Date:	Wednesday, March 11th, 2020
Commit:	79312c80 on better-rr
Hostname:	warfa with Racket 7.5
Seed:	2020071
Parameters:	256 points for 4 iterations
Flags:	`setup:simplifyrules:numericsrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:complexrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifygenerate:better-rrreduce:regimesreduce:avg-errorreduce:binary-searchreduce:branch-expressionsprecision:doubleprecision:fallback` `+o rules:numerics`

Details

Calls

387 calls:

5.8s	(sqrt (* U (* (* 2.0 n) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
5.7s	(/ (- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)) (fma 1.0 1.0 (fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
5.7s	(sqrt (* U (* (* 2.0 n) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))))
4.8s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.7s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

Algorithm

61×

intervals

Results

Algorithm

168×	egg-herbie

Accuracy

Total 43.0b remaining (24.5%)

Threshold costs 3.8b (2.2%)

10.4b	28.2%	Toniolo and Linder, Equation (13)
9.4b	38.5%	Henrywood and Agarwal, Equation (12)
6.2b	63.1%	Henrywood and Agarwal, Equation (3)
5.1b	78.6%	Toniolo and Linder, Equation (7)
3.2b	0%	Henrywood and Agarwal, Equation (13)

Algorithm

108×	rewrite-expression-head

Calls

387 calls:

88.0ms	(+ (* (/ (* d d) (* (* w h) D)) (/ c0 D)) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
85.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
79.0ms	(sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M)))
26.0ms	(sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
23.0ms	(/ (* (* (hypot (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3/2) (pow 1.0 3/2)) -2.0) (cos (/ K 2.0))) (/ (sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))) J))

Rules

970×	`*-commutative`
834×	`associate-l`
677×	`associate-r`
515×	`times-frac`
488×	`associate-*r/`
443×	`div-inv`
428×	`unpow-prod-down`
409×	`sqr-pow`
390×	`associate-/l*`
364×	`frac-times`
360×	`associate-/r*`
325×	`sqrt-div`
322×	`clear-num`
296×	`frac-2neg`
266×	`distribute-rgt-in` `distribute-lft-in`
212×	`flip--` `flip3--`
179×	`associate-*l/`
168×	`associate-/r/`
145×	`associate-/l/`
130×	`frac-add`
114×	`sub-neg`
108×	`prod-diff`
99×	`sqrt-prod`
77×	`flip-+` `flip3-+`
72×	`+-commutative`
67×	`associate-+l+`
58×	`neg-mul-1`
54×	`associate-+r+`
53×	`pow-to-exp`
51×	`tan-quot`
45×	`fma-def`
42×	`pow1/2`
36×	`fma-udef`
34×	`pow-unpow` `un-div-inv`
32×	`unswap-sqr` `frac-sub`
29×	`fma-neg`
28×	`associate--l+`
26×	`div-sub` `swap-sqr`
24×	`unpow2`
20×	`difference-of-squares`
17×	`unpow3`
15×	`pow-prod-down`
13×	`pow-neg`
10×	`inv-pow` `mul-1-neg`
8×	`exp-sum` `distribute-rgt-out--` `prod-exp` `pow-sub`
7×	`distribute-frac-neg` `neg-sub0`
6×	`cos-sum`
4×	`rec-exp` `asin-acos` `distribute-lft-out--` `distribute-neg-frac`
3×	`distribute-lft-neg-in` `pow-flip` `exp-diff` `exp-prod` `distribute-rgt-neg-out` `associate-+r-` `distribute-rgt-neg-in` `pow-pow` `hypot-udef`
2×	`pow-sqr` `difference-cubes` `pow-prod-up` `cos-diff` `log-div`
1×	`unsub-neg` `remove-double-div` `hypot-def` `sqrt-undiv` `distribute-rgt-out` `sqrt-pow2` `acos-asin` `distribute-lft-neg-out` `mul0` `distribute-lft-out` `exp-neg` `pow2` `exp-to-pow`