Date:Thursday, April 30th, 2020
Commit:79b0ceb2 on master
Hostname:warfa with Racket 7.5
Seed:2020121
Parameters:256 points for 4 iterations
Flags:
setup:simplifyrules:numericsrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:complexrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifyreduce:regimesreduce:avg-errorreduce:binary-searchreduce:branch-expressionsprecision:doubleprecision:fallback
+o rules:numerics

Details

series1.7m (37.0%)

Calls

444 calls:

4.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.4s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
1.9s
(expm1 (log1p (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))))
1.7s
(sqrt (* (* (* 2.0 n) U) (fma (* (cbrt (- t (* 2.0 (* l (/ l Om))))) (cbrt (- t (* 2.0 (* l (/ l Om)))))) (cbrt (- t (* 2.0 (* l (/ l Om))))) (- (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

sample1.6m (34.1%)

Algorithm
61×intervals
Results
18.9s248794×body80valid
18.0s31075×body1280valid
13.6s166984×body80nan
9.0s8781×body2560valid
8.4s21065×body640valid
5.3s3222×body5120valid
3.0s10362×body320valid
1.7s9205×body160valid
813.0ms1606×body1280nan
555.0ms1476×body640nan
373.0ms597×body5120exit
369.0ms2745×body80overflowed
192.0ms720×body320nan
144.0ms8256×pre80true
68.0ms431×body160nan

prune49.3s (17.7%)

Filtered
20320 candidates to 10556 candidates (51.9%)

simplify12.4s (4.5%)

Algorithm
178×egg-herbie

regimes9.8s (3.5%)

Accuracy

Total 43.7b remaining (22.3%)

Threshold costs 4.5b (2.3%)

8.6b40.6%Henrywood and Agarwal, Equation (3)
6.0b37%Toniolo and Linder, Equation (13)
5.7b7.4%Henrywood and Agarwal, Equation (12)
5.7b76%Toniolo and Linder, Equation (7)
5.5b24.5%Toniolo and Linder, Equation (10-)

rewrite4.8s (1.7%)

Algorithm
118×rewrite-expression-head
Calls

444 calls:

81.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))
77.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
40.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))
32.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
30.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))
Rules
31407×add-exp-log
21901×prod-exp
11297×pow-exp
9147×div-exp
5016×pow-to-exp
4155×times-frac
4119×add-sqr-sqrt
3971×*-un-lft-identity
3229×add-cube-cbrt
2625×add-cbrt-cube
1413×1-exp rec-exp
1098×pow1
993×cbrt-unprod
914×cbrt-prod
826×unpow-prod-down
789×associate-*r*
752×associate-*l*
709×sqrt-prod
583×cbrt-undiv
515×add-log-exp
447×expm1-log1p-u
445×log1p-expm1-u
412×associate-/r*
393×associate-*r/
361×div-inv
350×prod-diff
345×associate-/l*
333×pow-prod-down
316×pow-unpow
274×sqrt-div
273×exp-prod
271×distribute-lft-out
257×unswap-sqr
251×sqr-pow
234×flip-- flip3--
216×frac-times
207×distribute-rgt-in distribute-lft-in
193×distribute-rgt-neg-in
189×distribute-lft-out--
158×difference-of-squares
154×associate-/r/
144×*-commutative
137×associate-*l/
136×distribute-lft-neg-in
101×flip-+ clear-num flip3-+ frac-2neg
81×pow1/3
80×fma-def
64×sqrt-pow1
63×sub-neg
55×cbrt-div
48×associate-/l/
47×cos-sum
44×associate--r+ swap-sqr
42×cube-prod associate--l+
41×pow1/2
37×pow-pow
36×rem-sqrt-square
34×fma-udef
33×frac-sub
28×associate-+r+ div-sub
25×unpow2
24×tan-quot
22×sum-log
21×neg-sub0
19×pow-neg
18×+-commutative
17×fma-neg
16×pow-sub neg-mul-1
14×hypot-def
13×diff-log un-div-inv
12×exp-neg
10×pow-prod-up pow-sqr
9×pow-flip log-prod
8×distribute-rgt-neg-out
7×rem-exp-log exp-diff associate-+r-
6×cube-mult rem-cube-cbrt unpow3 inv-pow log-pow expm1-log1p expm1-udef
5×pow-plus pow2 unsub-neg
4×distribute-frac-neg acos-asin log-rec mul-1-neg
3×log1p-udef log1p-expm1 unpow-prod-up asin-acos exp-sum
2×cube-div associate-+l+ associate--l- frac-add cos-diff hypot-udef rem-cbrt-cube
1×e-exp-1 sin-sum mul0 rem-log-exp

localize2.2s (0.8%)

bsearch2.0s (0.7%)

end0.0ms (0.0%)