Date:Sunday, April 12th, 2020
Commit:48b457a7 on overflow-detection-both-ends
Hostname:warfa with Racket 7.5
Seed:2020103
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

sample2.1m (42.6%)

Algorithm
100×intervals
Results
47.0s8114×body5120exit
22.6s447947×body80valid
15.8s30586×body1280valid
7.5s23492×body640valid
4.2s3236×body1280nan
3.3s70164×body80nan
2.5s11893×body320valid
2.5s2623×body640nan
1.4s10116×body160valid
909.0ms49536×pre80true
835.0ms1275×body320nan
835.0ms8041×body80overflowed
481.0ms1509×body2560valid
259.0ms631×body160nan
193.0ms589×body5120valid

series1.2m (24.0%)

Calls

443 calls:

7.5s
(- (pow 1.0 3) (pow (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ (/ 1.0 (pow (fma 0.3275911 (fabs x) 1.0) 1/2)) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))) 3))
1.9s
(/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))
1.1s
(- (pow 1.0 3) (log1p (expm1 (pow (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ (/ 1.0 (pow (fma 0.3275911 (fabs x) 1.0) 1/2)) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))) 3))))
979.0ms
(/ (/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ 1 (fma beta alpha (* i (+ (+ alpha beta) i)))))
977.0ms
(/ (/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ 1 (fma beta alpha (* i (+ (+ alpha beta) i)))))

prune1.1m (22.7%)

Filtered
21052 candidates to 12497 candidates (59.4%)

simplify15.6s (5.4%)

Algorithm
252×egg-herbie

regimes5.9s (2.0%)

Accuracy

Total 45.9b remaining (31.4%)

Threshold costs 6.3b (4.3%)

9.1b25.4%_divideComplex, imaginary part
7.1b37.1%_divideComplex, real part
6.1b-1.6%math.sqrt on complex, real part
5.1b19.9%Octave 3.8, jcobi/2
4.6b22.4%math.sqrt on complex, imaginary part, im greater than 0 branch

rewrite5.4s (1.9%)

Algorithm
152×rewrite-expression-head
Calls

443 calls:

326.0ms
(/ (/ (/ (/ (+ beta (+ alpha (fma alpha beta 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (fma 1.0 2.0 (+ alpha beta))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
155.0ms
(* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp (- (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
132.0ms
(* (+ (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3))) (/ (* (+ (fma 1.875 (/ 1 (pow (fabs x) 6)) (* 0.75 (/ 1 (pow (fabs x) 4)))) 1) 1.0) (fabs x))) (* (/ 1.0 (sqrt PI)) (pow (exp (fabs x)) (/ (fabs x) 2))))
48.0ms
(/ (/ (/ (+ beta (+ alpha (fma alpha beta 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (fma 1.0 2.0 (+ alpha beta))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
43.0ms
(* (/ (/ 1.0 (sqrt 9.0)) (sqrt (- a (/ 1.0 3.0)))) rand)
Rules
20155×times-frac
16519×*-un-lft-identity
11221×add-sqr-sqrt
9881×add-cube-cbrt
4863×sqrt-prod
3483×distribute-lft-out
2469×add-exp-log
1639×add-cbrt-cube
1356×prod-diff
1295×associate-/l*
1200×pow1
1180×associate-*l*
826×unpow-prod-down
806×prod-exp
701×associate-*r*
671×add-log-exp
658×div-exp
598×associate-/r/
515×div-inv
453×flip-+ flip3-+
443×log1p-expm1-u expm1-log1p-u
442×associate-/r*
438×frac-add
422×cbrt-unprod
347×unswap-sqr
339×cbrt-undiv
325×sqrt-div
278×pow-prod-down
261×associate-*r/
252×difference-of-squares
235×distribute-lft-out--
226×sqr-pow
224×log-pow
222×fma-neg
213×frac-times
209×exp-sum
200×cube-prod
196×pow-exp
184×exp-prod
180×associate--l+
175×fma-def
172×distribute-rgt-in distribute-lft-in
168×1-exp
144×cbrt-prod
136×associate-*l/
135×log-prod
125×*-commutative rec-exp
101×flip3-- flip--
100×pow-to-exp
91×clear-num frac-2neg
89×sub-neg
82×pow-unpow
81×associate-/l/
79×diff-log
75×exp-neg
74×sqrt-pow1
63×swap-sqr
62×fma-udef
61×exp-diff
59×pow-sub associate-+l-
58×pow1/3
55×distribute-rgt-neg-in unpow3 cube-mult neg-sub0
53×pow1/2
51×distribute-lft-neg-in
49×sum-log pow-pow
45×cube-div
33×pow-prod-up pow-sqr
32×rem-sqrt-square
29×+-commutative
28×un-div-inv
25×neg-mul-1
24×cbrt-div
23×associate-+l+ pow-flip
22×rem-cube-cbrt
20×div-sub
19×inv-pow
16×associate--l-
14×associate-+r+
13×rem-exp-log hypot-def rem-log-exp
10×pow2 pow-plus
9×log-div
8×distribute-rgt-out neg-log
6×distribute-neg-in
5×distribute-rgt-neg-out
4×sin-sum hypot-udef cos-sum associate--r+ unpow2
2×distribute-lft1-in distribute-rgt1-in unpow-prod-up distribute-rgt-out-- frac-sub exp-to-pow
1×difference-cubes sqrt-pow2 distribute-lft-neg-out log1p-udef sqrt-unprod count-2 unsub-neg associate-+r-

localize2.6s (0.9%)

bsearch1.2s (0.4%)

end1.0ms (0.0%)