Details

simplify8.8m (64.6%)

prune1.8m (13.1%)

sample1.4m (10.1%)

Algorithm
73×intervals
Results
27.8s285416×body80valid
10.6s13589×body1280valid
9.9s25113×body160valid
4.3s3866×body2560valid
4.1s9505×body640valid
3.3s2153×body10240exit
2.7s100646×pre80true
2.4s6916×body320valid
1.3s19387×body80nan
237.0ms235×body5120valid
3.0ms100×pre80false

series48.8s (6.0%)

Calls

292 calls:

5.7s
(* (* (sqrt a) (sqrt (+ (+ b c) d))) (sqrt (* a (+ (+ b c) d))))
1.5s
(fma (sqrt (pow x 4.0)) (sqrt (pow x 4.0)) (- (pow y 4.0)))
932.0ms
(+ (* (* (* 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)) (* (fma 6.0 -1 6.0) (* x1 x1))))
731.0ms
(- (* (pow x 4.0) 9.0) (pow y 4.0))
662.0ms
(cbrt (+ (+ (* (* (* 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))))) (* (* x1 x1) (- 6.0))))

rewrite38.6s (4.7%)

Algorithm
105×rewrite-expression-head
Calls

292 calls:

4.7s
(+ (+ (* (* (* 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))))) (* (* x1 x1) (- 6.0)))
3.2s
(+ (+ (+ (* 333.75 (pow y 6.0)) (* (* x x) (- (- (- (* (* (* (* 11.0 x) x) y) y) (pow y 6.0)) (* 121.0 (pow y 4.0))) 2.0))) (* 5.5 (pow y 8.0))) (/ x (* 2.0 y)))
3.1s
(+ (+ (* 333.75 (pow y 6.0)) (* (* x x) (- (- (- (* (* (* (* 11.0 x) x) y) y) (pow y 6.0)) (* 121.0 (pow y 4.0))) 2.0))) (* 5.5 (pow y 8.0)))
2.3s
(cbrt (+ (+ (* (* (* 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))))) (* (* x1 x1) (- 6.0))))
2.3s
(cbrt (+ (+ (* (* (* 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))))) (* (* x1 x1) (- 6.0))))
Rules
9898×times-frac
9520×*-un-lft-identity
8333×add-sqr-sqrt
7263×add-cube-cbrt
5145×prod-diff
2275×add-exp-log
2180×add-cbrt-cube
1585×distribute-rgt-in distribute-lft-in
1081×pow1
913×prod-exp
875×cbrt-unprod
858×distribute-lft-out
798×div-inv
744×associate-*r*
712×frac-times
667×associate-*l*
580×add-log-exp div-exp
560×cbrt-undiv
484×sqrt-prod
447×associate-*r/
394×difference-of-squares
391×unpow-prod-down
389×flip3-- flip--
307×pow-prod-down
292×expm1-log1p-u log1p-expm1-u
289×associate-*l/
277×distribute-lft-out--
270×associate-+l+
266×associate-/l*
264×associate-/r/
254×cbrt-div
251×swap-sqr
243×fma-neg
219×associate-/r*
209×flip-+ flip3-+
156×sqr-pow
126×distribute-rgt-neg-in
120×sum-log
117×distribute-lft-neg-in
99×unswap-sqr
94×pow-prod-up
86×sqrt-pow1
83×sub-neg
80×log-pow
77×*-commutative
65×pow-sqr
62×log-prod fma-def
60×exp-prod
58×cbrt-prod
56×pow1/2
55×associate-/l/
54×sqrt-div
52×frac-2neg pow-plus clear-num diff-log
40×fma-udef
39×neg-mul-1
38×exp-sum
36×rem-sqrt-square
35×pow2
34×frac-add
22×pow1/3 div-sub
19×associate-+r+
18×+-commutative
16×frac-sub
14×1-exp rec-exp log-div
12×rem-log-exp
10×rem-exp-log
distribute-lft-neg-out associate--l- hypot-def
neg-sub0 pow3 sqrt-unprod
distribute-frac-neg neg-log associate--r+ exp-to-pow
pow-exp pow-unpow associate--l+ pow-to-exp rem-cbrt-cube un-div-inv
pow-flip exp-diff distribute-rgt-neg-out inv-pow rem-square-sqrt associate--r-
expm1-log1p expm1-udef distribute-rgt-out-- sub-div pow-pow hypot-udef unsub-neg

regimes6.0s (0.7%)

Accuracy

Total 43.0b remaining (16.5%)

Threshold costs 2.8b (1.1%)

10.3b55%Compound Interest
8.3b28.7%Complex division, imag part
7.3b-6.2%Complex division, real part
4.8b82.9%The quadratic formula (r1)
4.5b78.4%Kahan p9 Example

localize4.0s (0.5%)

bsearch1.8s (0.2%)

end1.0ms (0.0%)