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:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:complexrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifygenerate:better-rrreduce:regimesreduce:avg-errorreduce:binary-searchreduce:branch-expressionsprecision:doubleprecision:fallback` default

Details

Calls

403 calls:

6.0s	(sqrt (* U (* (* 2.0 n) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
5.8s	(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*)))))))
4.7s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.7s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
1.5s	(/ (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ (pow 1.0 3) (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3)))) (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))))))

Algorithm

61×

intervals

Results

Algorithm

168×	egg-herbie

Accuracy

Total 46.9b remaining (23.8%)

Threshold costs 3.2b (1.6%)

10.4b	28.2%	Toniolo and Linder, Equation (13)
8.8b	42.6%	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

403 calls:

217.0ms	(/ (- (* (* (* 1.0 (- (pow 1.0 3) (pow 0.5 3))) (* 1.0 (- (* 1.0 1.0) (* 0.5 0.5)))) (/ (hypot 1.0 x) 1.0)) (* (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) (+ 1.0 0.5)) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) 0.5))) (* (* (+ 1.0 0.5) (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5)))) (/ (hypot 1.0 x) 1.0)))
198.0ms	(* (* a a) (+ 1.0 a))
102.0ms	(- (* (* (* 1.0 (- (pow 1.0 3) (pow 0.5 3))) (* 1.0 (- (* 1.0 1.0) (* 0.5 0.5)))) (/ (hypot 1.0 x) 1.0)) (* (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) (+ 1.0 0.5)) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) 0.5)))
85.0ms	(+ (* (* c0 (* d d)) (/ 1 (* (* w h) (* D 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))))

Rules

9818×	`associate-*r/`
8256×	`frac-times`
5870×	`associate-*l/`
3435×	`frac-sub`
2820×	`clear-num`
2512×	`flip3-+` `flip-+`
2484×	`flip3--` `flip--`
1922×	`frac-2neg`
1775×	`associate-/l/`
1024×	`*-commutative`
914×	`un-div-inv`
869×	`associate-l`
744×	`associate-r`
509×	`times-frac`
496×	`associate-/l*`
446×	`sqr-pow`
386×	`unpow-prod-down`
379×	`div-inv`
373×	`associate-/r*`
361×	`sqrt-div`
352×	`distribute-rgt-in` `distribute-lft-in`
215×	`associate-/r/`
196×	`frac-add`
140×	`sub-neg`
129×	`tan-quot`
126×	`+-commutative`
106×	`associate-+r+` `associate-+l+`
102×	`sqrt-prod`
64×	`pow-to-exp`
62×	`associate--l+`
60×	`difference-of-squares`
59×	`unswap-sqr` `unpow2`
58×	`neg-mul-1`
43×	`pow1/2`
35×	`pow-unpow`
29×	`swap-sqr`
26×	`div-sub`
19×	`pow-prod-down`
16×	`pow-sub` `pow-neg`
14×	`neg-sub0`
13×	`distribute-rgt-neg-in` `distribute-lft-neg-in` `inv-pow` `distribute-rgt-out--`
11×	`prod-exp`
10×	`distribute-lft-neg-out`
9×	`pow2`
8×	`exp-sum`
7×	`distribute-frac-neg` `sum-cubes`
6×	`cos-sum` `distribute-lft-out--`
5×	`unpow3`
4×	`asin-acos`
3×	`pow-prod-up` `exp-diff` `pow-sqr` `exp-prod` `associate-+r-` `rec-exp`
2×	`sqrt-undiv` `sub-div` `cos-diff` `pow-pow` `log-div` `distribute-neg-frac`
1×	`pow-flip` `exp-neg` `div-exp` `acos-asin` `mul0` `exp-to-pow` `unsub-neg` `sqrt-pow1` `remove-double-div`