Details

simplify8.8m (71.5%)

sample1.3m (10.4%)

Algorithm
73×intervals
Results
28.5s294338×body80valid
8.8s13774×body1280valid
5.5s16947×body160valid
4.7s2268×body10240exit
4.2s3923×body2560valid
3.9s9388×body640valid
2.6s100628×pre80true
2.1s6812×body320valid
1.5s19527×body80nan
145.0ms214×body5120valid
6.0ms100×pre80false

prune58.0s (7.9%)

series45.8s (6.2%)

Calls

293 calls:

2.1s
(+ (pow y 6.0) (fma (pow y 4.0) 121.0 2.0))
1.0s
(cbrt (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
986.0ms
(cbrt (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
953.0ms
(+ (* (fma (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (/ 1 (+ (* x1 x1) 1.0)) (- (* (cbrt 3.0) (* (cbrt 3.0) (cbrt 3.0))))) (* (* 2.0 x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))) (fma (+ (- 3.0) 3.0) (* (/ (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0)) (* 2.0 x1)) (* (* x1 x1) (- (* 4.0 (/ (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0))) 6.0))))
949.0ms
(cbrt (* (* x1 x1) (* 4.0 (/ (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0)))))

rewrite21.6s (2.9%)

Algorithm
104×rewrite-expression-head
Calls

293 calls:

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))) (/ 77617.0 (* 2.0 33096.0)))
1.3s
(+ (+ (* 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)))
1.0s
(+ (* (* (* 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)))
1.0s
(- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)
731.0ms
(+ (+ (+ (+ e d) c) b) a)
Rules
7873×times-frac
7234×*-un-lft-identity
6447×add-sqr-sqrt
5555×add-cube-cbrt
3155×prod-diff
1182×add-exp-log
1038×add-cbrt-cube
980×sqrt-prod
685×associate-*r*
670×distribute-rgt-in distribute-lft-in
654×distribute-lft-out
595×add-log-exp
582×pow1
565×div-inv
481×associate-*l*
458×associate-/l*
450×unpow-prod-down
318×prod-exp
295×expm1-log1p-u
294×difference-of-squares
293×log1p-expm1-u
263×div-exp
259×cbrt-unprod
243×fma-neg
226×associate-/r*
219×cbrt-undiv
198×distribute-lft-out--
189×distribute-rgt-neg-in
180×distribute-lft-neg-in
173×flip-+ flip3-+
158×flip-- flip3--
153×frac-times
146×associate-*r/
142×associate-/r/
141×associate-+l+
138×sqr-pow
130×sum-log
129×unswap-sqr
127×cube-prod
122×cbrt-prod
117×pow-prod-down
104×associate-*l/
95×frac-sub
80×fma-def
79×exp-neg
68×neg-sub0 sub-neg
67×*-commutative
61×exp-diff
60×neg-mul-1
57×sqrt-div clear-num frac-2neg
55×associate-/l/
53×fma-udef
52×unpow3 diff-log
44×log-prod
35×swap-sqr
32×cube-mult
30×pow1/2 sqrt-pow1
28×+-commutative
27×associate-+r+
26×exp-prod
25×frac-add unpow2 pow-exp
24×cbrt-div
21×un-div-inv pow-to-exp
20×rem-sqrt-square
19×div-sub
18×1-exp rec-exp
16×pow-prod-up
15×pow-unpow log-pow
14×pow1/3
13×cube-div
12×pow-plus
10×distribute-lft1-in pow-sqr distribute-rgt-out log-div
8×distribute-lft-neg-out pow2
7×rem-cube-cbrt distribute-frac-neg associate--l+
6×rem-cbrt-cube distribute-neg-frac rem-log-exp
5×associate--l- hypot-udef pow-pow
4×expm1-udef inv-pow pow-flip hypot-def neg-log
3×expm1-log1p
2×log1p-udef log1p-expm1 unsub-neg distribute-rgt-out-- associate-+r- associate--r+
1×rem-exp-log sqrt-unprod pow3 sub-div rem-square-sqrt associate-+l-

regimes4.3s (0.6%)

Accuracy

Total 41.3b remaining (16.8%)

Threshold costs 3.5b (1.4%)

11.5b49.6%Compound Interest
7.5b31.7%Complex division, imag part
7.4b36.6%Complex division, real part
5.8b80.3%The quadratic formula (r2)
4.3b84.8%The quadratic formula (r1)

localize2.8s (0.4%)

bsearch1.2s (0.2%)

end1.0ms (0.0%)