Details

simplify5.9m (60.6%)

sample1.3m (12.9%)

Algorithm
73×intervals
Results
28.4s294310×body80valid
9.3s13712×body1280valid
5.8s16845×body160valid
4.6s3903×body2560valid
4.0s9310×body640valid
2.7s2227×body10240exit
2.3s100636×pre80true
1.5s6878×body320valid
1.3s19547×body80nan
163.0ms257×body5120valid
5.0ms100×pre80false

prune1.2m (11.9%)

series45.0s (7.7%)

Calls

302 calls:

2.6s
(+ (pow y 6.0) (fma (pow y 4.0) 121.0 2.0))
1.2s
(+ (* (* (* 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)) (* (* (* (cbrt (- (* 4.0 (/ (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0))) 6.0)) (cbrt (- (* 4.0 (/ (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0))) 6.0))) (* x1 x1)) (cbrt (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0))))
845.0ms
(expm1 (log1p (* (pow y 6.0) 333.75)))
642.0ms
(* (pow y 6.0) 333.75)
634.0ms
(+ (* (* (* 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)) (* (* (cbrt (- (* 4.0 (/ (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0))) 6.0)) (cbrt (- (* 4.0 (/ (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0))) 6.0))) (* (* x1 x1) (cbrt (- (* 4.0 (/ (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0))) 6.0)))))

rewrite31.6s (5.4%)

Algorithm
106×rewrite-expression-head
Calls

302 calls:

2.0s
(+ (+ (+ (* 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)))
1.7s
(+ (+ (* 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)))
1.5s
(+ (* (* (* 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)) (+ (* (* 4.0 (/ (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0))) (* x1 x1)) (* (- 6.0) (* x1 x1))))
1.4s
(+ (* (* (* 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)) (* (* (* (cbrt (- (* 4.0 (/ (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0))) 6.0)) (cbrt (- (* 4.0 (/ (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0))) 6.0))) (* x1 x1)) (cbrt (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0))))
1.3s
(+ (* (* (* 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)) (* (* (cbrt (- (* 4.0 (/ (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0))) 6.0)) (cbrt (- (* 4.0 (/ (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0))) 6.0))) (* (* x1 x1) (cbrt (- (* 4.0 (/ (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0))) 6.0)))))
Rules
10702×times-frac
9215×*-un-lft-identity
8699×add-sqr-sqrt
6439×add-cube-cbrt
2423×prod-diff
1870×add-exp-log
1793×sqrt-prod
1501×add-cbrt-cube
867×associate-*r*
818×associate-*l*
759×distribute-lft-out
757×pow1
746×difference-of-squares
686×unpow-prod-down
680×cbrt-div
633×distribute-rgt-in distribute-lft-in
618×associate-*r/
610×add-log-exp frac-times
594×flip3-- flip--
593×distribute-lft-out--
592×div-inv
585×prod-exp
547×div-exp
530×associate-*l/
529×associate-+l+
460×associate-/l*
455×cbrt-unprod
395×cube-prod
391×cbrt-undiv
352×associate-/r/
348×associate-/r*
303×log1p-expm1-u
302×expm1-log1p-u
296×frac-add
269×flip-+ flip3-+
247×unswap-sqr
203×fma-neg
200×pow-prod-down
199×swap-sqr
197×distribute-rgt-neg-in
194×sqr-pow
169×distribute-lft-neg-in
141×cbrt-prod
137×sum-log
111×fma-def
92×frac-sub
81×exp-neg
71×*-commutative neg-sub0
70×sqrt-div
69×sqrt-pow1
68×associate-/l/
66×clear-num frac-2neg
64×1-exp
62×exp-diff
60×sub-neg
57×neg-mul-1
55×rec-exp
47×pow1/2 diff-log
45×fma-udef
39×log-prod
35×pow-prod-up +-commutative
32×unpow3 cube-mult
28×rem-sqrt-square
26×un-div-inv
25×associate-+r+
24×pow1/3
23×pow-sqr
22×pow-exp
20×pow-plus
19×pow-to-exp div-sub
15×pow-unpow
14×pow2
13×exp-sum
11×unpow2
10×log-pow distribute-frac-neg exp-prod
distribute-lft-neg-out
rem-cube-cbrt associate--l- neg-log pow-pow
sqrt-undiv
inv-pow pow-flip rem-cbrt-cube log-div
associate--l+
cube-div rem-exp-log expm1-udef sqrt-unprod rem-square-sqrt associate-+r- associate-+l-
expm1-log1p unsub-neg associate--r+ rem-log-exp
sqrt-pow2 pow3 distribute-rgt-out

regimes4.8s (0.8%)

Accuracy

Total 41.7b remaining (17.1%)

Threshold costs 3.2b (1.3%)

10.3b58.2%Compound Interest
8.6b22.2%Complex division, real part
7.0b37%Complex division, imag part
5.7b80.2%The quadratic formula (r1)
5.5b77.2%The quadratic formula (r2)

localize2.6s (0.4%)

bsearch1.0s (0.2%)

end0.0ms (0.0%)