Details

simplify24.1m

Calls

12386 calls:

Slowest
1.4s
(/ (* (* (+ (/ (/ (fma 2 x2 (- (* x1 (* x1 3)) x1)) (hypot 1 x1)) (hypot 1 x1)) -3) (+ (/ (/ (fma 2 x2 (- (* x1 (* x1 3)) x1)) (hypot 1 x1)) (hypot 1 x1)) -3)) (+ (/ (/ (fma 2 x2 (- (* x1 (* x1 3)) x1)) (hypot 1 x1)) (hypot 1 x1)) -3)) (/ (* (* (/ (fma x1 x1 1) 2) (/ (fma x1 x1 1) 2)) (/ (fma x1 x1 1) 2)) (* (* (* (fma 2 x2 (- (* x1 (* x1 3)) x1)) (fma 2 x2 (- (* x1 (* x1 3)) x1))) (fma 2 x2 (- (* x1 (* x1 3)) x1))) (* (* x1 x1) x1))))
1.2s
(* (* (* (- (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (fma x1 x1 1)) 3) (- (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (fma x1 x1 1)) 3)) (- (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (fma x1 x1 1)) 3)) (* (* (* (* x1 2) (* x1 2)) (* x1 2)) (/ (* (* (- (fma x2 2 (* (* 3 x1) x1)) x1) (- (fma x2 2 (* (* 3 x1) x1)) x1)) (- (fma x2 2 (* (* 3 x1) x1)) x1)) (* (* (fma x1 x1 1) (fma x1 x1 1)) (fma x1 x1 1)))))
1.2s
(/ (* (* (+ (/ (/ (fma 2 x2 (- (* x1 (* x1 3)) x1)) (hypot 1 x1)) (hypot 1 x1)) -3) (+ (/ (/ (fma 2 x2 (- (* x1 (* x1 3)) x1)) (hypot 1 x1)) (hypot 1 x1)) -3)) (+ (/ (/ (fma 2 x2 (- (* x1 (* x1 3)) x1)) (hypot 1 x1)) (hypot 1 x1)) -3)) (/ (/ (* (* (fma x1 x1 1) (fma x1 x1 1)) (fma x1 x1 1)) (* (* 2 2) 2)) (* (* (* (fma 2 x2 (- (* x1 (* x1 3)) x1)) x1) (* (fma 2 x2 (- (* x1 (* x1 3)) x1)) x1)) (* (fma 2 x2 (- (* x1 (* x1 3)) x1)) x1))))
1.1s
(/ (* (* 1 1) 1) (* (* (* (* x x) x) (* (* x x) x)) (* (* x x) x)))
1.1s
(/ (* (* (+ (/ (/ (fma 2 x2 (- (* x1 (* x1 3)) x1)) (hypot 1 x1)) (hypot 1 x1)) -3) (+ (/ (/ (fma 2 x2 (- (* x1 (* x1 3)) x1)) (hypot 1 x1)) (hypot 1 x1)) -3)) (+ (/ (/ (fma 2 x2 (- (* x1 (* x1 3)) x1)) (hypot 1 x1)) (hypot 1 x1)) -3)) (/ (* (* (/ (fma x1 x1 1) 2) (/ (fma x1 x1 1) 2)) (/ (fma x1 x1 1) 2)) (* (* (* (fma 2 x2 (- (* x1 (* x1 3)) x1)) x1) (* (fma 2 x2 (- (* x1 (* x1 3)) x1)) x1)) (* (fma 2 x2 (- (* x1 (* x1 3)) x1)) x1))))

prune2.7m

sample1.4m

Algorithm
63×intervals
Results
36.9s263175×body80valid
10.3s12747×body1280valid
8.9s16842×body160valid
5.6s9055×body640valid
4.3s2731×body2560valid
4.0s75618×pre80true
3.1s6637×body320valid
3.1s1987×body10240exit
2.1s16633×body80nan
157.0ms122×body5120valid

series29.8s

Calls

268 calls:

Slowest
703.0ms
(fma (fma (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (fma x1 x1 1)) 4 -6) (* x1 x1) (/ (* (+ (fma (/ 1 (sqrt (fma x1 x1 1))) (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (sqrt (fma x1 x1 1))) (- (* (sqrt 3) (sqrt 3)))) 0) (* (* x1 2) (- (fma x2 2 (* (* 3 x1) x1)) x1))) (fma x1 x1 1)))
519.0ms
(* (+ (fma (/ 1 (sqrt (fma x1 x1 1))) (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (sqrt (fma x1 x1 1))) (- (* (sqrt 3) (sqrt 3)))) 0) (* (* x1 2) (- (fma x2 2 (* (* 3 x1) x1)) x1)))
498.0ms
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
483.0ms
(cbrt (* (sqrt 0.12900613773279798) (* (* x x) x)))
478.0ms
(fma (* (/ 1 (+ b a)) (/ PI (- b a))) (/ -1 b) (/ (/ 1 (+ b a)) (* (/ a PI) (- b a))))

rewrite17.8s

Algorithm
95×rewrite-expression-head
Calls

268 calls:

Slowest
1.5s
(exp (log (exp (+ e (+ d (+ b (+ a c)))))))
1.2s
(exp (log (* (exp e) (* (exp d) (* (exp b) (* (exp a) (exp c)))))))
1.2s
(+ (+ (+ (* 333.75 (pow 33096 6)) (* (* 77617 77617) (+ (+ (+ (* (* 11 (* 77617 77617)) (* 33096 33096)) (- (pow 33096 6))) (* -121 (pow 33096 4))) -2))) (* 5.5 (pow 33096 8))) (/ 77617 (* 2 33096)))
909.0ms
(+ (+ (* 333.75 (pow 33096 6)) (* (* 77617 77617) (+ (+ (+ (* (* 11 (* 77617 77617)) (* 33096 33096)) (- (pow 33096 6))) (* -121 (pow 33096 4))) -2))) (* 5.5 (pow 33096 8)))
895.0ms
(+ (+ (* 333.75 (pow 33096 6)) (* (* 77617 77617) (+ (+ (+ (* (* 11 (* 77617 77617)) (* 33096 33096)) (- (pow 33096 6))) (* -121 (pow 33096 4))) -2))) (* 5.5 (pow 33096 8)))
Rules
17173×times-frac
12857×*-un-lft-identity
12361×add-sqr-sqrt
11362×add-cube-cbrt
8550×prod-diff
3406×exp-sum
2771×sqrt-prod
1979×associate--r+
1810×distribute-rgt-in distribute-lft-in
1061×pow1
1047×add-exp-log
964×add-cbrt-cube
802×div-inv
615×associate-*l*
564×associate-*r*
561×distribute-lft-out
558×add-log-exp
436×cbrt-prod
351×pow-prod-down
348×associate-/l* sub-neg
319×associate-/r*
303×prod-exp
283×difference-of-squares
281×cbrt-unprod
272×expm1-log1p-u
268×log1p-expm1-u insert-posit16
219×div-exp
210×distribute-lft-out--
195×fma-neg
171×cbrt-undiv
165×sqrt-div
160×unswap-sqr
156×flip-+ flip3-+
150×swap-sqr
142×sum-log
139×associate-*r/
132×fma-def
125×pow-prod-up associate-/r/
121×sqrt-pow1
120×distribute-rgt-neg-in
107×distribute-lft-neg-in
105×pow1/2
97×frac-times
85×flip3-- flip--
75×exp-prod
70×*-commutative
64×pow-sqr
60×associate-*l/
56×frac-2neg pow-plus clear-num
54×neg-mul-1
48×fma-udef
47×cbrt-div
38×pow1/3 diff-log
31×log-pow
30×pow2 associate-/l/
28×+-commutative unpow-prod-down
26×rem-sqrt-square
24×sqrt-unprod
23×1-exp
21×rec-exp
15×pow-flip
14×associate-+l+ div-sub rem-exp-log
13×log-prod
12×associate--l+
11×sqr-pow
distribute-frac-neg
frac-sub
distribute-lft-neg-out pow-exp pow-to-exp hypot-def frac-add
associate-+r+ distribute-neg-frac
pow3 rem-square-sqrt
neg-sub0 distribute-rgt-out-- cube-unmult log1p-expm1 inv-pow hypot-udef log1p-udef
expm1-udef pow-unpow associate--l-
neg-log rem-log-exp
expm1-log1p distribute-lft1-in associate-+r- sub-div pow-pow un-div-inv unsub-neg associate--r-

regimes4.4s

Accuracy

Total 35.2b remaining (23%)

12.0b50.4%Compound Interest
6.7b36.5%Complex division, real part
5.2b81.3%The quadratic formula (r2)
4.7b75.4%Kahan p9 Example
2.0b0%Complex division, imag part

localize3.4s

bsearch1.3s

end1.0ms