Date:Saturday, April 11th, 2020
Commit:a26a9b61 on overflow-detection-both-ends
Hostname:warfa with Racket 7.5
Seed:2020102
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 (45.6%)

Algorithm
100×intervals
Results
51.0s12118×body5120exit
23.4s450872×body80valid
16.0s30925×body1280valid
7.5s23041×body640valid
3.7s69661×body80nan
3.6s3210×body1280nan
2.6s12231×body320valid
2.1s2584×body640nan
1.5s10287×body160valid
902.0ms49536×pre80true
811.0ms1350×body320nan
458.0ms1447×body2560valid
277.0ms687×body160nan
179.0ms559×body5120valid
139.0ms4042×body80overflowed

series1.1m (23.4%)

Calls

454 calls:

2.2s
(pow (exp (* (cbrt (log (fma (/ (cbrt (pow (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)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) 3)) (exp (* (fabs x) (fabs x)))) (/ (- 1.0) (fma (fabs x) 0.3275911 1.0)) 1.0))) (cbrt (log (fma (/ (cbrt (pow (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)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) 3)) (exp (* (fabs x) (fabs x)))) (/ (- 1.0) (fma (fabs x) 0.3275911 1.0)) 1.0))))) (cbrt (log (fma (/ (cbrt (pow (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)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) 3)) (exp (* (fabs x) (fabs x)))) (/ (- 1.0) (fma (fabs x) 0.3275911 1.0)) 1.0))))
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))))
1.1s
(* (/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
899.0ms
(expm1 (log1p (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))))
851.0ms
(log1p (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)))

prune56.4s (20.1%)

Filtered
18618 candidates to 11743 candidates (63.1%)

simplify14.4s (5.2%)

Algorithm
258×egg-herbie

rewrite7.1s (2.5%)

Algorithm
158×rewrite-expression-head
Calls

454 calls:

610.0ms
(* 0.0001789971 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))
599.0ms
(* 0.0001789971 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))
169.0ms
(* (- (/ (/ beta (+ alpha (+ beta (fma i 2.0 2.0)))) (fma i 2.0 (+ alpha beta))) (/ (/ alpha (+ alpha (+ beta (fma i 2.0 2.0)))) (fma i 2.0 (+ alpha beta)))) (+ alpha beta))
167.0ms
(+ (* (- (/ (/ beta (+ alpha (+ beta (fma i 2.0 2.0)))) (fma i 2.0 (+ alpha beta))) (/ (/ alpha (+ alpha (+ beta (fma i 2.0 2.0)))) (fma i 2.0 (+ alpha beta)))) (+ alpha beta)) 1.0)
150.0ms
(/ (* (* (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)))
Rules
10303×*-un-lft-identity
9569×times-frac
7240×add-sqr-sqrt
6007×add-cube-cbrt
3357×add-exp-log
2587×add-cbrt-cube
2343×distribute-lft-out
2067×pow1
1606×prod-exp
1423×prod-diff
1216×cbrt-unprod
1021×associate-*l*
1003×sqrt-prod
970×pow-prod-down
880×associate-*r*
694×associate-/l*
646×div-exp
623×add-log-exp
615×cbrt-prod
540×div-inv
470×frac-add
455×log1p-expm1-u expm1-log1p-u
398×associate-/r*
355×cbrt-undiv
351×associate-/r/
335×unpow-prod-down
315×flip-+ flip3-+
277×distribute-lft-out--
275×difference-of-squares
272×exp-sum
259×associate-*r/
248×unswap-sqr
230×log-pow
214×fma-neg
185×cube-prod
168×associate-/l/
156×fma-def
153×1-exp
149×distribute-rgt-in distribute-lft-in
146×frac-times
144×sqrt-div
140×associate--l+
132×*-commutative
130×flip3-- flip--
127×pow1/3
124×associate-*l/
120×pow-exp
119×swap-sqr
109×log-prod
103×exp-prod
102×pow-unpow
101×cbrt-div
91×frac-2neg clear-num
81×sqr-pow sub-neg
78×pow-to-exp rec-exp
71×associate--r+
70×associate-+l- sqrt-pow1
67×diff-log
59×pow-sub
54×pow1/2
46×fma-udef
40×pow-prod-up pow-sqr
35×pow-pow
33×rem-sqrt-square
29×unpow3 cube-mult
27×sum-log
21×distribute-rgt-neg-in rem-cube-cbrt distribute-lft-neg-in neg-mul-1
19×+-commutative
18×pow2 pow-plus
17×hypot-def div-sub
16×distribute-rgt-out--
14×associate-+l+ associate--l-
13×cube-div exp-diff
11×pow-flip
10×inv-pow
9×frac-sub
8×rem-log-exp
6×rem-cbrt-cube
5×rem-exp-log sub-div
4×un-div-inv sin-sum distribute-rgt-neg-out unpow2
3×distribute-lft-neg-out unpow-prod-up log-div
2×pow-div log1p-udef sqrt-unprod log1p-expm1 expm1-log1p hypot-udef unsub-neg neg-sub0 neg-log expm1-udef
1×sqrt-undiv sqrt-pow2 cos-sum associate--r- exp-to-pow

regimes5.4s (1.9%)

Accuracy

Total 38.9b remaining (37.9%)

Threshold costs 6.1b (5.9%)

7.7b30.6%_divideComplex, real part
7.3b-15.3%Octave 3.8, jcobi/2
4.7b22.8%math.sqrt on complex, real part
4.7b18.5%math.sqrt on complex, imaginary part, im greater than 0 branch
3.4b73.8%Octave 3.8, jcobi/1

localize2.4s (0.9%)

bsearch1.1s (0.4%)

end1.0ms (0.0%)