Details

simplify8.6m (69.9%)

sample1.3m (10.4%)

Algorithm
73×intervals
Results
26.7s293998×body80valid
9.6s13537×body1280valid
5.4s16920×body160valid
5.1s3833×body2560valid
5.0s9617×body640valid
3.5s2180×body10240exit
3.2s100662×pre80true
1.8s19413×body80nan
1.6s6765×body320valid
247.0ms246×body5120valid
7.0ms100×pre80false

prune59.7s (8.1%)

series53.9s (7.3%)

Calls

299 calls:

2.1s
(+ (pow y 6.0) (fma (pow y 4.0) 121.0 2.0))
1.3s
(fma (sqrt (+ (+ e d) c)) (sqrt (+ (+ e d) c)) (+ b a))
1.2s
(log (hypot (pow 1.0 3/2) (pow x 3/2)))
1.0s
(/ (fma (pow (* (cbrt (+ 1.0 (/ i n))) (cbrt (+ 1.0 (/ i n)))) n) (pow (cbrt (+ 1.0 (/ i n))) n) (- 1.0)) (/ i n))
1.0s
(+ (* (* (* 2.0 x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (+ (fma (/ 1 (sqrt (fma x1 x1 1.0))) (/ (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (sqrt (fma x1 x1 1.0))) (- 3.0)) (+ (- 3.0) 3.0))) (* (* x1 x1) (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0)))

rewrite23.9s (3.2%)

Algorithm
105×rewrite-expression-head
Calls

299 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))) (/ 77617.0 (* 2.0 33096.0)))
1.5s
(+ (+ (* 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)))
1.1s
(+ (* (* (* 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)) (* (* x1 x1) (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0)))
944.0ms
(- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)
767.0ms
(+ (+ (+ (+ e d) c) b) a)
Rules
7676×*-un-lft-identity
7175×times-frac
6612×add-sqr-sqrt
5529×add-cube-cbrt
3830×prod-diff
1309×add-exp-log
1107×add-cbrt-cube
858×distribute-lft-out
685×pow1
630×associate-*r*
629×distribute-rgt-in distribute-lft-in
611×associate-*l*
566×add-log-exp
555×associate-+r+
519×div-inv
455×unpow-prod-down
398×sqrt-prod
386×prod-exp
374×difference-of-squares
299×log1p-expm1-u expm1-log1p-u
296×cbrt-unprod
295×associate-/r/ div-exp
256×associate-/l*
236×cbrt-undiv
234×flip-+ distribute-lft-out-- flip3-+
221×associate-/r*
181×fma-neg
178×sqr-pow
168×distribute-rgt-neg-in
163×frac-times
158×cbrt-prod
155×flip3-- flip--
154×distribute-lft-neg-in
152×associate-*r/
148×associate-+l+
146×unswap-sqr
143×cube-prod
126×associate-*l/
125×pow-prod-down
118×fma-def
107×sum-log
92×frac-sub
76×exp-neg
71×swap-sqr
68×*-commutative
64×neg-sub0
61×sub-neg
57×exp-diff
54×clear-num frac-2neg
53×fma-udef
50×pow-prod-up diff-log
49×associate-/l/
48×neg-mul-1
47×unpow3 cube-mult
43×log-prod
39×sqrt-div
38×pow1/3
37×pow1/2 sqrt-pow1
36×exp-prod
34×pow-sqr log-pow
32×+-commutative
29×1-exp frac-add rec-exp
27×pow-plus
25×un-div-inv
22×rem-sqrt-square pow2
20×pow-to-exp pow-exp
18×div-sub
17×cbrt-div
16×pow-unpow
11×unpow2
8×log-div
7×associate--r+ rem-log-exp pow-pow
6×associate--l- distribute-lft-neg-out pow-flip distribute-frac-neg distribute-rgt-out-- associate--l+
5×cube-div neg-log
4×inv-pow associate-+r-
3×unpow-prod-up hypot-def rem-cbrt-cube
2×sub-div expm1-udef distribute-neg-frac
1×rem-exp-log sqrt-pow2 unsub-neg sqrt-unprod expm1-log1p rem-square-sqrt distribute-rgt-out associate--r- associate-+l-

regimes3.8s (0.5%)

Accuracy

Total 41.9b remaining (17.6%)

Threshold costs 2.8b (1.2%)

10.8b56.6%Compound Interest
10.2b25.7%Complex division, imag part
7.7b32.2%Complex division, real part
4.6b83.7%The quadratic formula (r1)
4.6b84.1%The quadratic formula (r2)

localize3.0s (0.4%)

bsearch1.4s (0.2%)

end0.0ms (0.0%)