Date:Tuesday, February 25th, 2020
Commit:61e80a61 on faster-rr
Hostname:warfa with Racket 7.5
Seed:2020056
Parameters:256 points for 4 iterations
Flags:
setup:simplifyrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:complexrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifyreduce:regimesreduce:avg-errorreduce:binary-searchreduce:branch-expressionsprecision:doubleprecision:fallback
default

Details

series10.9m (75.1%)

Calls

478 calls:

20.1s
(- (pow 1.0 3) (/ (pow (* (* 1.0 (- (* 0.254829592 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 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))) (* (/ 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 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))))))) (exp (- (* (fabs x) (fabs x))))) 3) (pow (* (+ 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 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) 3)))
3.2s
(- (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 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))) 3))
2.4s
(/ (* (/ (/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
2.3s
(/ (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
2.2s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))

sample1.9m (12.7%)

Algorithm
98×intervals
Results
48.3s15781×body10240exit
18.0s434409×body80valid
14.0s30719×body1280valid
6.6s23690×body640valid
2.7s3221×body1280nan
2.6s70235×body80nan
2.1s11834×body320valid
1.6s2548×body640nan
716.0ms6191×body160valid
672.0ms49536×pre80true
547.0ms1221×body320nan
327.0ms1394×body2560valid
189.0ms648×body160nan
148.0ms593×body5120valid

prune1.2m (7.9%)

simplify15.5s (1.8%)

Algorithm
260×egg-herbie

rewrite9.2s (1.1%)

Algorithm
164×rewrite-expression-head
Calls

482 calls:

391.0ms
(+ (/ (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ 1 (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)
376.0ms
(+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)
339.0ms
(* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 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))))
179.0ms
(* 0.0008327945 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))
177.0ms
(* 0.0005064034 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))
Rules
20095×times-frac
17884×*-un-lft-identity
10928×add-sqr-sqrt
8781×add-cube-cbrt
5106×distribute-lft-out
3862×add-exp-log
2602×add-cbrt-cube
2299×pow1
2165×prod-exp
2063×sqrt-prod
1317×flip-+ flip3-+
1239×associate-*l*
1206×associate-/r/
1119×associate-*r*
1118×cbrt-unprod
921×pow-prod-down
879×associate-*r/
755×associate-/r* frac-times
754×add-log-exp
742×difference-of-squares
729×associate-/l*
686×sqrt-div
684×frac-add
680×div-inv
586×distribute-lft-out--
521×div-exp
506×associate-*l/
486×cbrt-div
480×pow-exp
422×unpow-prod-down
404×cbrt-undiv
371×cbrt-prod
301×unswap-sqr
260×sqr-pow
259×pow-to-exp
224×exp-sum
215×log-pow
214×cube-prod
189×associate-/l/
171×pow-unpow
165×*-commutative
152×sqrt-pow1
150×flip3-- flip--
136×distribute-rgt-in distribute-lft-in
124×swap-sqr
118×pow1/2
99×sub-neg
98×pow-prod-up log-prod
92×clear-num frac-2neg
89×diff-log
75×pow1/3
70×pow-sqr
69×associate-+l-
62×sum-log
55×rem-sqrt-square pow-pow
54×pow-plus
43×1-exp
42×distribute-neg-frac
40×exp-diff
39×pow-sub +-commutative distribute-rgt-neg-in associate--l+
37×pow2
34×rec-exp
33×distribute-lft-neg-in
30×cube-div
29×exp-neg exp-prod
27×neg-sub0
23×unpow3 cube-mult
20×associate-+r+
18×associate-+l+
16×rem-cube-cbrt associate--l-
15×div-sub
12×sin-sum associate--r+
11×pow-flip neg-mul-1
10×un-div-inv inv-pow
7×unpow2
6×rem-exp-log distribute-neg-in
5×rem-cbrt-cube rem-log-exp
4×sqrt-unprod unpow-prod-up frac-sub distribute-rgt-neg-out log-div
3×sqrt-pow2 mul-1-neg difference-of-sqr-1
2×sqrt-undiv difference-cubes pow3 rem-square-sqrt neg-log
1×cos-sum unsub-neg associate-+r- cos-mult associate--r- exp-to-pow

regimes6.7s (0.8%)

Accuracy

Total 116.9b remaining (48.5%)

Threshold costs 4.5b (1.9%)

23.9b35.3%math.sqrt on complex, imaginary part, im greater than 0 branch
11.0b56.1%math.log10 on complex, real part
10.9b56.2%math.log/2 on complex, real part
10.8b56.5%math.log/1 on complex, real part
10.3b57.3%math.abs on complex

localize2.7s (0.3%)

bsearch2.7s (0.3%)

end1.0ms (0.0%)