Date:Friday, March 6th, 2020
Commit:044801c1 on master
Hostname:warfa with Racket 7.5
Seed:2020066
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

sample1.8m (40.9%)

Algorithm
100×intervals
Results
46.4s15464×body10240exit
18.3s440075×body80valid
14.4s29920×body1280valid
6.5s23063×body640valid
2.7s2924×body1280nan
2.6s71648×body80nan
2.2s11609×body320valid
1.7s2520×body640nan
1.2s10285×body160valid
653.0ms49536×pre80true
632.0ms1241×body320nan
368.0ms1575×body2560valid
213.0ms662×body160nan
146.0ms627×body5120valid

series1.1m (24.5%)

Calls

476 calls:

3.3s
(* (+ (sqrt (+ (- (* d1 d2) (* d1 d3)) (* d4 d1))) d1) (- (sqrt (+ (- (* d1 d2) (* d1 d3)) (* d4 d1))) d1))
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))))
1.8s
(/ (* (* (- (* (+ (+ 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))))
912.0ms
(/ (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) z)) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- z 0))) (/ -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)))) (* (exp (+ (+ (- z 1.0) 7.0) 0.5)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5))))
838.0ms
(- 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
18065 candidates to 11613 candidates (64.3%)

simplify14.9s (5.5%)

Algorithm
257×egg-herbie

rewrite5.8s (2.1%)

Algorithm
157×rewrite-expression-head
Calls

476 calls:

164.0ms
(/ (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) z)) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- z 0))) (/ -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)))) (* (exp (+ (+ (- z 1.0) 7.0) 0.5)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5))))
158.0ms
(/ (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- z 0))) (/ -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)))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
152.0ms
(/ (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- z 1.0) 1.0))) (/ -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)))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
146.0ms
(* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- z 0))) (/ -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
(/ (* (* (* (pow (+ z 6.5) (- z 0.5)) (sqrt 2.0)) (sqrt PI)) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- z 0))) (/ -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)))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
Rules
7188×*-un-lft-identity
6184×add-sqr-sqrt
6076×times-frac
4858×add-cube-cbrt
2249×add-exp-log
1905×sqrt-prod
1816×prod-diff
1677×pow1
1670×add-cbrt-cube
1022×distribute-lft-out
851×associate-*r*
756×prod-exp
742×frac-add
731×add-log-exp
690×associate-*l*
534×associate-/l*
524×div-exp
496×associate-/r*
477×log1p-expm1-u expm1-log1p-u
452×cbrt-unprod
442×flip-+ flip3-+
425×associate-/r/
393×pow-prod-down
375×associate-*r/
374×cbrt-prod
341×div-inv
329×difference-of-squares
313×unpow-prod-down cbrt-undiv
307×distribute-rgt-in distribute-lft-in
280×sqrt-pow1
254×fma-neg
252×distribute-lft-out--
244×unswap-sqr
211×sqrt-div
210×log-pow
209×associate-/l/
177×log-prod
175×exp-sum
168×fma-def
164×associate-*l/
158×frac-times
154×pow1/2
149×pow-prod-up
143×flip3-- flip--
140×associate--r+
139×associate--l+
136×*-commutative
131×cube-prod
118×swap-sqr
111×1-exp
106×pow-exp
100×sub-neg
98×sqr-pow frac-2neg clear-num
92×pow-sub
87×diff-log
80×pow-unpow
78×pow-plus
77×pow1/3
75×pow-to-exp
72×associate-+l-
71×pow-sqr
69×rec-exp
63×cbrt-div
58×sum-log
55×associate-+l+
44×fma-udef
42×rem-sqrt-square
36×pow2
33×pow-flip
31×+-commutative
30×distribute-rgt-neg-in distribute-lft-neg-in
28×neg-mul-1
25×exp-prod
24×associate-+r+
21×pow-pow unpow3 cube-mult
16×inv-pow
15×frac-sub div-sub associate--l-
14×rem-cube-cbrt hypot-udef
13×exp-diff unpow-prod-up log-div
12×hypot-def
11×rem-log-exp
10×pow-div cube-div distribute-rgt-out
9×pow3
8×sqrt-unprod
5×rem-exp-log distribute-lft1-in rem-square-sqrt
4×un-div-inv sin-sum difference-of-sqr-1 unpow2
3×expm1-log1p rem-cbrt-cube expm1-udef
2×log1p-udef log1p-expm1 neg-sub0 neg-log associate--r- distribute-rgt-neg-out
1×sqrt-pow2 associate-+r- log-rec cos-sum

regimes5.5s (2.0%)

Accuracy

Total 49.5b remaining (44.9%)

Threshold costs 6.1b (5.5%)

8.9b26.5%_divideComplex, imaginary part
8.8b45.5%Octave 3.8, jcobi/4
7.0b37.5%_divideComplex, real part
5.5b18%Octave 3.8, jcobi/2
4.5b22.7%math.sqrt on complex, imaginary part, im greater than 0 branch

localize2.6s (0.9%)

bsearch871.0ms (0.3%)

end1.0ms (0.0%)