Details

simplify5.6m (58.8%)

sample1.3m (13.3%)

Algorithm
73×intervals
Results
28.9s293756×body80valid
11.2s13892×body1280valid
5.6s16772×body160valid
4.3s9318×body640valid
4.2s3867×body2560valid
3.3s2226×body10240exit
3.2s100598×pre80true
2.1s6939×body320valid
1.9s19601×body80nan
309.0ms238×body5120valid
7.0ms100×pre80false

prune1.2m (12.5%)

series48.2s (8.5%)

Calls

318 calls:

2.3s
(+ (pow y 6.0) (fma (pow y 4.0) 121.0 2.0))
1.8s
(+ (* (* (* 2.0 x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (fma (/ (* (cbrt (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1)) (cbrt (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1))) (sqrt (+ (* x1 x1) 1.0))) (/ (cbrt (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1)) (sqrt (+ (* x1 x1) 1.0))) (- (* (cbrt 3.0) (* (cbrt 3.0) (cbrt 3.0)))))) (fma (* x1 x1) (- (* 4.0 (/ (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0))) 6.0) (* (+ (- 3.0) 3.0) (* (/ (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0)) (* 2.0 x1)))))
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)) (* (* (* (cbrt (- (* 4.0 (/ (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0))) 6.0)) (cbrt (- (* 4.0 (/ (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0))) 6.0))) (* x1 x1)) (cbrt (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0))))
842.0ms
(/ 1 (/ (+ (pow (sqrt (/ (* 2.0 t) (+ 1.0 t))) (+ 3 1)) 2.0) (+ 1.0 (pow (sqrt (/ (* 2.0 t) (+ 1.0 t))) (+ 3 1)))))
766.0ms
(expm1 (log1p (sqrt (/ (- 1.0 x) (+ 1.0 x)))))

rewrite30.0s (5.3%)

Algorithm
108×rewrite-expression-head
Calls

318 calls:

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)))
1.7s
(+ (+ (* 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)))
1.2s
(+ (* (* (* 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)) (* (* (* (cbrt (- (* 4.0 (/ (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0))) 6.0)) (cbrt (- (* 4.0 (/ (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0))) 6.0))) (* x1 x1)) (cbrt (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0))))
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)) (* (* x1 x1) (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0)))
952.0ms
(- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)
Rules
13090×times-frac
12322×*-un-lft-identity
11382×add-sqr-sqrt
9370×add-cube-cbrt
6637×prod-diff
1658×add-exp-log
1434×add-cbrt-cube
1067×distribute-lft-out
1009×unpow-prod-down
913×difference-of-squares
870×div-inv
814×associate-*r*
794×associate-+l+
686×distribute-rgt-in distribute-lft-in
667×pow1
646×add-log-exp
616×cube-prod
499×associate-*l*
498×prod-exp
434×associate-/l*
429×distribute-lft-out--
419×div-exp
412×cbrt-unprod
386×associate-/r*
384×flip-- flip3--
377×associate-/r/
356×sqr-pow
345×cbrt-undiv
343×frac-times
340×associate-*l/
326×sqrt-prod fma-neg
319×log1p-expm1-u
318×expm1-log1p-u
308×associate-*r/
284×cbrt-div
242×flip-+ flip3-+
226×cbrt-prod
153×frac-add
142×pow-prod-down
131×distribute-rgt-neg-in
129×sum-log
127×unpow3 cube-mult
126×fma-def
117×unswap-sqr
114×distribute-lft-neg-in
98×frac-sub
87×swap-sqr
83×associate-/l/
80×sub-neg
72×exp-neg
69×clear-num frac-2neg
68×*-commutative
64×diff-log
62×neg-sub0
54×exp-diff
44×pow-unpow
41×fma-udef
38×neg-mul-1
36×pow-exp
33×+-commutative rec-exp 1-exp
29×sqrt-div
28×pow-to-exp
24×div-sub exp-sum
23×un-div-inv associate-+r+
22×pow-prod-up pow-pow
21×pow-plus
20×pow1/3
19×exp-prod
18×log-pow
16×pow-sqr
15×pow2
14×pow1/2 rem-sqrt-square sqrt-pow1
13×difference-cubes
rem-cube-cbrt
distribute-frac-neg
log-prod rem-cbrt-cube
inv-pow hypot-udef pow-flip
associate--l- expm1-udef unpow2
cube-div expm1-log1p neg-log associate-+l-
sqrt-pow2 log1p-udef distribute-lft-neg-out log1p-expm1 unpow-prod-up distribute-rgt-neg-out rem-log-exp log-div
associate-+r- unpow1/3 pow3 unsub-neg distribute-rgt-out hypot-def associate--l+

regimes4.2s (0.7%)

Accuracy

Total 33.5b remaining (14.7%)

Threshold costs 4.8b (2.1%)

12.8b52.9%Compound Interest
6.7b37.4%Complex division, real part
4.6b83.5%The quadratic formula (r1)
3.4b87.7%The quadratic formula (r2)
1.2b0%Rosa's DopplerBench

localize2.8s (0.5%)

bsearch1.9s (0.3%)

end0.0ms (0.0%)