Date:Sunday, March 15th, 2020
Commit:1a959946 on master
Hostname:warfa with Racket 7.5
Seed:2020075
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

prune2.0m (35.6%)

Filtered
32881 candidates to 19331 candidates (58.8%)

sample1.9m (33.6%)

Algorithm
100×intervals
Results
49.1s16099×body10240exit
19.4s461348×body80valid
14.1s30579×body1280valid
6.5s23092×body640valid
2.9s3052×body1280nan
2.6s70553×body80nan
2.2s12400×body320valid
1.7s2542×body640nan
1.2s9993×body160valid
693.0ms49536×pre80true
672.0ms1371×body320nan
364.0ms1555×body2560valid
203.0ms625×body160nan
139.0ms572×body5120valid

series1.1m (19.4%)

Calls

470 calls:

2.1s
(/ (* (* (- (* (+ (+ 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))))
1.9s
(/ (* (- (* (+ (+ 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))))
1.2s
(pow (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (log (/ 1 u1)) 1.0))) 0.5)
852.0ms
(/ (/ i (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (+ (+ alpha beta) i))) (/ (fma i 2.0 (+ alpha beta)) (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma i 2.0 (+ alpha beta)))))
842.0ms
(log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))

simplify21.5s (6.3%)

Algorithm
257×egg-herbie

rewrite8.5s (2.5%)

Algorithm
157×rewrite-expression-head
Calls

470 calls:

205.0ms
(/ (/ i (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (+ (+ alpha beta) i))) (/ (fma i 2.0 (+ alpha beta)) (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma i 2.0 (+ alpha beta)))))
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)))))
154.0ms
(/ (* (* (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)))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
150.0ms
(/ (* (* (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)))) (exp (+ (- z 1.0) 7.0)))
143.0ms
(* (* (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))))
Rules
73275×times-frac
43526×*-un-lft-identity
34512×add-sqr-sqrt
28586×add-cube-cbrt
7331×distribute-lft-out
6352×sqrt-prod
3082×difference-of-squares
2767×add-exp-log
2095×div-inv
1774×add-cbrt-cube
1547×prod-diff
1464×associate-/r/
1437×pow1
1319×distribute-lft-out--
922×prod-exp
892×div-exp
854×associate-/r*
696×flip-+ flip3-+
695×add-log-exp
677×associate-/l*
652×frac-add
628×associate-*r*
604×associate-*l*
585×cbrt-prod
493×cbrt-unprod
477×unpow-prod-down
472×log1p-expm1-u
471×expm1-log1p-u
412×pow-prod-down
370×cbrt-undiv associate-*r/
283×sqrt-div
264×cube-prod
253×distribute-rgt-in distribute-lft-in
231×1-exp
221×pow-exp
205×fma-neg
202×log-pow
200×exp-sum
186×unswap-sqr
183×fma-def
175×associate--l+
165×frac-times
159×associate-/l/
151×flip3-- flip--
149×sqrt-pow1
143×pow-to-exp
116×*-commutative
114×rec-exp
112×sqr-pow
107×associate-*l/
106×pow1/2
98×log-prod
97×frac-2neg clear-num cbrt-div
96×pow1/3
95×sub-neg
93×swap-sqr
85×diff-log
84×associate-+l-
73×pow-sub
67×pow-unpow
64×fma-udef
56×distribute-rgt-neg-in
54×distribute-lft-neg-in
42×pow-prod-up sum-log
34×unpow3 pow-sqr cube-mult
33×rem-sqrt-square
32×neg-mul-1
25×+-commutative
23×exp-prod
19×pow-pow
18×associate--l-
17×hypot-def div-sub
16×associate-+l+ pow-plus rem-log-exp
15×pow-flip
14×pow2
12×inv-pow unpow2
11×rem-cube-cbrt
10×sqrt-unprod
8×cube-div rem-exp-log frac-sub
7×exp-diff
6×distribute-rgt-out-- associate--r+
5×hypot-udef log-div
4×sin-sum unpow-prod-up
3×un-div-inv rem-square-sqrt
2×log1p-udef distribute-neg-in log1p-expm1 sub-div expm1-log1p neg-sub0 neg-log distribute-rgt-neg-out expm1-udef
1×sqrt-undiv sqrt-pow2 associate-+r+ unpow1/2 cos-sum rem-cbrt-cube

regimes4.9s (1.4%)

Accuracy

Total 49.9b remaining (35.8%)

Threshold costs 6.4b (4.6%)

9.5b0.5%math.sqrt on complex, real part
8.0b36.6%_divideComplex, imaginary part
7.4b34%_divideComplex, real part
5.9b8%Octave 3.8, jcobi/2
4.4b29.7%math.sqrt on complex, imaginary part, im greater than 0 branch

localize2.7s (0.8%)

bsearch1.1s (0.3%)

end3.0ms (0.0%)