.0 t) (+ 1.0 t)) (/ (* 2.0 t) (+ 1.0 t)))) (* 2.0 (* (/ (* 2.0 t) (+ 1.0 t)) (/ (* 2.0 t) (+ 1.0 t))))))) (cbrt (+ (* 2.0 2.0) (- (* (* (/ (* 2.0 t) (+ 1.0 t)) (/ (* 2.0 t) (+ 1.0 t))) (* (/ (* 2.0 t) (+ 1.0 t)) (/ (* 2.0 t) (+ 1.0 t)))) (* 2.0 (* (/ (* 2.0 t) (+ 1.0 t)) (/ (* 2.0 t) (+ 1.0 t))))))))
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)))
1.8s
(+ (* (* (* 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)))) (* (* x1 x1) (- 6.0))))
1.8s
(+ (+ (+ (* 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)))
Rules
4875×times-frac
4331×*-un-lft-identity
4277×add-sqr-sqrt
2767×add-cube-cbrt
1689×add-exp-log
1421×add-cbrt-cube
1114×associate-*r*
770×pow1
745×sqrt-prod
732×add-log-exp
690×associate-*r/
603×frac-times
581×cbrt-div
544×associate-*l*
543×flip-- difference-of-squares flip3--
539×prod-exp
514×unpow-prod-down
451×distribute-lft-out
432×cbrt-unprod
412×div-exp
393×flip-+ flip3-+
384×distribute-lft-out--
380×associate-/r*
355×cbrt-prod
327×associate-/l* associate-*l/
320×cbrt-undiv
316×associate-/r/
292×frac-add
288×div-inv
205×sqr-pow
201×pow-prod-down
192×cube-prod
182×unswap-sqr
163×sum-log
162×distribute-rgt-neg-in
137×associate-/l/
129×distribute-lft-neg-in
124×frac-sub
104×sqrt-div
91×sub-neg
83×diff-log
80×exp-neg
78×*-commutative
73×neg-sub0
70×swap-sqr unpow2
66×exp-diff clear-num frac-2neg
63×sqrt-pow1
50×pow-exp
46×pow-to-exp
45×distribute-rgt-in distribute-lft-in
43×+-commutative neg-mul-1
42×pow1/2
37×pow-prod-up
33×1-exp
32×un-div-inv pow1/3
31×pow-unpow
30×rec-exp
29×associate-+l+
28×rem-sqrt-square
23×associate-+r+
21×pow-sqr
19×pow-plus unpow3 cube-mult
16×cube-div div-sub
14×associate--l+
13×pow2 pow-pow
11×associate--l- log-prod
10×neg-log
exp-prod
associate--r+ log-div
associate-+r- exp-sum
inv-pow distribute-lft-neg-out pow-flip rem-cbrt-cube
rem-cube-cbrt distribute-frac-neg
unsub-neg log-pow distribute-rgt-neg-out
difference-cubes rem-exp-log distribute-lft1-in sqrt-unprod rem-square-sqrt distribute-rgt-out associate-+l-
sqrt-pow2 pow3 cube-unmult distribute-rgt-out-- sub-div exp-to-pow rem-log-exp

prune48.0s (11.4%)

series40.0s (9.5%)

Calls

316 calls:

784.0ms
(+ (* (* (* 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) (* (cbrt (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0)) (cbrt (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0)))) (cbrt (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0))))
746.0ms
(cbrt (pow (- (* 9.0 (pow x 4.0)) (pow y 4.0)) 3))
708.0ms
(- (* 9.0 (pow x 4.0)) (pow y 4.0))
670.0ms
(- (* 9.0 (pow x 4.0)) (* (* y y) (* y y)))
635.0ms
(- (* 9.0 (pow x 4.0)) (pow y 4.0))

regimes4.9s (1.2%)

Accuracy

Total 40.8b remaining (9.1%)

Threshold costs 3.8b (0.8%)

13.8b51.3%Compound Interest
6.9b-1600.6%Rosa's TurbineBenchmark
5.0b75%Kahan p9 Example
3.3b88.5%The quadratic formula (r2)
3.1b-2.2%Complex division, real part

localize2.9s (0.7%)

bsearch2.2s (0.5%)

end1.0ms (0.0%)