Date:Wednesday, April 15th, 2020
Commit:b8df7a50 on overflow-detection-both-ends
Hostname:warfa with Racket 7.5
Seed:2020106
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 (39.5%)

Algorithm
100×intervals
Results
46.1s7878×body5120exit
25.9s470702×body80valid
16.1s30837×body1280valid
7.8s23108×body640valid
4.1s3105×body1280nan
3.5s71045×body80nan
2.6s12088×body320valid
2.4s2529×body640nan
1.4s10056×body160valid
943.0ms49536×pre80true
884.0ms1303×body320nan
829.0ms7897×body80overflowed
480.0ms1477×body2560valid
286.0ms667×body160nan
199.0ms591×body5120valid

series1.3m (25.1%)

Calls

448 calls:

20.5s
(+ (pow (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow 1.0 3))
2.0s
(/ (* (* (- (* (+ (+ 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))))
903.0ms
(* (fma (* (/ 1 (exp (pow (fabs x) 2))) (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) 1.0) (/ (/ (* (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) 1.0) (fma 0.3275911 (fabs x) 1.0)) (exp (pow (fabs x) 2))))
847.0ms
(- 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))))))
846.0ms
(log (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))

prune1.3m (24.7%)

Filtered
26962 candidates to 14852 candidates (55.1%)

simplify16.2s (5.0%)

Algorithm
251×egg-herbie

rewrite9.1s (2.8%)

Algorithm
151×rewrite-expression-head
Calls

448 calls:

1.5s
(+ (pow (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow 1.0 3))
553.0ms
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
343.0ms
(* (* (* (* (sqrt 2.0) (exp (* -1 (* (log (+ z 6.5)) (- 0.5 z))))) (sqrt PI)) (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))))
167.0ms
(* (* (/ (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) z)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 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))))
157.0ms
(* (* (* (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
34247×times-frac
26166×*-un-lft-identity
19099×add-sqr-sqrt
14740×add-cube-cbrt
4044×distribute-lft-out
3663×fma-def
3286×add-exp-log
2496×prod-diff
2407×unpow-prod-down
2238×cube-prod
2033×add-cbrt-cube
1856×difference-of-squares
1854×sqrt-prod
1831×distribute-lft-out--
1614×frac-add
1508×associate-/r/
1254×pow1
1218×prod-exp
1171×flip-+ flip3-+
989×div-exp
982×associate-/l*
973×associate-*r*
945×div-inv
911×associate-*l*
837×associate-/r*
746×frac-times
676×associate-*r/
667×add-log-exp
612×cbrt-unprod
462×associate-*l/
457×cbrt-undiv
450×log1p-expm1-u
448×expm1-log1p-u
298×pow-prod-down
296×distribute-rgt-in distribute-lft-in
278×exp-neg
266×1-exp
263×cbrt-prod
262×exp-sum
258×unswap-sqr
257×fma-neg
256×cbrt-div
233×flip3-- flip--
228×sqr-pow
184×log-pow
167×rec-exp
153×unpow3 cube-mult
151×associate-/l/
133×*-commutative
132×exp-diff
128×exp-prod
125×neg-sub0
115×pow-exp
113×un-div-inv
111×swap-sqr
106×associate--l+
104×mul-1-neg
101×sqrt-div sub-neg
94×clear-num frac-2neg
90×pow-to-exp
88×pow-unpow
87×log-prod
70×frac-sub diff-log
67×sqrt-pow1
55×associate-+l- pow1/3
54×pow1/2 pow-sub
51×fma-udef
48×distribute-rgt-neg-in distribute-lft-neg-in
45×sum-log
35×pow-pow
32×pow-flip
29×rem-sqrt-square
28×pow-prod-up
26×rem-exp-log neg-mul-1
24×unpow-prod-up pow-sqr
23×inv-pow distribute-rgt1-in distribute-rgt-out
21×+-commutative
20×rem-cube-cbrt
18×neg-log
17×pow-plus
14×cube-div div-sub hypot-def
13×pow2
12×associate-+l+ rem-log-exp
10×associate--l-
8×associate--r+
5×unpow2
4×sin-sum distribute-neg-in exp-to-pow log-div
2×difference-cubes distribute-lft-neg-out log1p-udef sqrt-unprod log1p-expm1 expm1-log1p distribute-rgt-out-- distribute-rgt-neg-out expm1-udef associate-+r+
1×sqrt-pow2 sum-cubes pow3 hypot-udef cos-sum associate--r- rem-cbrt-cube

regimes5.8s (1.8%)

Accuracy

Total 43.5b remaining (32.8%)

Threshold costs 4.6b (3.5%)

8.0b35.9%_divideComplex, imaginary part
7.7b35.6%_divideComplex, real part
6.0b9.3%Octave 3.8, jcobi/2
4.5b22.2%math.sqrt on complex, imaginary part, im greater than 0 branch
4.0b30%math.sqrt on complex, real part

localize2.4s (0.7%)

bsearch1.1s (0.4%)

end1.0ms (0.0%)