Date:Saturday, May 9th, 2020
Commit:4f3ba49d on doc-tweaks
Hostname:warfa with Racket 7.5
Seed:2020130
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

series3.5m (49.3%)

Calls

450 calls:

4.2s
(+ (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3) (pow 1.0 3))
2.5s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (* (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (/ 1 (+ (+ 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))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (+ (+ alpha beta) (* 2.0 i)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) 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))))
2.0s
(exp (log (- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (* (sqrt (+ 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))))))))) (sqrt (/ (- (* 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))))))))) (- 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 (neg (* (fabs x) (fabs x))))))))

sample2.0m (28.2%)

Algorithm
98×intervals
Results
46.3s8025×body5120exit
21.1s429502×body80valid
15.9s29897×body1280valid
7.7s22963×body640valid
4.0s3073×body1280nan
3.3s70173×body80nan
2.6s11749×body320valid
2.5s2594×body640nan
1.4s9980×body160valid
859.0ms1303×body320nan
831.0ms7974×body80overflowed
733.0ms41536×pre80true
495.0ms1516×body2560valid
284.0ms686×body160nan
195.0ms565×body5120valid

prune1.0m (14.4%)

Filtered
22136 candidates to 12881 candidates (58.2%)

simplify16.7s (3.9%)

Algorithm
249×egg-herbie

rewrite8.1s (1.9%)

Algorithm
153×rewrite-expression-head
Calls

453 calls:

558.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (+ (+ alpha beta) (* 2.0 i)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
277.0ms
(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
171.0ms
(/ (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
147.0ms
(* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (* (exp (neg (+ (+ (- 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)))))
145.0ms
(- (+ (/ (/ x (- (* wj wj) (* 1 1))) (/ (exp wj) (- wj 1))) wj) (/ wj (+ wj 1)))
Rules
25209×times-frac
16430×*-un-lft-identity
13450×add-sqr-sqrt
11116×add-cube-cbrt
6850×sqrt-prod
2851×add-exp-log
2752×associate-*r*
2295×pow1
2230×distribute-lft-out
2228×add-cbrt-cube
1646×frac-add
1274×associate-/l*
1148×prod-exp
1078×flip-+ flip3-+
1057×associate-/r/
984×associate-*l*
952×associate-*r/
827×difference-of-squares
794×cbrt-unprod
786×log-pow
729×frac-times
721×add-log-exp
657×associate-/r*
608×div-inv
585×sqrt-div
584×div-exp
531×pow-prod-down
475×distribute-lft-out--
431×associate-*l/
430×cbrt-undiv
315×unswap-sqr
283×exp-neg
206×flip-- flip3--
185×sqrt-pow1
154×*-commutative
151×exp-diff
149×unpow-prod-down
148×cbrt-div
147×neg-sub0
141×cbrt-prod
118×mul-1-neg log-prod
115×associate-+l-
113×pow-exp
111×pow-sub
109×pow1/2
107×associate-/l/
106×swap-sqr
92×distribute-rgt-in frac-2neg clear-num distribute-lft-in
91×un-div-inv
90×diff-log
84×sub-neg
78×pow-to-exp
71×sqr-pow
61×difference-of-sqr-1
58×pow-prod-up 1-exp rec-exp sum-log
57×rem-sqrt-square
56×cube-prod
50×pow-sqr pow1/3
45×associate--l+
33×+-commutative
30×exp-prod
28×pow-unpow
26×pow-plus
21×pow2
17×log-div
16×unpow3 associate-+l+ cube-mult exp-sum
15×div-sub
13×associate--l-
12×associate-+r+ associate--r+
11×pow-pow rem-log-exp
10×cube-div frac-sub
8×rem-exp-log inv-pow pow-flip
6×sin-sum
5×exp-to-pow unpow2
4×cos-sum rem-cube-cbrt distribute-neg-in
3×sqrt-unprod distribute-rgt-out-- unpow-prod-up rem-cbrt-cube
2×sub-div rem-square-sqrt sum-cubes
1×associate-+r- associate--r- log-rec

regimes6.3s (1.5%)

Accuracy

Total 90.5b remaining (33.1%)

Threshold costs 3.7b (1.3%)

13.7b51.6%math.sqrt on complex, real part
10.1b57.8%math.log10 on complex, real part
10.1b58.5%math.log/2 on complex, real part
9.8b58.9%math.log/1 on complex, real part
9.6b58.3%math.abs on complex

localize2.5s (0.6%)

bsearch1.6s (0.4%)

end1.0ms (0.0%)

Profiling

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