Details

simplify8.9m (33.8%)

rewrite6.1m (23.0%)

Algorithm
114×rewrite-expression-head
Calls

417 calls:

17.0s
(/ (- (* (* 1.0 (* 1.0 1.0)) (* (* 1.0 (* 1.0 1.0)) (* 1.0 (* 1.0 1.0)))) (* (* (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (fma (* 1.0 (* 1.0 1.0)) (* 1.0 (* 1.0 1.0)) (* (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (fma (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 1.0 (* 1.0 1.0))))))
5.6s
(- (* (* 1.0 (* 1.0 1.0)) (* (* 1.0 (* 1.0 1.0)) (* 1.0 (* 1.0 1.0)))) (* (* (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
3.6s
(* (* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
3.5s
(pow (* (* (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) 3)
2.0s
(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (* (/ c0 w) (/ d D)) (/ (/ d D) h)))
Rules
42742×add-exp-log
27507×prod-exp
17175×pow-exp
16157×div-exp
14515×times-frac
7852×add-sqr-sqrt
7120×*-un-lft-identity
6968×pow-to-exp
6840×add-cube-cbrt
3961×unpow-prod-down
2644×1-exp
2643×rec-exp
2266×add-cbrt-cube
2039×sqrt-prod
1606×pow1
1137×associate-*r*
1060×div-inv
1020×cbrt-prod
808×cbrt-unprod
742×associate-*l*
725×sqr-pow
711×associate-*r/
578×associate-/r/
506×cbrt-undiv
487×tan-quot
479×pow-prod-down
464×associate-/r*
460×add-log-exp
415×expm1-log1p-u log1p-expm1-u
369×associate-/l*
331×unswap-sqr
286×prod-diff
264×associate-*l/
245×pow-unpow
237×pow1/3
220×pow-prod-up
191×frac-times
153×swap-sqr
133×sqrt-div
132×pow-sqr
129×sqrt-pow1
124×*-commutative
110×distribute-lft-out
95×flip-+ flip3-+
89×flip3-- flip--
85×pow-plus
83×difference-of-squares frac-2neg clear-num
80×distribute-rgt-in distribute-lft-in
74×pow1/2
60×pow2
53×distribute-lft-out--
48×exp-prod cos-sum rem-sqrt-square
47×associate-/l/
45×cbrt-div
40×fma-neg
36×pow-pow fma-def
35×distribute-lft-neg-in distribute-rgt-neg-in
30×sub-neg
26×fma-udef
24×log-pow frac-add
23×div-sub
22×pow-sub
19×pow-neg
16×neg-sub0
14×sum-log hypot-def
12×+-commutative
log-prod
cos-diff diff-log
distribute-frac-neg unpow2
associate-+l-
neg-mul-1 un-div-inv
pow-flip pow3 inv-pow rem-cbrt-cube
frac-sub cube-unmult acos-asin
associate--l+ sqrt-unprod hypot-udef asin-acos rem-exp-log rem-square-sqrt rem-log-exp
associate-+l+ exp-diff cos-mult sqrt-undiv exp-sum sin-mult sub-div sqr-sin

series4.8m (18.3%)

Calls

415 calls:

1.6m
(/ (- (* (* 1.0 (* 1.0 1.0)) (* (* 1.0 (* 1.0 1.0)) (* 1.0 (* 1.0 1.0)))) (* (* (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (fma (* 1.0 (* 1.0 1.0)) (* 1.0 (* 1.0 1.0)) (* (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (fma (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 1.0 (* 1.0 1.0))))))
9.8s
(- (* (* 1.0 (* 1.0 1.0)) (* (* 1.0 (* 1.0 1.0)) (* 1.0 (* 1.0 1.0)))) (* (* (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
9.5s
(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0)))
9.3s
(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))) 2.0)))
9.0s
(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))) 2.0)))

sample3.2m (12.1%)

Algorithm
60×intervals
Results
43.6s249631×body80valid
36.6s26359×body1280valid
27.8s160143×body80nan
19.5s19894×body640valid
17.3s9016×body2560valid
12.0s3411×body5120valid
6.7s9569×body320valid
3.8s8709×body160valid
1.5s652×body10240exit
542.0ms348×body320nan
516.0ms661×body1280nan
271.0ms598×body640nan
239.0ms8256×pre80true
128.0ms202×body160nan

prune2.8m (10.5%)

regimes26.1s (1.6%)

Accuracy

Total 55.2b remaining (28.7%)

Threshold costs 5.0b (2.6%)

8.0b30.1%Toniolo and Linder, Equation (13)
8.0b0%Henrywood and Agarwal, Equation (13)
7.6b-2%Henrywood and Agarwal, Equation (12)
6.1b52.9%Henrywood and Agarwal, Equation (3)
5.4b38.6%Toniolo and Linder, Equation (10-)

localize8.3s (0.5%)

bsearch2.6s (0.2%)

end1.0ms (0.0%)