Details

simplify5.3m (59.1%)

sample1.3m (14.3%)

Algorithm
73×intervals
Results
28.9s294792×body80valid
9.3s13889×body1280valid
6.0s16858×body160valid
3.9s9364×body640valid
3.6s3872×body2560valid
3.5s2182×body10240exit
2.6s100661×pre80true
2.1s6830×body320valid
1.4s19374×body80nan
225.0ms234×body5120valid
7.0ms100×pre80false

prune1.0m (11.2%)

series47.0s (8.7%)

Calls

298 calls:

2.0s
(+ (pow y 6.0) (fma (pow y 4.0) 121.0 2.0))
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)) (* (* (* (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
(cbrt (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
1.1s
(cbrt (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
1.0s
(cbrt (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))

rewrite27.4s (5.1%)

Algorithm
105×rewrite-expression-head
Calls

298 calls:

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))) (/ 77617.0 (* 2.0 33096.0)))
1.6s
(+ (+ (* 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)))
1.3s
(+ (* (* (* 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))))
1.2s
(+ (* (* (* 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)) (* (* x1 x1) (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0)))
1.1s
(- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)
Rules
10464×times-frac
9496×*-un-lft-identity
8322×add-sqr-sqrt
7062×add-cube-cbrt
4256×prod-diff
1366×add-exp-log
1166×add-cbrt-cube
948×distribute-lft-out
700×associate-*r*
674×distribute-rgt-in distribute-lft-in
671×div-inv
629×pow1
613×add-log-exp
550×associate-+r+
507×associate-*l/
492×associate-*l*
490×unpow-prod-down
470×difference-of-squares
452×frac-times
440×cbrt-div
410×flip3-- flip--
401×sqrt-prod
391×prod-exp
354×associate-*r/
332×div-exp
319×associate-/l*
315×cbrt-unprod
307×cube-prod
299×log1p-expm1-u
298×expm1-log1p-u
296×distribute-lft-out--
295×distribute-rgt-neg-in
292×associate-/r*
290×distribute-lft-neg-in
271×cbrt-undiv
270×associate-+l+
251×associate-/r/
228×fma-neg
225×flip-+ flip3-+
195×sqr-pow
185×cbrt-prod
157×frac-add
138×pow-prod-down
133×sum-log
131×unswap-sqr
112×fma-def
101×frac-sub
98×neg-mul-1
93×unpow3 cube-mult
74×exp-neg
73×associate-/l/
68×sub-neg
66×swap-sqr
65×neg-sub0
62×*-commutative
59×clear-num frac-2neg
56×exp-diff
54×diff-log
48×fma-udef
41×sqrt-div
36×pow1/3
32×+-commutative
25×pow-unpow
24×div-sub
23×un-div-inv 1-exp pow-to-exp rec-exp pow-exp
20×pow1/2 sqrt-pow1
19×rem-sqrt-square
18×pow-prod-up log-prod
16×pow-sqr log-pow
14×unpow2 pow-plus
12×exp-prod
11×pow2 associate--l+
10×pow-pow
neg-log
associate--l-
associate-+r- distribute-frac-neg log-div
rem-exp-log unsub-neg rem-cbrt-cube
rem-cube-cbrt expm1-udef hypot-def rem-log-exp
cube-div distribute-lft-neg-out expm1-log1p
sqrt-undiv log1p-udef inv-pow log1p-expm1 unpow-prod-up hypot-udef pow-flip distribute-rgt-out associate-+l- associate--r+

regimes4.3s (0.8%)

Accuracy

Total 34.7b remaining (15%)

Threshold costs 3.6b (1.6%)

12.7b51.4%Compound Interest
7.8b30.9%Complex division, real part
4.5b84.3%The quadratic formula (r1)
3.7b86.5%The quadratic formula (r2)
1.2b0%Rosa's DopplerBench

localize2.5s (0.5%)

bsearch1.5s (0.3%)

end1.0ms (0.0%)