Details

simplify6.8m (58.7%)

prune2.0m (17.3%)

sample1.2m (10.7%)

Algorithm
73×intervals
Results
26.4s285938×body80valid
10.4s25067×body160valid
8.5s13777×body1280valid
4.3s9416×body640valid
3.5s3731×body2560valid
3.3s2198×body10240exit
2.4s100640×pre80true
2.4s6899×body320valid
1.3s19502×body80nan
193.0ms244×body5120valid
6.0ms100×pre80false

rewrite41.3s (5.9%)

Algorithm
107×rewrite-expression-head
Calls

317 calls:

4.1s
(+ (* (* (* 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)) (+ (* (* (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) x1) x1) (* (- 6.0) (* x1 x1))))
4.1s
(+ (/ (* (* (* 2.0 x1) (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1)) (- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)) (+ (* x1 x1) 1.0)) (+ (* (* (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) x1) x1) (* (- 6.0) (* x1 x1))))
2.0s
(- (+ (/ (exp (* x (- eps 1.0))) eps) (exp (* x (- eps 1.0)))) (/ (exp (- (* x (+ eps 1.0)))) eps))
1.9s
(+ (* (* (* 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)) (+ (* (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (* x1 x1)) (* (- 6.0) (* x1 x1))))
1.8s
(- (+ (/ (exp (* x (- eps 1.0))) eps) (exp (* x (- eps 1.0)))) (/ (exp (- (* x (+ eps 1.0)))) eps))
Rules
11256×times-frac
9824×*-un-lft-identity
9326×add-sqr-sqrt
7352×add-cube-cbrt
3234×prod-diff
3041×add-exp-log
2717×add-cbrt-cube
2233×sqrt-prod
1229×prod-exp
1096×pow1
1093×cbrt-unprod
1051×associate-*r*
922×distribute-rgt-in distribute-lft-in
888×div-exp
737×cbrt-undiv
728×div-inv
705×difference-of-squares
676×frac-times
662×distribute-lft-out--
600×add-log-exp
579×distribute-lft-out
569×associate-/l*
546×associate-/r*
537×associate-*l*
412×associate-*r/
398×associate-+l+
369×pow-prod-down
364×flip3-- flip--
334×associate-/r/
317×expm1-log1p-u log1p-expm1-u
312×swap-sqr
309×flip-+ flip3-+
307×associate-*l/
244×fma-neg
222×cbrt-prod
197×distribute-rgt-neg-in
164×associate-/l/
159×unswap-sqr
156×distribute-lft-neg-in
109×sum-log
108×frac-sub
99×fma-def
91×sqrt-pow1 unpow-prod-down
89×exp-prod
88×*-commutative
80×exp-neg
78×frac-2neg clear-num
77×sub-neg
69×neg-sub0
67×pow-prod-up
65×associate--r+
62×exp-diff
58×diff-log
55×exp-sum
53×cbrt-div
52×sqr-pow neg-mul-1
51×sqrt-div log-pow
48×distribute-neg-in
44×pow-sqr
43×1-exp rec-exp
41×frac-add
39×pow1/2
38×log-prod
35×div-sub
33×pow1/3
28×pow-plus fma-udef
26×rem-sqrt-square
25×pow-exp pow-to-exp
21×un-div-inv
20×pow2 +-commutative
18×associate-+r+
10×distribute-lft-neg-out
associate--l- hypot-def
associate-+r- neg-log rem-exp-log
pow-flip pow-unpow inv-pow
sqrt-undiv rem-log-exp
associate--l+ distribute-frac-neg associate-+l- unsub-neg
log-div
pow-div pow3 sqrt-unprod pow-pow hypot-udef rem-square-sqrt
distribute-rgt-out-- cube-unmult sub-div exp-to-pow unpow1/3 rem-cbrt-cube associate--r-

series39.3s (5.6%)

Calls

317 calls:

1.0s
(- (* 9.0 (pow x 4.0)) (pow y 4.0))
708.0ms
(- (* 9.0 (pow x 4.0)) (pow y 4.0))
666.0ms
(cbrt (* (* (- (* 9.0 (pow x 4.0)) (pow y 4.0)) (- (* 9.0 (pow x 4.0)) (pow y 4.0))) (- (* 9.0 (pow x 4.0)) (pow y 4.0))))
661.0ms
(- (* 9.0 (pow x 4.0)) (pow y 4.0))
626.0ms
(- (* 9.0 (pow x 4.0)) (pow y 4.0))

regimes6.4s (0.9%)

Accuracy

Total 39.5b remaining (16.3%)

Threshold costs 2.6b (1.1%)

11.4b48.6%Compound Interest
7.7b32.9%Complex division, real part
7.3b35.6%Complex division, imag part
4.7b83.6%The quadratic formula (r1)
4.6b83.7%The quadratic formula (r2)

localize4.9s (0.7%)

bsearch1.2s (0.2%)

end1.0ms (0.0%)