Details

simplify8.5m (71.8%)

sample1.3m (11.0%)

Algorithm
73×intervals
Results
30.0s293719×body80valid
9.2s13893×body1280valid
5.4s16752×body160valid
4.7s9486×body640valid
4.4s3851×body2560valid
3.2s2115×body10240exit
2.9s100670×pre80true
1.9s6834×body320valid
1.4s19321×body80nan
169.0ms207×body5120valid
3.0ms100×pre80false

prune51.8s (7.3%)

series39.9s (5.6%)

Calls

272 calls:

2.0s
(+ (pow y 6.0) (fma (pow y 4.0) 121.0 2.0))
776.0ms
(expm1 (log1p (* (pow y 6.0) 333.75)))
622.0ms
(+ (* (* (* 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) (* (/ (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0)) 4.0)) (* (* x1 x1) (- 6.0))))
621.0ms
(+ (* (* (* 2.0 x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (fma (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (- (* (* x1 x1) (* x1 x1)) (* 1.0 1.0))) (- (* x1 x1) 1.0) (- 3.0))) (+ (/ (* (* x1 x1) (* (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) 4.0)) (fma x1 x1 1.0)) (* (* x1 x1) (- 6.0))))
604.0ms
(+ (* (* (* 2.0 x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (fma (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (- (* (* x1 x1) (* x1 x1)) (* 1.0 1.0))) (- (* x1 x1) 1.0) (- 3.0))) (+ (* (* x1 x1) (* (/ (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0)) 4.0)) (* (* x1 x1) (- 6.0))))

rewrite22.9s (3.2%)

Algorithm
100×rewrite-expression-head
Calls

272 calls:

1.9s
(+ (+ (+ (* 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)))
1.2s
(+ (* (* (* 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) (* (/ (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0)) 4.0)) (* (* x1 x1) (- 6.0))))
1.1s
(- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)
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)))
Rules
4781×*-un-lft-identity
4718×add-sqr-sqrt
4181×times-frac
3620×add-cube-cbrt
2031×prod-diff
1226×add-exp-log
1062×add-cbrt-cube
788×associate-*r*
621×associate-*l*
576×add-log-exp
574×pow1
526×distribute-rgt-in distribute-lft-in
451×unpow-prod-down
405×cbrt-prod
380×prod-exp
378×distribute-lft-out
365×difference-of-squares
342×div-inv
310×cbrt-unprod
278×associate-+l+
272×log1p-expm1-u expm1-log1p-u
269×sqrt-prod
255×div-exp
237×distribute-lft-out--
218×associate-/l*
210×cbrt-undiv
193×fma-neg
183×associate-/r*
180×distribute-rgt-neg-in
175×unswap-sqr
171×distribute-lft-neg-in
169×cube-prod
165×associate-*r/
156×flip-+ sqr-pow flip3-+
153×frac-times
145×pow-prod-down exp-prod
144×log-pow
139×sum-log
137×flip3-- flip--
128×associate-/r/
111×associate-*l/
95×fma-def
90×frac-sub
78×exp-neg
70×*-commutative
67×neg-sub0
60×exp-diff sub-neg
59×neg-mul-1
49×fma-udef clear-num frac-2neg
44×cbrt-div
43×diff-log
42×associate-/l/
34×frac-add
33×+-commutative
30×pow1/3
25×un-div-inv 1-exp log-prod rec-exp
24×associate-+r+ swap-sqr
21×sqrt-div
19×pow-exp
18×pow-unpow pow-to-exp
16×unpow3 cube-mult div-sub
15×unpow2
14×sqrt-pow1
13×rem-sqrt-square
12×pow1/2
10×distribute-frac-neg
pow-flip
cube-div
inv-pow distribute-lft-neg-out neg-log rem-cbrt-cube associate-+r-
associate--l- pow-prod-up pow-sqr distribute-rgt-neg-out pow-pow
rem-cube-cbrt pow2 pow-plus associate--l+
rem-exp-log unsub-neg distribute-rgt-out
log-div
expm1-udef distribute-lft1-in rem-log-exp
expm1-log1p hypot-udef associate-+l- associate--r+

regimes3.7s (0.5%)

Accuracy

Total 39.7b remaining (16%)

Threshold costs 2.6b (1.1%)

10.2b53.8%Compound Interest
9.8b14.2%Complex division, imag part
7.5b33%Complex division, real part
5.2b82.2%The quadratic formula (r2)
3.2b86.8%The quadratic formula (r1)

localize2.5s (0.3%)

bsearch1.4s (0.2%)

end1.0ms (0.0%)