Details

simplify5.6m (61.5%)

sample1.2m (13.6%)

Algorithm
73×intervals
Results
25.8s294310×body80valid
9.5s13712×body1280valid
5.7s16845×body160valid
4.2s9310×body640valid
4.2s3903×body2560valid
3.3s2227×body10240exit
3.0s100636×pre80true
2.2s6878×body320valid
1.3s19547×body80nan
622.0ms257×body5120valid
6.0ms100×pre80false

prune59.9s (11.0%)

series42.3s (7.7%)

Calls

292 calls:

2.1s
(+ (pow y 6.0) (fma (pow y 4.0) 121.0 2.0))
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)) (* (* (* (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))))
991.0ms
(* (pow y 6.0) 333.75)
730.0ms
(expm1 (log1p (* (pow y 6.0) 333.75)))
672.0ms
(- (* 9.0 (pow x 4.0)) (pow y 4.0))

rewrite25.8s (4.7%)

Algorithm
106×rewrite-expression-head
Calls

292 calls:

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))) (/ 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)))
1.3s
(+ (* (* (* 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)) (+ (* (* 4.0 (/ (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0))) (* x1 x1)) (* (- 6.0) (* x1 x1))))
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))))
932.0ms
(+ (* (* (* 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)) (* (* x1 x1) (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0)))
Rules
8392×times-frac
7821×add-sqr-sqrt
7776×*-un-lft-identity
5356×add-cube-cbrt
3530×sqrt-prod
2261×prod-diff
1587×add-exp-log
1384×add-cbrt-cube
1352×difference-of-squares
1073×unpow-prod-down
782×cube-prod
717×pow1
666×distribute-lft-out
643×sqr-pow
604×associate-*r*
582×add-log-exp
568×distribute-rgt-in distribute-lft-in
558×associate-/l*
552×distribute-lft-out--
527×associate-*l*
505×prod-exp
453×div-inv
445×associate-*l/
423×cbrt-unprod
404×cbrt-div
402×div-exp
399×associate-+l+
396×flip3-- flip--
395×frac-times
340×cbrt-undiv
329×associate-*r/
322×associate-/r*
292×log1p-expm1-u expm1-log1p-u
186×flip-+ flip3-+
185×associate-/r/
179×fma-neg
178×pow-prod-down
166×frac-add
132×sum-log
123×cbrt-prod
120×unswap-sqr
106×distribute-rgt-neg-in
103×distribute-lft-neg-in
98×fma-def
93×frac-sub
81×exp-neg
76×swap-sqr
70×sqrt-pow1
67×*-commutative
66×neg-sub0
65×associate-/l/
64×sqrt-div
63×clear-num frac-2neg
62×exp-diff
57×sub-neg
56×difference-cubes
48×pow1/2
44×fma-udef
43×diff-log
39×log-prod
35×neg-mul-1
34×pow-prod-up
32×unpow3 cube-mult
31×+-commutative
29×rem-sqrt-square
28×1-exp rec-exp
25×associate-+r+
24×un-div-inv
22×pow-sqr pow1/3
20×pow-plus
19×pow-to-exp pow-exp
17×div-sub
14×pow2
13×exp-sum
12×pow-unpow
11×unpow2
10×log-pow distribute-frac-neg exp-prod
distribute-lft-neg-out
pow-pow
rem-cbrt-cube associate--l+ log-div
sqrt-undiv inv-pow pow-flip
rem-exp-log rem-cube-cbrt associate--l- neg-log associate-+r-
cube-div expm1-udef sqrt-unprod unsub-neg rem-square-sqrt associate--r+ rem-log-exp
sqrt-pow2 pow3 expm1-log1p distribute-rgt-out hypot-def associate-+l-

regimes4.5s (0.8%)

Accuracy

Total 44.5b remaining (18.2%)

Threshold costs 3.3b (1.3%)

11.1b22.8%Complex division, real part
10.3b58.2%Compound Interest
7.0b37%Complex division, imag part
6.0b82.2%The quadratic formula (r1)
5.5b77.2%The quadratic formula (r2)

localize2.6s (0.5%)

bsearch1.1s (0.2%)

end1.0ms (0.0%)