Details

simplify5.3m (59.4%)

sample1.2m (13.3%)

Algorithm
73×intervals
Results
26.4s294792×body80valid
10.2s13889×body1280valid
5.5s16858×body160valid
4.7s9364×body640valid
4.0s3872×body2560valid
2.9s100661×pre80true
2.5s6830×body320valid
2.5s2182×body10240exit
1.6s19374×body80nan
185.0ms234×body5120valid
4.0ms100×pre80false

prune1.0m (11.5%)

series48.7s (9.1%)

Calls

289 calls:

2.3s
(+ (pow y 6.0) (fma (pow y 4.0) 121.0 2.0))
1.4s
(+ (* (* (* 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) (+ (* x1 x1) 1.0))) (cbrt (/ (- (+ (* (* 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))) (- (* (cbrt 3.0) (* (cbrt 3.0) (cbrt 3.0)))))) (fma (/ (* (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (* 2.0 x1)) (fma x1 x1 1.0)) (+ (- 3.0) 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))) (* (cbrt (- (* 4.0 (/ (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0))) 6.0)) (* x1 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))))
989.0ms
(cbrt (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
973.0ms
(cbrt (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))

rewrite26.8s (5.0%)

Algorithm
104×rewrite-expression-head
Calls

289 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)))
1.3s
(+ (+ (* 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))))
1.0s
(- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)
1.0s
(+ (* (* (* 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)))
Rules
10168×times-frac
9683×*-un-lft-identity
7949×add-sqr-sqrt
6666×add-cube-cbrt
3888×prod-diff
1404×add-exp-log
1220×distribute-lft-out
1207×add-cbrt-cube
852×distribute-rgt-in distribute-lft-in
719×associate-*r*
668×div-inv
637×pow1
575×add-log-exp
536×associate-*l*
524×associate-*l/
476×difference-of-squares
457×frac-times
442×cbrt-div
409×flip3-- flip--
394×prod-exp
363×associate-/l*
362×div-exp
360×associate-*r/
330×cbrt-unprod
321×distribute-rgt-neg-in
305×unpow-prod-down associate-/r*
302×associate-/r/
299×distribute-lft-neg-in
293×cbrt-undiv
290×distribute-lft-out-- log1p-expm1-u
289×expm1-log1p-u
273×associate-+l+
253×flip-+ flip3-+
244×sqrt-prod
189×cbrt-prod
169×fma-neg
160×frac-add
145×unswap-sqr
144×pow-prod-down
136×sqr-pow
121×cube-prod sum-log
103×fma-def
101×neg-mul-1
100×frac-sub
75×swap-sqr
74×exp-neg
69×associate-/l/
68×neg-sub0
64×*-commutative
61×clear-num sub-neg frac-2neg
56×exp-diff
47×diff-log
44×fma-udef
39×sqrt-div
36×pow1/3
32×unpow3 cube-mult +-commutative
25×1-exp rec-exp
24×pow-unpow
23×associate-+r+
22×un-div-inv
20×pow1/2 pow-to-exp pow-exp sqrt-pow1
19×pow-prod-up
18×rem-sqrt-square log-prod
17×pow-sqr
16×log-pow div-sub
15×unpow2 pow-plus
12×pow2 exp-prod
11×associate--l+
10×neg-log pow-pow
associate--l- distribute-frac-neg log-div
rem-exp-log unsub-neg pow-flip rem-cbrt-cube associate-+r-
rem-cube-cbrt expm1-udef associate-+l- rem-log-exp
cube-div inv-pow distribute-lft-neg-out expm1-log1p hypot-def
log1p-udef log1p-expm1 distribute-rgt-out associate--r+

regimes4.7s (0.9%)

Accuracy

Total 38.4b remaining (16%)

Threshold costs 3.2b (1.3%)

12.7b51.4%Compound Interest
7.8b30.9%Complex division, real part
7.1b35.9%Complex division, imag part
3.7b86.5%The quadratic formula (r2)
1.6b93.9%The quadratic formula (r1)

localize2.4s (0.5%)

bsearch1.7s (0.3%)

end1.0ms (0.0%)