Date:Wednesday, April 29th, 2020
Commit:293eb8dd on gh-actions
Hostname:warfa with Racket 7.5
Seed:2020120
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

sample2.1m (45.0%)

Algorithm
100×intervals
Results
46.8s7959×body5120exit
23.4s452364×body80valid
16.3s30778×body1280valid
7.7s23624×body640valid
4.1s3148×body1280nan
3.3s70392×body80nan
2.6s11990×body320valid
2.4s2556×body640nan
1.4s9990×body160valid
925.0ms49536×pre80true
887.0ms1316×body320nan
818.0ms8005×body80overflowed
475.0ms1471×body2560valid
251.0ms594×body160nan
198.0ms566×body5120valid

prune1.0m (22.6%)

Filtered
20335 candidates to 12924 candidates (63.6%)

series59.4s (21.4%)

Calls

454 calls:

2.7s
(pow (exp (* (cbrt (log (fma (/ (log (* (pow (exp (/ 1.0 (fma (fabs x) 0.3275911 1.0))) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.061405429 -1.453152027) 1.421413741) -0.284496736)) (exp 0.254829592))) (exp (* (fabs x) (fabs x)))) (/ (- 1.0) (fma (fabs x) 0.3275911 1.0)) 1.0))) (cbrt (log (fma (/ (log (* (pow (exp (/ 1.0 (fma (fabs x) 0.3275911 1.0))) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.061405429 -1.453152027) 1.421413741) -0.284496736)) (exp 0.254829592))) (exp (* (fabs x) (fabs x)))) (/ (- 1.0) (fma (fabs x) 0.3275911 1.0)) 1.0))))) (cbrt (log (fma (/ (log (* (pow (exp (/ 1.0 (fma (fabs x) 0.3275911 1.0))) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.061405429 -1.453152027) 1.421413741) -0.284496736)) (exp 0.254829592))) (exp (* (fabs x) (fabs x)))) (/ (- 1.0) (fma (fabs x) 0.3275911 1.0)) 1.0))))
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))))
1.3s
(* (sqrt (/ 1.0 (sqrt PI))) (+ (* (sqrt (/ 1.0 (sqrt PI))) (fma (fabs x) 2.0 (* (pow (fabs x) 3) (/ 2.0 3.0)))) (* (sqrt (/ 1.0 (sqrt PI))) (fma (/ 1.0 5.0) (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0))))))
880.0ms
(expm1 (log1p (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))))
815.0ms
(log1p (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))

simplify16.2s (5.8%)

Algorithm
255×egg-herbie

regimes5.4s (1.9%)

Accuracy

Total 44.4b remaining (39%)

Threshold costs 6.3b (5.6%)

8.3b30.6%_divideComplex, imaginary part
8.2b29.2%_divideComplex, real part
5.2b19.5%Octave 3.8, jcobi/2
4.7b20.9%math.sqrt on complex, real part
4.7b18%math.sqrt on complex, imaginary part, im greater than 0 branch

rewrite5.2s (1.9%)

Algorithm
155×rewrite-expression-head
Calls

454 calls:

328.0ms
(* (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (fma 1.0 2.0 (+ alpha beta)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))) (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (fma 2.0 1.0 1.0))))
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))))
142.0ms
(* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp (- (+ z 6.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 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))))
65.0ms
(/ (+ (+ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* 0.0424060604 (* (* x x) (* x x)))) (* 0.0072644182 (* (* (* x x) (* x x)) (* x x)))) (* 0.0005064034 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0001789971 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (+ (+ (+ (+ (+ (+ 1.0 (* 0.7715471019 (* x x))) (* 0.2909738639 (* (* x x) (* x x)))) (* 0.0694555761 (* (* (* x x) (* x x)) (* x x)))) (* 0.0140005442 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0008327945 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (* (* 2.0 0.0001789971) (* (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)) (* x x)))))
61.0ms
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
Rules
15653×times-frac
12474×*-un-lft-identity
10194×add-sqr-sqrt
8702×add-cube-cbrt
2416×sqrt-prod
2208×add-exp-log
1802×distribute-lft-out
1705×prod-diff
1586×add-cbrt-cube
1182×pow1
1074×associate-*l*
928×associate-*r*
834×frac-add
715×prod-exp
682×div-inv
679×add-log-exp
625×associate-/l*
616×unpow-prod-down
547×cbrt-prod
539×div-exp
519×associate-/r*
456×expm1-log1p-u
454×log1p-expm1-u
422×cbrt-unprod
395×associate-/r/
372×flip-+ flip3-+
350×frac-times
328×unswap-sqr
319×associate-*r/ difference-of-squares
315×cbrt-undiv
297×distribute-lft-out--
262×pow-prod-down
261×exp-sum
247×distribute-rgt-in distribute-lft-in
226×fma-neg
187×associate-*l/
184×log-prod
183×log-pow associate--l+
169×fma-def
157×sqr-pow
154×cube-prod
149×pow-exp
130×1-exp
124×*-commutative
119×flip3-- flip--
109×swap-sqr
107×associate-+l-
106×exp-neg
105×pow-sub
104×sqrt-div
100×sub-neg
92×clear-num frac-2neg
89×rec-exp diff-log
83×pow-unpow
81×pow-to-exp exp-prod
78×associate-/l/
76×exp-diff
74×neg-sub0
71×associate--r+
69×pow1/3
66×sqrt-pow1
61×fma-udef
59×pow1/2
49×cbrt-div
44×distribute-rgt-neg-in distribute-lft-neg-in
43×un-div-inv
35×pow-pow
32×sum-log
30×unpow3 cube-mult
27×rem-sqrt-square neg-mul-1
24×pow-prod-up
21×pow-flip
20×rem-exp-log pow-sqr div-sub
18×associate--l-
17×hypot-udef
16×rem-cube-cbrt rem-log-exp
14×inv-pow hypot-def
13×+-commutative neg-log
12×associate-+l+
11×cube-div pow2 pow-plus
7×unpow2
5×distribute-neg-in
4×sin-sum frac-sub sum-cubes rem-cbrt-cube distribute-rgt-neg-out
3×unpow-prod-up exp-to-pow log-div
2×pow-div sqrt-pow2 log1p-udef sqrt-unprod log1p-expm1 expm1-log1p rem-square-sqrt expm1-udef
1×sqrt-undiv distribute-lft-neg-out unsub-neg cos-sum associate--r-

localize2.4s (0.9%)

bsearch1.2s (0.4%)

end1.0ms (0.0%)