Details

simplify29.2m

Calls

13159 calls:

Slowest
1.4s
(/ (* (* (/ 1 x) (/ 1 x)) (/ 1 x)) (* (* (/ 1 (expm1 x)) (/ 1 (expm1 x))) (/ 1 (expm1 x))))
1.4s
(cbrt (* (* (+ (pow a 3) (pow (+ (+ b c) d) 3)) (+ (pow (+ a (+ b c)) 3) (pow d 3))) (+ (pow a 3) (pow (+ (+ b c) d) 3))))
1.3s
(* (* (* (fma (/ 1 (* (cbrt (fma x1 x1 1)) (cbrt (fma x1 x1 1)))) (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (cbrt (fma x1 x1 1))) (- 3)) (fma (/ 1 (* (cbrt (fma x1 x1 1)) (cbrt (fma x1 x1 1)))) (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (cbrt (fma x1 x1 1))) (- 3))) (fma (/ 1 (* (cbrt (fma x1 x1 1)) (cbrt (fma x1 x1 1)))) (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (cbrt (fma x1 x1 1))) (- 3))) (* (* (* (* x1 x1) x1) (* (* 2 2) 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)))))
1.3s
(* (* (* (fma (/ 1 (* (cbrt (fma x1 x1 1)) (cbrt (fma x1 x1 1)))) (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (cbrt (fma x1 x1 1))) (- 3)) (fma (/ 1 (* (cbrt (fma x1 x1 1)) (cbrt (fma x1 x1 1)))) (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (cbrt (fma x1 x1 1))) (- 3))) (fma (/ 1 (* (cbrt (fma x1 x1 1)) (cbrt (fma x1 x1 1)))) (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (cbrt (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
(cbrt (* (* (+ a (+ (+ b c) d)) (+ (pow (+ a (+ b c)) 3) (pow d 3))) (+ (pow a 3) (pow (+ (+ b c) d) 3))))

prune2.8m

sample1.4m

Algorithm
64×intervals
Results
36.4s270330×body80valid
11.5s13861×body1280valid
8.2s16810×body160valid
5.4s9305×body640valid
5.2s3954×body2560valid
4.7s75644×pre80true
2.4s1927×body10240exit
2.2s6817×body320valid
2.2s19435×body80nan
756.0ms255×body5120valid

series31.4s

Calls

266 calls:

Slowest
3.6s
(cbrt (fma (fma (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (fma x1 x1 1)) 4 -6) (* x1 x1) (* (- (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (fma x1 x1 1)) 3) (* (* x1 2) (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (fma x1 x1 1))))))
678.0ms
(cbrt (fma c (* -4 a) (* b b)))
677.0ms
(fma (fma (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (fma x1 x1 1)) 4 -6) (* x1 x1) (* (* (cbrt (fma (/ 1 (* (cbrt (fma x1 x1 1)) (cbrt (fma x1 x1 1)))) (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (cbrt (fma x1 x1 1))) (- 3))) (cbrt (fma (/ 1 (* (cbrt (fma x1 x1 1)) (cbrt (fma x1 x1 1)))) (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (cbrt (fma x1 x1 1))) (- 3)))) (* (cbrt (fma (/ 1 (* (cbrt (fma x1 x1 1)) (cbrt (fma x1 x1 1)))) (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (cbrt (fma x1 x1 1))) (- 3))) (* (* x1 2) (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (fma x1 x1 1))))))
623.0ms
(fma (fma (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (fma x1 x1 1)) 4 -6) (* x1 x1) (* (fma (/ 1 (* (cbrt (fma x1 x1 1)) (cbrt (fma x1 x1 1)))) (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (cbrt (fma x1 x1 1))) (- 3)) (* (* x1 2) (/ (- (fma x2 2 (* (* 3 x1) x1)) x1) (fma x1 x1 1)))))
513.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)

rewrite18.7s

Algorithm
94×rewrite-expression-head
Calls

266 calls:

Slowest
4.0s
(+ (log (exp (log (exp (+ e (+ (+ d b) c)))))) a)
974.0ms
(+ (+ (* 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)))
919.0ms
(+ (+ (+ (* 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))) (/ 77617 (* 2 33096)))
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)))
892.0ms
(+ (+ (* 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
8313×*-un-lft-identity
8066×times-frac
7644×add-sqr-sqrt
6705×add-cube-cbrt
6015×prod-diff
3428×exp-sum
1979×associate--r+
1886×distribute-rgt-in distribute-lft-in
1127×add-exp-log
998×sqrt-prod
904×add-cbrt-cube
720×pow1
594×add-log-exp
572×distribute-lft-out
451×associate-/r*
450×associate-/l*
377×difference-of-squares
364×div-inv
345×sub-neg
328×div-exp
282×associate-*r*
269×expm1-log1p-u associate-*l*
266×log1p-expm1-u insert-posit16
255×distribute-lft-out--
253×prod-exp
239×frac-times
224×flip-+ flip3-+
207×cbrt-unprod
201×cbrt-undiv
200×exp-prod
192×distribute-rgt-neg-in
189×associate-/r/
178×pow-prod-down
155×sum-log
132×associate-*r/
129×associate-*l/
128×fma-neg
124×fma-def
117×distribute-lft-neg-in cbrt-div
113×log-pow
81×unswap-sqr
79×sqrt-div
65×frac-2neg clear-num
64×flip-- flip3--
56×cbrt-prod
54×associate-/l/
47×1-exp rec-exp *-commutative
45×pow-prod-up
42×diff-log
39×neg-mul-1
36×sqrt-pow1 pow1/2
35×+-commutative
32×fma-udef
31×swap-sqr pow-sqr
30×rem-sqrt-square
26×log-prod
25×associate-+l+
22×pow-plus
21×pow1/3
20×unpow-prod-down
15×div-sub
14×rem-exp-log
13×associate-+r+ pow-flip pow2
12×hypot-def
11×inv-pow
9×frac-sub sqr-pow
7×neg-sub0 distribute-frac-neg un-div-inv
6×frac-add
5×pow-exp pow-to-exp
4×cube-prod neg-log associate--l- distribute-lft-neg-out
3×pow-unpow cube-unmult associate--l+ log1p-expm1 exp-to-pow log1p-udef
2×remove-posit16 sqrt-undiv pow3 rem-log-exp rem-cbrt-cube
1×expm1-udef distribute-lft1-in associate-+r- unpow3 sqrt-unprod hypot-1-def cube-mult pow-pow hypot-udef associate-+l- rem-square-sqrt unsub-neg associate--r-

regimes5.9s

Accuracy

Total 34.9b remaining (20.2%)

11.5b52.3%Compound Interest
10.8b25%Complex division, real part
4.3b84.5%The quadratic formula (r2)
2.7b0%Complex division, imag part
1.9b0%Expression, p6

localize3.8s

bsearch1.0s

end1.0ms