Date:Tuesday, March 31st, 2020
Commit:2cac45bc on simpler-alts
Hostname:warfa with Racket 7.5
Seed:2020091
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

sample1.9m (40.4%)

Algorithm
100×intervals
Results
46.1s15663×body10240exit
19.4s459100×body80valid
14.2s30517×body1280valid
6.5s23357×body640valid
2.8s3069×body1280nan
2.4s68746×body80nan
2.2s12003×body320valid
1.7s2521×body640nan
1.2s10185×body160valid
671.0ms49536×pre80true
575.0ms1207×body320nan
345.0ms1495×body2560valid
192.0ms630×body160nan
129.0ms564×body5120valid

series1.1m (24.8%)

Calls

449 calls:

2.2s
(/ (* (* (/ i (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (+ alpha beta) i) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (/ (fma i 2.0 (+ alpha beta)) (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma i 2.0 (+ alpha beta)))))
1.9s
(/ (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
1.9s
(* (* (/ i (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (+ alpha beta) i) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))
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))))
963.0ms
(- 1.0 (* (* (/ 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))))))

prune1.1m (23.7%)

Filtered
20926 candidates to 12810 candidates (61.2%)

simplify15.3s (5.5%)

Algorithm
254×egg-herbie

rewrite6.0s (2.2%)

Algorithm
154×rewrite-expression-head
Calls

449 calls:

428.0ms
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
161.0ms
(/ (* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) z)) (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)))) (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5)))
151.0ms
(* (* (* (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))))
147.0ms
(* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) z)) (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))))
146.0ms
(* (* (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)))))
Rules
16512×times-frac
13755×*-un-lft-identity
10565×add-sqr-sqrt
8209×add-cube-cbrt
3726×add-exp-log
2903×add-cbrt-cube
2023×distribute-lft-out
1716×frac-add
1616×pow1
1548×prod-diff
1481×prod-exp
1319×fma-def
1073×div-exp
1069×cbrt-unprod
1049×sqrt-prod
932×associate-*l*
895×frac-times
878×difference-of-squares
855×distribute-lft-out--
796×associate-/r/
785×flip-+ flip3-+
778×associate-*r*
764×associate-/l*
741×cbrt-undiv
734×associate-/r*
718×associate-*r/
673×add-log-exp
642×associate-*l/
554×div-inv
468×sqrt-div
452×expm1-log1p-u
450×log1p-expm1-u
326×pow-prod-down
283×exp-sum
243×distribute-rgt-in distribute-lft-in
225×cbrt-prod fma-neg unswap-sqr
218×log-prod
199×pow-prod-up
193×log-pow
192×swap-sqr
178×exp-neg
162×pow-plus
159×1-exp
157×flip-- flip3--
149×associate-/l/
139×associate--l+
134×*-commutative
132×unpow-prod-down
131×exp-diff
126×neg-sub0
115×associate-+l-
113×pow-sub
96×sub-neg
92×rec-exp
90×frac-2neg clear-num
88×sqrt-pow1
83×diff-log
75×pow-sqr
74×pow-exp
73×associate--r+
69×pow1/3
68×fma-udef
61×pow1/2
60×un-div-inv
59×pow-to-exp
57×sqr-pow
53×pow2
49×pow-unpow
42×cbrt-div
39×sum-log
32×exp-prod cube-prod
28×rem-sqrt-square unpow-prod-up
27×pow-pow +-commutative
24×distribute-rgt-neg-in distribute-lft-neg-in
22×pow-flip neg-mul-1
20×rem-log-exp
18×associate-+l+
15×associate--l-
14×inv-pow hypot-def
12×div-sub
10×rem-exp-log unpow3 cube-mult
9×associate-+r+
8×pow3 distribute-neg-in
7×log-div
5×distribute-rgt-neg-out
4×log1p-udef sin-sum log1p-expm1 expm1-log1p frac-sub expm1-udef unpow2
3×rem-cube-cbrt hypot-udef
2×sqrt-unprod rem-square-sqrt neg-log exp-to-pow
1×sqrt-pow2 e-exp-1 distribute-lft-neg-out unsub-neg associate--r- cos-sum

regimes5.6s (2.0%)

Accuracy

Total 43.3b remaining (32%)

Threshold costs 6.2b (4.6%)

8.3b30.9%_divideComplex, imaginary part
6.9b37.6%_divideComplex, real part
6.4b0.1%Octave 3.8, jcobi/2
4.3b28.8%math.sqrt on complex, real part
4.0b32.7%math.sqrt on complex, imaginary part, im greater than 0 branch

localize2.5s (0.9%)

bsearch1.3s (0.5%)

end1.0ms (0.0%)