Date:	Wednesday, March 18th, 2020
Commit:	7c9a4fcd on better-rr
Hostname:	warfa with Racket 7.5
Seed:	2020078
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

415 calls:

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)))))))))
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*)))))
4.6s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))
4.6s	(sqrt (* n (* (* 2.0 U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))))

Algorithm

61×

intervals

Results

Algorithm

173×	egg-herbie

Accuracy

Total 45.5b remaining (23.5%)

Threshold costs 3.5b (1.8%)

10.0b	36.9%	Toniolo and Linder, Equation (13)
9.1b	37.6%	Henrywood and Agarwal, Equation (12)
6.2b	62.9%	Henrywood and Agarwal, Equation (3)
6.1b	74.4%	Toniolo and Linder, Equation (7)
3.4b	-6.2%	Henrywood and Agarwal, Equation (13)

Algorithm

113×	rewrite-expression-head

Calls

415 calls:

89.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
86.0ms	(+ (* (/ (* c0 d) (* D D)) (/ d (* w h))) (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)))
28.0ms	(- (* (pow 1.0 3) (pow 1.0 3)) (* (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)))
24.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (/ (hypot (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3/2) (pow 1.0 3/2)) (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)))))))

Rules

882×	`*-commutative`
739×	`associate-l`
635×	`sqr-pow`
558×	`clear-num`
547×	`associate-r`
529×	`frac-2neg`
497×	`div-inv`
477×	`times-frac`
460×	`associate-*r/`
423×	`sqrt-div`
412×	`frac-times`
387×	`frac-add`
354×	`associate-/r*`
296×	`unpow-prod-down`
286×	`associate-/l*`
280×	`flip--` `flip3--`
242×	`associate-*l/`
227×	`prod-diff` `frac-sub`
224×	`associate-/l/`
221×	`associate-/r/`
176×	`sqrt-prod`
169×	`distribute-rgt-in` `distribute-lft-in`
137×	`unpow3`
116×	`flip-+` `flip3-+`
96×	`swap-sqr`
80×	`sub-neg`
78×	`div-sub`
77×	`unswap-sqr`
74×	`+-commutative`
67×	`unpow2`
62×	`pow-to-exp`
54×	`neg-mul-1`
51×	`fma-def`
48×	`pow-sub`
47×	`pow1/2`
45×	`fma-udef`
41×	`tan-quot` `fma-neg`
40×	`distribute-neg-frac`
36×	`associate-+r+` `associate-+l+`
33×	`pow-unpow`
31×	`un-div-inv`
28×	`difference-of-squares`
24×	`associate--l+`
22×	`distribute-rgt-neg-in` `distribute-lft-neg-in`
17×	`neg-sub0`
11×	`inv-pow`
10×	`distribute-frac-neg` `distribute-lft-neg-out`
9×	`prod-exp`
8×	`associate--r+` `distribute-rgt-out--`
7×	`pow-prod-down`
6×	`sub-div` `difference-cubes` `pow-neg` `pow-pow`
5×	`hypot-udef` `sqrt-pow2` `distribute-lft-out--`
4×	`remove-double-div`
3×	`unsub-neg` `exp-diff` `exp-neg` `exp-prod` `sqrt-undiv` `div-exp` `associate-+r-`
2×	`rec-exp` `acos-asin` `asin-acos` `associate--r-` `associate--l-` `cos-sum`
1×	`pow-flip` `hypot-def` `distribute-rgt-out` `mul0` `sum-cubes` `distribute-rgt-neg-out` `cos-diff`