Details

simplify9.2m (70.0%)

prune1.5m (11.1%)

sample1.2m (9.4%)

Algorithm
73×intervals
Results
25.4s286450×body80valid
10.2s13861×body1280valid
10.0s25107×body160valid
4.1s3831×body2560valid
3.9s9354×body640valid
3.4s2227×body10240exit
2.3s100605×pre80true
2.1s6845×body320valid
1.3s19460×body80nan
202.0ms253×body5120valid
6.0ms100×pre80false

series40.3s (5.1%)

Calls

285 calls:

2.0s
(+ (fma 121.0 (pow y 4.0) 2.0) (pow y 6.0))
1.5s
(fma (sqrt (pow x 4.0)) (sqrt (pow x 4.0)) (- (pow y 4.0)))
747.0ms
(+ (* (* (* 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)) (+ (* (fma 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) (- (* (sqrt 6.0) (sqrt 6.0)))) (* x1 x1)) (* (+ (- 6.0) (* (sqrt 6.0) (sqrt 6.0))) (* x1 x1))))
741.0ms
(- (* 9.0 (pow x 4.0)) (pow y 4.0))
683.0ms
(- (* 9.0 (pow x 4.0)) (pow y 4.0))

rewrite22.6s (2.9%)

Algorithm
101×rewrite-expression-head
Calls

285 calls:

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)))
1.4s
(- (+ (exp (* x (- eps 1.0))) (/ (exp (* x (- eps 1.0))) eps)) (/ (exp (- (* x (+ eps 1.0)))) eps))
898.0ms
(+ (* (* (* 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)) (* (* (cbrt (* (* x1 x1) (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0))) (cbrt (* (* x1 x1) (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0)))) (cbrt (* (* x1 x1) (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0)))))
851.0ms
(+ (* (* (* 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)) (+ (* (fma 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) (- (* (sqrt 6.0) (sqrt 6.0)))) (* x1 x1)) (* (+ (- 6.0) (* (sqrt 6.0) (sqrt 6.0))) (* x1 x1))))
834.0ms
(+ (* (* (* 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) (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0)))
Rules
6701×times-frac
6661×*-un-lft-identity
6495×add-sqr-sqrt
5160×add-cube-cbrt
3012×prod-diff
1371×add-exp-log
1277×add-cbrt-cube
982×sqrt-prod
876×pow1
867×distribute-rgt-in distribute-lft-in
640×associate-*r/
618×add-log-exp
609×associate-*r*
543×difference-of-squares
500×div-inv
456×prod-exp
437×cbrt-unprod
416×associate-*l*
412×distribute-lft-out--
410×flip3-- flip--
404×associate-+l+
396×frac-times
388×distribute-lft-out cbrt-div
365×associate-/l*
309×associate-/r*
287×expm1-log1p-u
286×div-exp
285×log1p-expm1-u
269×pow-prod-down
246×cbrt-undiv
243×fma-neg
228×associate-*l/
193×flip-+ flip3-+
171×frac-add
168×cbrt-prod
165×associate-/r/
158×unpow-prod-down
139×sum-log
126×distribute-rgt-neg-in
118×distribute-lft-neg-in
112×exp-sum
101×frac-sub
99×unswap-sqr
91×sub-neg
77×sqr-pow fma-def exp-neg
75×*-commutative
71×associate-/l/
66×diff-log
64×neg-sub0
58×exp-diff frac-2neg clear-num
55×pow-prod-up
48×pow1/3
46×swap-sqr
42×pow-plus
40×log-prod sqrt-pow1 neg-mul-1
39×associate--l+
38×pow1/2
35×sqrt-div
33×pow-sqr
31×fma-udef
30×associate-+r+
26×+-commutative
24×div-sub distribute-neg-in
21×rem-sqrt-square
20×un-div-inv
19×pow2 log-pow
16×1-exp
11×associate--l-
10×rec-exp log-div
pow-flip pow3 distribute-frac-neg sqrt-unprod associate--r+
exp-prod
pow-exp neg-log pow-to-exp hypot-def distribute-rgt-out
distribute-lft-neg-out cube-prod
pow-unpow inv-pow rem-log-exp
associate-+r- log1p-expm1 hypot-udef rem-exp-log rem-cbrt-cube associate--r- log1p-udef
expm1-log1p expm1-udef unpow3 pow-pow rem-square-sqrt cube-mult unsub-neg

regimes7.6s (1.0%)

Accuracy

Total 37.7b remaining (14.8%)

Threshold costs 2.4b (0.9%)

10.7b53.1%Compound Interest
7.5b34.2%Complex division, real part
4.4b79.1%Kahan p9 Example
4.1b85.9%The quadratic formula (r2)
3.4b0%Complex division, imag part

localize4.4s (0.6%)

bsearch896.0ms (0.1%)

end1.0ms (0.0%)