Details

simplify5.7m (67.5%)

prune1.0m (11.9%)

series45.2s (8.9%)

Calls

300 calls:

2.0s
(+ (pow y 6.0) (fma (pow y 4.0) 121.0 2.0))
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)) (* (* (* (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))))
847.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))
807.0ms
(+ (expm1 (log1p (* (pow y 6.0) 333.75))) (fma (- (* (* (* (* 11.0 x) x) y) y) (+ (pow y 6.0) (fma (pow y 4.0) 121.0 2.0))) (* x x) (fma 5.5 (pow y 8.0) (/ x (* 2.0 y)))))
736.0ms
(expm1 (log1p (* (pow y 6.0) 333.75)))

rewrite27.6s (5.5%)

Algorithm
106×rewrite-expression-head
Calls

300 calls:

2.1s
(+ (+ (+ (* 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)))
1.4s
(+ (* (* (* 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)) (+ (* (* 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))))
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)))
Rules
6109×*-un-lft-identity
5852×add-sqr-sqrt
5782×times-frac
4440×add-cube-cbrt
2237×prod-diff
1702×add-exp-log
1471×add-cbrt-cube
1042×sqrt-prod
771×associate-*r*
744×pow1
604×associate-*l*
602×add-log-exp
573×difference-of-squares
568×distribute-rgt-in distribute-lft-in
547×prod-exp
504×distribute-lft-out
473×unpow-prod-down
468×associate-*l/
453×cbrt-unprod
442×div-exp
438×associate-/l*
427×div-inv
406×frac-times
404×cbrt-div
400×flip3-- flip--
399×associate-+l+
367×cbrt-undiv
340×associate-*r/
333×distribute-lft-out--
318×associate-/r*
300×log1p-expm1-u expm1-log1p-u
243×sqr-pow
206×associate-/r/
205×flip-+ flip3-+
197×distribute-rgt-neg-in
190×pow-prod-down
185×fma-neg
182×cube-prod
169×distribute-lft-neg-in
166×frac-add
163×unswap-sqr
134×sum-log
129×sqrt-div
123×cbrt-prod
108×fma-def
92×frac-sub
81×exp-neg
79×sqrt-pow1
76×swap-sqr
71×*-commutative neg-sub0
69×associate-/l/
66×clear-num frac-2neg
62×exp-diff
58×sub-neg
57×neg-mul-1
55×pow1/2
47×diff-log
44×fma-udef
39×log-prod
34×pow-prod-up
32×unpow3 cube-mult +-commutative
31×1-exp rec-exp
27×rem-sqrt-square
25×associate-+r+
24×un-div-inv
22×pow-sqr pow1/3
20×pow-plus
19×pow-to-exp pow-exp
18×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-flip
neg-log
difference-cubes sqrt-unprod associate--l- pow-pow
inv-pow rem-cbrt-cube associate--l+ log-div
rem-exp-log rem-cube-cbrt associate-+r- associate-+l-
cube-div expm1-udef unsub-neg rem-square-sqrt associate--r+ rem-log-exp
sqrt-undiv sqrt-pow2 pow3 expm1-log1p distribute-rgt-out

sample27.1s (5.4%)

Algorithm
56×intervals
Results
10.8s144706×body80valid
5.4s14856×body160valid
1.6s68636×pre80true
1.4s1830×body640valid
1.2s3079×body1280valid
540.0ms2955×body320valid
539.0ms252×body10240exit
519.0ms8598×body80nan
400.0ms741×body2560valid
7.0ms100×pre80false
7.0msbody5120valid

localize2.5s (0.5%)

regimes2.1s (0.4%)

Accuracy

Total 2.0b remaining (1.2%)

Threshold costs 0.6b (0.4%)

1.4b0%Rosa's DopplerBench
0.3b0%fma_test1
0.2b0%NMSE Section 6.1 mentioned, B
0.1b0%Rosa's Benchmark
0.0b0%arccos

bsearch14.0ms (0.0%)

end0.0ms (0.0%)